LIBRARY ANNEX — — . _ — — — — \ THE GIFT OF 1 >j— 7n^vil^JU-*Xv./0M 678^2 QD 561.N95""'""'™'""""'™'^ "■"he electrical conductivity of aqueous 3 1924 012 372 748 Jf2 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924012372748 THE ELECTRICAL CONDUCTIVITY OF AQUEOUS SOLUTIONS A REPORT PRESENTED BY Arthur A. Noyes UPON A SERIES OF EXPERIMENTAL INVESTIGATIONS EXECUTED BY A. A. NoYES, W. D. CooLiDGE, A. C. Melcher, H. C. Cooper, YoGORO Kato, R. B. Sosman, G. W. Eastman, C. W. Kanolt, and W. Bottger WASHINGTON, D. C. Published by the Carnegie Institution of Washington 1907 T) CARNEGIE INSTITUTION OF WASHINGTON, PUBLICATION No. 63 CONTRIBUTIONS FROM THE RESEARCH LABORATORY OF PHYSICAL CHEMISTRY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY NO. 19. CONTENTS. Part I. General Outline of the Investigation. By Arthur A. Noyes. Part II. Original Apparatus and Method. Conductivity and Ionization of Sodium and Potassium Chlorides up to 306°. By Arthur A. Noyes and William D. Coolidge. 1. The conductivity vessel or bomb 9 2. The conductivity measuring apparatus ... ... 11 3. The heaters 11 4. Thermometers .... 13 5. Details of the construction of the bomb 13 6. Procedure for the conductivity measurements ... 23 7. Procedure for the specific-volume measurements 26 8. Standardization of the apparatus 27 9. Preparation of the substances and solutions 30 10. Discussion of the systematic errors and their correction . 30 11. The specific-volume data 35 13. Summary of the specific-volume values ... 35 13. The conductance-capacity of the apparatus ... . . 37 14. The vifater correction . 39 15. The conductivity data . . . 39 16. Summary of the eqtiivalent-conductance values reduced to round temperatures and concentrations 43 17. Change of equivalent conductance with the concentration .... 48 18. Change of the equivalent conductance with the temperature . . 52 19. lonization-values and their change with the concentration and temperature . 54 20. Summary . . . .... 53 Part III. I^ater Modifications of the Apparatus and Method. By William D. Coolidge. 21. New material for the shell of the bomb . . . 59 23. Screwrthread on the steel shell . 59 33. Special lathe-chuck used in the construction of the bomb . . 60 24. A new composite lining for the bomb 60 25. A method for removing the lining by hydraulic pressure .... 61 26. A more delicate leakage test ... ... 62 27. Solid platinum-iridium electrodes . ). 62 28. Apparatus and method for rotating the bomb in the heaters . . 64 39. A vapor bath far heating the rotating bomb ... .... 66 30. A liquid bath fir the rotating bomb . . . 67 Part IV. Conductivity and Ionization of Silver Nitrate, Potassium Sulphate, AND Barium Nitrate up to 306°, and of Magnesium Sulphate up to 218° By Arthur A. Noyes a^d Arthur C. Melcher. 31. Outline of the investigation . 71 32. Description of the apparatus and method ... . 71 33. Preparation of the substances and solutions . 73 34. Systematic errors and their elimination ...... 74 35. The conductance-capacity and the water correction , . . 76 IV CONTENTS. Part IV. Conductivity and Ionization of Silver Nitrate, etc. — Continued. 36. Variation of the conductance-capacity with the temperature ... 78 37. The specific-volume data ^^ 38. Summary of the specific-volume values 82 39. The conductivity data *^ 40. Summary of the equivalent-conductance values . 95 41. Equivalent-conductance values at round concentrations . . . 103 42. Change of the equivalent conductance with the concentration . . 104 43. Change of the equivalent conductance with the temperature . 105 44. lonization-values and their change with the concentration and temperature 107 45. Summary 110 Part V. Conductivity and Ionization of Hydrochloric Acid, Acetic Acid, and Sodium Acetate up to 218° Hydrolysis of Sodium Acetate and Ionization OF Water at 218°. By Arthur A. Noyes and Hermon C. Cooper. 46. Outline of the investigation 115 47. Apparatus and method of procedure . . . 116 48. Preparation of the substances and solutions 119 49. Systematic errors and their elimination . . . 121 50. Conductance-capacity of the apparatus 124 51. The water correction 125 53. Conductivity data for sodium chloride, hydrochloric acid, acetic acid, and sodium acetate 126 53. Summary of the equivalent-conductance values .... . . 133 54. Equivalent-conductance values at round concentrations .... 137 55. Change of the equivalent conductance with the concentration and temperature 139 56. lonization-values and their change with the concentration and temperature 141 57. Conductivity data for mixtures of sodium acetate and acetic acid 143 58. Hydrolysis of sodium acetate and ionization of water ; . . 143 59. Summary 149 Part VI. Conductivity and Ionization of Sodium Hydroxide up to 218° and of Ammonium Hydroxide and Chloride up to 156°. Hydrolysis of Ammonium Acetate and Ionization of Water at 100° and 156°. By Arthur A. Noyes and Yogoro Kato. 60. Outline of the investigation 153 61. Apparatus and method of procedure . . ... ... 154 62. Preparation of the substances and solutions . . . . 156 63. The conductance-capacity of the apparatus 159 64. The water correction 16i 65. Conductivity data for the solutions of sodium hydroxide, am- monium hydroxide, and ammonium chloride 162 66. Summary and discussion of the equivalent-conductance values and their correction to round temperatures 169 67. Equivalent conductance at round concentrations 173 68. Change of the equivalent conductance with the concentration and temperature X75 69. lonization-values and their change with the concentration and temperature 177 70. Description of the hydrolysis experiments 179 71. Conductivity data for ammonium acetate 179 72. Summary of the specific conductance values 182 73. The hydrolysis of ammonium acetate and the ionization-con- stant of water . . Ig5 74. Summary Igg CONTENTS. V Part VII. Conductivity and Ionization of Ammonium Hydroxide, Ammonium Chloride, and Acetic Acid at 318° and 306°, and of Sodium Acetate at 306°. Hydrolysis of Ammonium Acetate and Ionization of Water at 218° and 306° By Robert B. Sosman. 75. Outline of the investigation .... . . 193 76. Apparatus and procedure . 193 77. Instrumental errors and their corrections . . . 196 78. Preparation of the substances and solutions . . 197 79. Errors affecting the solutions and their correction . . 201 80. The specific-volume data 209 81. Conductance-capacity of the apparatus ... . . 210 83. The conductivity data 213 83. Equivalent-conductance values at round temperatures . 320 84. Final values of the equivalent conductance and their variation with the concentration and temperature . . . . ... 334 85. lonization-values and their variation with the concentration and temperature 237 86. Hydrolysis of ammonium acetate and ionization of water at 218° and 306° 329 87. Summary 234 Part VIII. Conductivity and Ionization of Hydrochloric, Nitric, and Sul- phuric Acids up to 306°, and of Phosphoric Acid and Barium Hydroxide up TO 156° By Arthur A. Noyes and Guy W. Eastman. 88. Outline of the investigation .... 239 89. Description of the apparatus and method ... .... 339 90. Preparation of the substances and solutions . ... 241 91. Discussion of errors and corrections 245 92. Conductance-capacity of the bomb 247 93. The conductivity data ... .... ... ... 248 94. Summary of the values of the equivalent conductance . . . . 256 95. Final values of the equivalent conductance at round concen- trations ... . 361 96. Change of the equivalent conductance with the concentration and the temperature 264 97. Ionization of the substances and its change with the concentra- tion and the temperature 267 98. Summary . 379 Part IX. Ionization of Water at 0°, 18°, and 25° derived from Conductivity Measurements of the Hydrolysis of the Ammonium Salt of Diketotetra- hydrothiazole. By C. W. Kanolt. 99. Outline of the investigation . . . 385 100. Preparation of the substances and solutions . . . . 286 101. Apparatus and method 288 102. The conductivity and ionization-constants of ammonium hy- droxide and diketotetrahydrothiazole . • • • ^^^ 103. Conductivity and hydrolysis of the ammonium salt of diketo- tetrahydrothiazole . . . 392 104. The ionization of water 296 105. Summary . 298 Part X. Solubility of Silver Chloride, Bromide, and Sulphocyanate at 100° By William Bottger. 106. Outline of the investigation . . . . 301 107. Description of the experiments . . 301 108. The conductivity data ........ . sns 109. Final conductance values for the saturated solutions . . 307 110. The solubility values 308 VI CONTENTS. Part XI. The Equivalent Conductance of the Hydrogen-Ion derived from TSANSFBRENCE EXPERIMENTS WITH NiTRIC AciD. By ArTHUR A. NoYES AND YoGORo Kato. 111. Outline of the investigation ^^^ 112. Preparation and standardization of the solutions 314 113. Description of the experiments 316 114. The experimental data 318 115. Summary of the transference numbers 334 116. Summary and discussion . . . . . . 326 Part XII. General Summary of the Results. By Arthur A. Noyes. . . . 333 Part I. General Outline of the Investigation. By Arthur A. Noyes. Part I, GENERAL OUTLINE OF THE INVESTIGATION. The investigation to be described in the following series of articles was undertaken for the purpose of studying through a wide range of tempera- ture, extending from 18° to the critical temperature and above, the elec- trical conductivity of aqueous solutions and such other physical and chem- ical properties of them as are related to it or can be determined through measurements of it. Aside from its direct physical significance, it is well known that the electrical conductivity of solutions is a property of funda- mental importance in connection with the ionic theory; for it gives the simplest and most direct measure of the ionization of substances, upon which their chemical behavior in solution depends. A full investigation of this property at all temperatures would therefore furnish a comprehensive knowledge of the chemical equilibrium of dissolved substances in water ; and if supplemented by determinations of the solubility of solid salts, which determinations can also be made by measuring the conductance of their saturated solutions, a fairly complete basis for the development of the chemistry of aqueous solutions of electrolytes would be obtained. A large number of such investigations had previously been carried out at ordinary temperatures, especially at 0°, 18°, and 25°, and a few of them had been extended to somewhat higher temperatures; yet even at 100°, where the results have much practical importance owing to the frequent use of boiling solutions and owing to the fact that it is the limiting temper- ature attainable in open vessels, few, if any, accurate data had been obtained owing to the difficulties arising from evaporation and from con- tamination when glass vessels are used. This temperature has therefore been selected in this investigation as one of those at which each substance will be studied. Above 100° only a few isolated conductivity measure- ments have been published.* Yet the solubiHty of substances and their chemical condition in solution at these higher temperatures is of much importance, not only from the standpoint of physical and chemical science, but also from that of chemical geology and the chemical technology of reactions under pressure. ♦Thus Sack (Wied. Ann., 43, 312-324, 1891) investigated the conductivity of three copper sulphate solutions up to 130°. Maltby (Z. phys. Chem., 18, 155. 1895) found that upon heating up to 337° the conductance of an aqueous potassium chloride solution steadily diminished. Hagenbach (Drude's Ann., 5, 276-312. 1901) observed a maximum in the equivalent conductance of a 0.01 normal KCl solution. In all of these experiments the conductivity cell was made of glass and was necessarily very small; therefore, owing to the solubility of glass at these temperatures and to the danger of polarization of the small electrodes used, the results have little significance. 3 ^ Conductivity of Aqueous Solutions. — Part I. It was not, however, primarily the direct value, however great, of the physical and chemical constants of specific substances at high tempera- tures that led to this investigation, but rather the hope that, by determining them under widely varied conditions of temperature and pressure, general principles might be established relating to the influence of these factors on the migration-velocity of ions, on the ionization of dissolved substances of different types and of water itself, on the hydrolytic dissociation of salts of weak acids or bases, and on the solubility of substances, and that rela- tions might be shown to exist between some of these properties and other properties of the solvent, such as its density, viscosity, and dielectric con- stant. Additional light might also be thrown on the cause of the complete divergence of the change in the ionization of largely ionized compounds with the concentration from the requirements of the mass-action law* — ■ a divergence which constitutes one of the most serious imperfections of the theory of solutions, and which may well conceal a discovery of great importance. The first and most difficult part of this research consisted in the con- struction of a conductivity vessel composed internally of material unacted upon by aqueous solutions and capable of withstanding without leakage the high vapor-pressure of such solutions up to the critical temperature. This portion of the work was carried out by Dr. W. D. Coolidge. After three years' continuous work upon this problem, the mechanical difficulties were overcome and a platinum-lined bomb with insulated electrodes was constructed which remains perfectly tight at any rate up to 306°, which occasions only an unimportant contamination even in salt solutions as dilute as -g^rg- normal, which yields conductivity measurements accurate to 0.3 per cent, or less, and which at the same time makes possible specific- volume determinations, which are essential to the interpretation of the results. Now that a knowledge of the necessary mechanical devices has been acquired, the making of such a bomb is an easy task for a skilled instrument-maker. Therefore, in Part II of this publication will be first described in full detail, with the help of working drawings, the apparatus used in the first measurements, and especially the construction of the bomb, in order to make it readily available for investigators who desire to pursue researches of the same kind or those requiring similar apparatus (such, for example, as a calorimetric bomb). This description, together with the results with sodium and potassium chlorides referred to in the next paragraph, was published in November, 1903, in the Proceedings of the American Academy of Arts and Sciences.f It is reproduced here, in *For a brief general discussion of this matter, see Noyes, Congress of Arts and Sciences, 4, 311-323 (1904) ; Science, 20, 577-587 (1904) ; reviewed in Z nhvs Chem S2, 634-636 (1905). ^ ^ v^nem., tProc. Am. Acad., 39, 161-219 (1903). Also in Z. phys. Chem., 46, 333-378 and m somewhat abbreviated form in J. Am. Chem. Soc, 26, 134-170. ' General Outline of the Investigation. 5 somewhat revised form, for the sake of completeness and on account of its close relation to the new material that is to be presented. I desire in this connection to express my great indebtedness to the American Academy for the liberal grants made to me from the Rumford Fund in the early stages of the work. During the past four years the work has been continued under the auspices of the Carnegie Institution of Washington, and its progress has been largely due to the assistance thus afforded. I have also been fortu- nate in having had associated with me a number of able research workers, by whom the work has been prosecuted on its different sides. With this apparatus and method in its original form, conductance and specific-volume measurements were made by Dr. W. D. Coolidge and myself with two substances, sodium and potassium chlorides, at various temperatures between 26° and 306° and at various concentrations between 0.1 and 0.0005 normal. The results of these experiments are also pre- sented in Part II. Since their original publication several corrections of a minor character have been applied to the data. As was to be expected a number of important improvements in the apparatus and method suggested themselves in the course of these experi- ments, and these -were subsequently worked out by Dr. Coolidge, who presents a description of them for the first time in Part III of this publi- cation. The method is now being further developed so as to adapt it to still higher temperatures extending above the critical one, where a control of the pressure, entire elimination of the vapor space in the bomb, and measurements at small intervals of temperature will be essential. Mr. A. C. Melcher has made measurements with another salt of the uni-univalent di-ionic type (silver nitrate), and has then extended the investigation to salts of other types (potassium sulphate, barium nitrate, and magnesium sulphate), at a series of temperatures up to 306°, namely, 18°, 100°, 156°, 218°, 381°, and 306°. The results of these experiments, as well as some additional ones with sodium and potassium chlorides, are presented in Part IV. Dr. H. C. Cooper, Mr. Yogoro Kato, and Mr. R. B. Sosman have studied the conductivity and ionization up to 218° of certain acids and bases ; namely, of hydrochloric and acetic acids and of sodium and ammo- nium hydroxides. They have also determined by conductivity measure- ments the hydrolysis of sodium acetate at 318° and that of ammonium acetate at 100°, 156°, and 218°, and have calculated therefrom at these temperatures the ionization-constant of water itself, upon which in large measure the phenomenon of hydrolysis depends. This work is described in Parts V, VI, and VII; the share of each investigator being indicated under the separate titles of these parts. Mr. R. B. Sosman has made an entirely similar series of measurements at 306° with ammonium hydroxide. 6 Conductivity of Aqueous Solutions. — Part I. acetic acid, and ammonium acetate, and has derived from them the ioniza- tion of water at that temperature. The results are also presented in Part VII. Mr. G. W. Eastman has investigated a number of other acids, namely, nitric, phosphoric, and sulphuric acids, and potassium hydrogen sulphate, and the base, barium hydroxide, at 25° or 28° intervals from 18° to 156°, and has extended some of these measurements and the previous ones with hydrochloric acid to 260° and 306°. The data and conclusions in regard to these substances are presented in Part VIII. In order to obtain at temperatures of 0° to 25° values for the ionization of water more accurate than those previously existing. Dr. C. W. Kanolt has studied by the same conductivity method as was used with ammonium acetate at higher temperatures the hydrolysis of an ammonium salt of a much weaker acid, diketotetrahydrothiazole. The results of this work are presented in Part IX. Only a beginning has been made in the study of the solubility of salts at high temperatures. Dr. Wilhelm Bottger has, however, already deter- mined that of three difficultly soluble silver salts at 100°, and the results are recorded in Part X. It has also seemed advisable to include in this publication an account of a research carried out by Mr. Yogoro Kato and myself with the view of determining the equivalent conductance of the hydrogen ion ; for though this consisted in transference experiments at 20° with nitric acid of various concentrations, and was thus distinct as far as the method is concerned from the other researches to be here described, yet the knowl- edge furnished by it has a direct bearing on the interpretation of conduc- tivity results. The investigation is described in Part XL It is entirely analogous to one previously made with hydrochloric acid by Noyes and Sammet* for the same purpose. Finally a general summary and discussion of the more important results of the whole series of investigations are presented in Part XII. The reader who is interested only in the more general conclusions drawn from the work is recommended to turn at once to this summary in Part XII. Anyone who desires fuller information in regard to the con- ductivity and ionization of the specific substances and to the method of discussion of the results will find this information as a rule in the last five or six sections of the separate parts. The earlier sections in each part are devoted to a detailed description of the experiments and presen- tation of the original data, and will be of interest principally to investi- gators who desire to make similar experiments and to those who wish to criticize the results or form an estimate of their accuracy. *The Equivalent Conductivity of the Hydrogen Ion derived from Transference Experiments with Hydrochloric Acid. J. Am. Chem. Soc, 24, 944-968 (1903), or Z. phys. Chem., 43, 49-74 (1903), Part II. Original Apparatus and Method. Conductivity AND Ionization of Sodium and Potassium Chlorides up to 306°. By Arthur A. Noyes and William D. Coolidge. Part II. ORIGINAL APPARATUS AND METHOD. CONDUCTIVITY AND IONIZA- TION OF SODIUM AND POTASSIUM CHLORIDES UP TO 306°. I. THE CONDUCTIVITY VESSEL OR BOMB. A vertical section of the conductivity vessel used throughout these inves- tigations is shown in half size in fig. 1. It is a cylindrical vessel A, with a cover B, which is held in place by the large nut C. A, B, and C are made of soft crucible steel. To prevent contamination, the bomb is lined throughout with sheet platinum 0.41 mm. thick. The cover joint is made tight by a little packing ring, made of pure gold wire, which fits into a shallow V-shaped groove. As may be seen in the diagram, the platinum lining, indicated by a heavy line, goes under this ring and a little distance beyond it, the outer edge being fastened to the shell by eight small steel screws, of which two are shown. The lower vessel has a capacity of about 122 c.cm. The body of the bomb serves as one electrode, connection being made with it by means of the large binding post on top of the nut C. The second electrode is brought in through the bottom of the bomb and is insulated from the latter by means of the mica washer M, the air space S, and the quartz-crystal piece Q. The body of this electrode is of steel, but its upper part is covered with sheet platinum. On the bottom of the crystal piece is turned a single sharp V-shaped ridge, and this rests on a flat gold washer which is inserted between the crystal and the bottom of the bomb. Another gold washer is placed between the upper part of the electrode and a second V-shaped ridge turned on the upper face of the crystal. The nut N fitting on the lower, threaded end of the electrode, draws the latter down, thus forcing the ridges of the crystal into the soft gold and making the joints tight. Z is a brass washer which by its greater expansion-coefficient makes up for the difference in the expan- sion, upon heating, of the quartz-crystal and of that part of the steel electrode which lies within. The second nut, on the lower end of the elec- trode, serves to bolt on a small copper tag to which the wire L^ is silver- soldered. The quartz piece Q is extended in the form of a cup above the electrode, so as to increase the resistance-capacity of the cell. In the cover 5 is a narrow cylindrical chamber provided with an "auxihary electrode," which is insulated in just the same way as the lower electrode. The purpose of this small chamber with the auxiliary electrode is twofold : first, it serves as a safety device, showing that the bomb has 10 Conductivity of Aqueous Solutions. — Part II. not become completely full of liquid ; and secondly, it furnishes a means of measuring the specific volume of the solutions. The first provision is necessary since the bomb is designed to withstand the vapor pressure, but not the fluid pressure of the liquid. A knowledge of the specific volume is required in order to calculate the equivalent from the observed conduct- ance. A measurement of the resistance between L^ and Lg, together with a measurement of that between L^ and L2, when preceded by a calibra- tion which may be made once for all, shows, as will be explained more fully in section 8, at any time after the solution has expanded suf- ficiently to come into contact with the auxiliary electrode, just how high the liquid stands, and therefore how much vapor space remains. The small platinum tube Ti serves to exhaust the air from the bomb. The method of doing this will be apparent from the diagram and the following description. The hollow screw K is connected by means of rubber tubing with a Richards water pump, and is at first raised so that air can come out under the little steel bicycle ball which rests on the upper end of the platinum tube. After the air is removed until a pressure gauge shows a pressure within of about 2 cm., and while the pump is still in operation, the part K is screwed down, thus forcing the steel ball upon its seat and closing the end of the tube. The solution comes into contact with nothing but platinum, quartz- crystal, and gold, except at the top of the narrow tube, T^, where it may touch the steel ball. The latter could be gold-plated ; but this has proved unnecessary, since there is scarcely any circulation through the narrow tube. The lower electrode, as well as the auxiliary electrode and its sur- rounding tube, are well platinized. The body of the lining is not platin- ized, since on account of its great surface this is not necessary. Sections 2 and j. — The Conductiznty Apparatus. 11 2. THE CONDUCTIVITY MEASURING APPARATUS. The conductance was measured by the ordinary Kohlrausch-Wheat- stone bridge method, using the induction coil and telephone. The slide wire was of platinum-iridium ; it was 1 meter in length and 0.4 mm. in diameter. The resistance coils, 3,000 ohms in all (or 4,000 ohms in a few measurements), were of manganine. The whole conductivity apparatus was mounted on a small portable table so that it could be moved about as the bomb was changed from one heating bath to another. It was always kept at a distance from the heaters. No temperature correction needed to be applied to the resistance coils. Heavy flexible copper leads were used up to within a few centimeters of the top of the heaters, where the}- were joined by means of brass connectors to the smaller copper wires, £1, L2, L„, coming from the bomb. A double-throw switch served to con- nect the conductivity apparatus with L^ and Lj or with L^ and L3. 3. THE HEATERS. Conductance measurements were made at about 26°, 140°, 218°, 281°, and 306°. The first of these temperatures was attained by immersing the bomb in a bath of commercial xylene contained in a double-walled, well- jacketed, metal cylinder. This substance has the advantages that it is a good insulator, non-corrosive, and not very volatile, and that the bomb can be transferred from it directly, without cleaning, into the xylene-vapor bath by which the next higher temperature is attained. The liquid was stirred by a small propeller, and was heated electrically at will with the help of a platinum helix immersed in it. For all the higher temperatures, vapor baths were employed, as these furnish the only safe and rapid method of heating. The temperature adjusts itself automatically, and can never rise much above the ordinary boiling-point, thus giving protection against overheating and undue expan- sion of the liquid within the bomb, which by completely filling it might cause it to burst. Moreover, if the bomb should spring a leak, it would be dangerous in the case of a liquid bath; for the steam, escaping under such pressure, might throw some of the hot liquid upon the observer. Steam leaking out into the hot vapor, on the other hand, causes no annoy- ance further than that arising from the odor of the vapor and the loss of the material in the case of the expensive substances. An air bath would, of course, not be open to this objection; but the heating would be ex- tremely slow and non-automatic. An elevation of one of the heaters — all of which were substantially alike — with the bomb in place is presented in fig. 2. The bath is made of a piece of wrought-iron pipe A, 16 cm. in diameter and 40 cm. long, 12 Conductivity of Aqueous Solutions. — Part II. with a bottom piece welded in. Near the top two pieces of iron pipe C about 2 cm. in diameter and 35 cm. long are screwed in, to serve as con- densers. These condenser tubes are given a slight pitch, but their outer ends should not be higher than the top of the heater. To increase their efficiency, a loose roll of iron-wire gauze is put into each of them. The top of the bath, which should be turned off square in the lathe, is covered with a large watch-glass D, in which holes are drilled for the thermometer T, and the lead-wires to the bomb. A tube of thin sheet iron Q, about 12 cm. in diameter, with a flange at the bottom, is placed in the heater and held in the middle by projecting pins. Small holes are drilled through this tube at the bottom, and two rows of large holes at the top. The func- tion of this tube is to prevent the bottom of the bomb from getting hotter than the top ; for, if it does this by ever so little, a constant evaporation and condensa- tion goes on in the bomb, vi^hich interferes with the readings of the auxiliary electrode and the specific-volume determinations. The inverted mica cone A'^ is put in for the same purpose; it prevents the cold condensed vapor from dripping upon the top of the bomb. These arrangements also protect the bomb more effectually from radiation and convection-currents from the walls of the heater. The holes in the glass cover through which the lead-wires and the thermometer enter are but little larger than these, so as to prevent loss of vapor. The thermometer is supported by means of a cork stopper which rests on the top of the watch-glass. The insertion of cork stoppers in the holes is not advisable, as they cause the hot liquid to escape through their pores. The bomb is supported in the heater by means of a brass frame F^ and suspen- sion wires W, which hang on two steel pins screwed into the walls of the heater. At the top of each of the two suspension wires is a loop, so that by inserting a steel hook in each of these loops, the bomb is easily removed from the bath while still hot. The sides of the heater are well jacketed with asbestos. It is supported on a metal tripod by means of three steel pins, which project through the asbestos covering. It is heated by gas- burners below, one sufficing after the bomb and heater have become hot. Commercial xylene was first used for the 140° bath, but the pure meta- xylene was found to give a more constant temperature and one more uniform in the upper and lower parts of the bomb. To prevent the escape Fig. 2. Section 4. — Thermometers. j? of the vapor, it was necessary in this case to cause water to circulate through a jacket surrounding one of the condenser tubes. Pure naph- thalene from Kahlbaum was used to give a temperature of 318°, and was found to be an ideal substance. a-Bromnaphthalene was employed for the next higher temperature (281°), as it seemed to be the only available substance ; it is not convenient, however, since it decomposes slowly upon boiling with formation of tar and hydrobromic acid (which attacks the outside of the bomb) ; it must therefore be frequently removed from the heater and redistilled. The highest temperature (306°) was maintained with benzophenone, which shows no change of boiling-point even after many da^'s of continuous heating. 4. THERMOMETERS. The temperature of the liquid xylene bath was measured with an ordi- nary thermometer reading directly to tenths of a degree, and this was checked from time to time against a standard Tonnelot thermometer. For the higher temperatures French mercurial thermometers, made by Alvergniat, with a range of 360° and graduation in degrees, were used. By the use of a little reading telescope these thermometers were read with certainty to 0.1°. They were standardized as described in section 8 of this article. The mercury column was always completely immersed in the vapor, and to take a reading the thermometer was quickly raised onh' enough to render the meniscus visible above the top of the heater. Repeated trials showed that the temperature of the bath throughout the space surrounding the bomb varied less than 0.1°, so that the exact posi- tion of the thermometer made no difference. Care had to be taken, how- ever, that the mica shield above the bomb did not come in contact with the thermometer stem, thus allowing the condensed vapor coming from the shield to run down and cool the bulb. It was feared that the vapor con- densing on the upper part of the thermometer itself would have the same effect ; but this was proved not to be the case by fastening a small inverted watch-glass about midway on the thermometer stem; this carried off the drip from the upper part of the stem, but did not affect the reading. 5. DETAILS OF THE CONSTRUCTION OF THE BOMB. The shell is made of the softest crucible steel obtainable, ductility being desired rather than high tensile strength. Extra weight is not objection- able here, as it would be in the case of a calorimetric bomb; moreover, fear was entertained that a high-carbon steel might be weakened by the repeated heating and cooling to which the bomb was to be subjected. The i/f. Conductivity of Aqueous Solutions. — Fart II. shell was designed for approximately equal strength throughout. The large nut C has an ordinary V-shaped thread of 18 turns to the inch. To tighten the nut, the lower part of the bomb is held at R, which is hex- agonal, by a wrench bolted to a firm table; while a second wrench, with an effective length of 46 cm., is placed on the hexagonal part R' of the nut itself. In this way sufficient pressure can be exerted on the gold packing- ring to make the metal of which it is composed actually flow into the groove beneath, filling any little scratches or other depressions which may exist in the latter. Since there is a certain thickness of gold and platinum interposed between the cover and the lower part of the bomb, and since these both expand less than steel upon heating, it becomes necessary to use a compensating brass washer W between the nut and the cover. The proper thickness can be calculated from the known coefficients of expan- sion of the three metals. Care must be taken that the bearing surface of the nut C on the washer W is so large that the upward force of the steam acting on the cover does not compress the brass washer, and thus allow the cover to rise. Care must also be taken — and this is very important — that the distance from the center of this bearing surface to the axis of the bomb is less than the radius of the gold packing-ring; other- wise the cover might turn on the ring while the nut was being tightened, which would prevent a tight joint from being secured. For lubrication a little finely powdered graphite is rubbed on the top of the brass washer and into the threads of the large nut. To facilitate the removal of the platinum lining, the inside of the steel shell was made slightly tapering (about 0.05 mm. in 10 cm.), and the little grooves left by the boring tool were carefully ground out. In working with the bomb it proved to be necessary to drill through the steel shell a number of small holes, one of which is shown at H in fig. 1. In the present bomb there are about 75 of these (probably half as many would have sufficed) well distributed over all its parts. A, B, and C. These holes are 0.66 mm. in diameter — so small that they do not seriously weaken the shell, and that the platinum lining is capable of withstanding the pressure over their areas. These holes are made necessary by the fact that without them some water gets trapped between the lining and the shell, owing to slight leakage or permeation of the platinum itself when the bomb is first heated, the lining then being not in close contact with the shell at every point; and this water on subsequent heating exerts, owing to its expansion in the liquid state, an enormous pressure against the lin- ing, causing little indentations in it and causing some water to flow back into the bomb, whereby contamination of the solution with iron is pro- duced. The holes remedy entirely this difficulty, which otherwise will become aggravated on each successive heating. They also help to locate Section 5. — Construction of the Bomb. 75 a leak in case one exists, for when the bomb is connected to the hydraulic pump to be tested, as will be explained later, they permit the water to escape at a point near where it gets through the platinum lining. To fur- ther this end a small hole is also drilled from the outside obliquely into the air space around each of the electrode rods. The lining of the lower part of the bomb A was made of a platinum- iridium alloy (2 per cent iridium) 0.40 mm. thick. The flange F was orig- inally made of the same material, but the closing of the bomb compressed the platinum each time under the ring so that it grew hard and thin and finally cracked at the bottom of the groove. For this reason platinum- iridium alloy containing 15 per cent iridium had to be substituted for the flange. This is so hard that it bids fair to wear indefinitely, and yet it is not so brittle that it can not be forced into the groove in the steel without cracking. The flange could just as well be welded to the platinum cup, but in our bomb it was soldered to it with pure gold. Pure gold was also used freely in making repairs on the present lining when it tore, as it fre- quently did at the start, before the necessity of the small holes in the shell and of several other precautions was understood. The lining is made so as to fit as well as possible at the start. It is then inserted in the shell, and expanded by driving in plugs of cotton as hard as possible, with a hammer and piece of hard wood. The shell is then placed in the lathe, and the lining is still further expanded by the use of an agate burnisher lubricated with soap. The flange is next hammered over to fit the steel, sheet lead being used under the hammer to prevent injury to the platinum alloy. The most delicate operation connected with the lining of the bomb is perhaps the next step, which consists in making a depres- sion in the flange to fit the V-shaped groove in the steel below. This groove in the steel should not be sharp as shown in fig. 1, but should be slightly rounded at the bottom (to prevent cracking the hard flange) and its sides should make an angle of 90° with one another. The depth of the groove is such that when a wire 0.8 mm. in diameter is laid in it, about one-half of the wire lies outside the groove. A little steel roller is made to fit the groove in the shell, and this roller, after being hardened and polished, is pivoted in a fork which fits into the tool post of the lathe. The shell with the lining in it is then slowly rotated in the lathe while the roller, well lubricated with soap, is firmly pressed against the flange over the groove. After the lining has been made to fit as closely as possible, it should be removed from the shell and heated to redness to anneal it. Even the flange had better be treated in this way, since it is hard enough even after annealing. To remove the lining after it has been fitted in in the preceding manner, the following plan was adopted : Take a stick of soft wood, per- I6 Conductivity of Aqueous Solutions. — Part II. haps 20 cm. long and 5 cm. square, and whittle one end down so that it will slip easily into the bomb. Then take a piece of cotton cloth moistened with alcohol to remove any grease, wrap it over the small end of the stick, and then with a hammer drive the latter tightly into the bomb. Now holding the bomb in the vise, grasp the projecting end of the stick firmly in the hands or in a wooden clamp and twist out the lining. This method never fails, provided the steel shell was ground reasonably smooth at the start. A hole is drilled in the lining at the bottom so as to correspond with the hole in the steel shell. It is then best to close this hole temporarily with the steel piece shown in fig. 3, using a lead washer under the V-shaped ridge for packing. Then, in order to bring the lining into perfect contact with the shell and at the same time to test it for possible faults, the lower part of the bomb is connected by means of the auxiliary cover shown in figure 4 w i t h a Cailletet pump or its equivalent — a water reservoir being interposed between the pump and the bomb so to force water as instead of oil into the bomb. For this f'8- 5. testing of the lining a pressure of 300 ■ Fig. 3. Fig. 4. atmospheres has been used, the steel shell having previously been similarly tested up to 600 atmospheres pressure. The lining must be fitted as closely as possible before the hydraulic pressure is applied, since otherwise this will always result in tearing the lining. Even after expanding the lining with hydraulic pressure, there is no trouble in removing it, in case a leak develops, by the method given above. The next step is to fasten the edge of the flange to the shell. If this is not done, when substances like benzophenone, solid at ordinary tempera- ture, are employed for heating the bomb, they will be drawn under the flange and into the groove in the shell, where they will solidify ; upon heat- ing the bomb the next time, the solid melts and escapes, thus relieving the pressure on the packing-ring and allowing the bomb to leak ; moreover, if the edge is not fastened down, there is danger of bending it when the bomb is opened and handled. To secure the flange eight small steel screws are used. The steel shell has to be recessed at this place, as shown in fig. 1 ; otherwise the screw heads would interfere with the cover. Section 5. — Construction of the Bomb. 77 The lower electrode is made of two steel parts, as shown in fig. 5, the horizontal part C being afterwards inclosed in a platinum box, which is made as follows: The top A of this box, is made by forcing a circular disk of pure sheet platinum (about 0.25 mm. thick) through a brass die by means of a brass punch. It is better, since it strains the platinum less, to interrupt this operation at least twice, annealing the metal each time. This box should be made to fit so tightly over C that it has to be forced on. In the same way a tight-fitting bottom B is made for this box. A hole is drilled in the center of this just large enough to permit the passage of the steel rod through it. It is then forced on over A. It then remains only to solder B to A with pure gold. This is easily accomplished by putting several pieces of gold on the crack D and directing a hot flame from the blast lamp downwards upon the box. This flame must not be too small, since the whole of the soldering must be done at once and as quickly as possible. Doing it a piece at a time involves keeping the steel rod hot for a longer time, and consequently oxidizing it more; and worse than this, the gold gets inside and alloys with the iron, bringing the latter eventually to the surface. Before soldering it is better to cover the steel rod below the box with pieces of asbestos, binding them on tightly by means of a wire, so as to diminish the oxidation. Before adopting quartz crystal as the insulator various other substances were tried. Mica was tried first of all, using both of the methods sub- sequently employed by Knipp* in his work on surface tension. Our experience agreed with his — that it is impossible to secure an absolutely tight joint with mica because of the formation of radial cracks. Nor was it an ideal substance chemically. Carnelian, flint, and agate were next tried because of their known toughness. It was with the last-named sub- stance that we developed the method finally employed for making an abso- lutely tight joint; the substance itself, however, proved to be chemically unsuitable, since the hydrated silica which it contains dissolves readily in the hot water. The method which we finally employed for securing a tight joint put very little strain on the agate, so that there was no longer any reason for avoiding a substance because of its brittleness. Quartz crystal was then the natural substance to try. Japanese quartz, however, proved a failure, owing to included water or carbon dioxide, which caused it to crack upon heating ; but the Arkansas quartz which we next tried was not affected by heat and has proved to be very satisfactory. Since the thermal coefficient of expansion is so different in the directions parallel to and perpendicular to the main axis of the crystal, the axis of the cup was made parallel to the main axis of the crystal. *Phys. Rev., 11, 129-154 (1900). i8 Conductivity of Aqueous Solutions. — Part II. The process employed for making the quartz cup is as follows: A crystal is selected which is perfectly clear and free from imperfections. A slice, in thickness a little greater than the height of the finished cup, is then sawed out at right angles to the main axis. For this operation a thin tinned-iron disk, whose edge is charged with diamond powder, is rotated in the lathe ; and the piece, supported on a sawing table, is pressed lightly against the saw by hand, a wet sponge being held against the edge of the saw with the other hand. This operation of sawing is discussed at some length by Threlfall.* It is both easy and rapid if the saw is in good con- dition. Care must be taken in this and the subsequent operations that the work is not crowded too hard against the abrading surface, as this causes a local rise of temperature which may crack the crystal. A hollow drill, whose internal diameter is but little greater than the external diameter of the finished cup, is then run through the crystal piece at right angles to the sawed surfaces. Such a drill consists merely of a tinned-iron tube pro- vided with a slit running lengthwise, and mounted so that it can be rotated in the lathe. The outer end of the tube is turned off square and is then charged with diamond powder. A small piece of wet sponge is then placed in the tube. Powdered carborundum can be used in place of diamond, and, although it is somewhat slower in starting, it appears to be equally satisfactory afterwards. The core is then taken from the drill and the ends of the cylinder are ground down flat ; for the saw has left them some- what irregular. This operation of grinding is conveniently carried out by means of a carborundum wheel rotated in the lathe, the wheel being kept wet by holding a sponge against it. Before grinding either surface, its bounding edges must be ground off (beveled) ; otherwise the edges will break out irregularly. To cup out the cylinder, a hollow drill, whose external diameter is but little less than the internal diameter of the finished cup, is then run into one end to a depth almost equal to that of the desired cavity. The core which is left from this drill is too strong to be broken out without danger of injuring the outside of the cup; so another, smaller one is next run in to the same depth as the first and concentrically with it. This leaves two fragile pieces, a small rod and a thin tube, which are easily broken out. The cup is next mounted so that it can be rotated in the lathe. This is best accomplished by fastening it with stick shellac to the end of a brass rod held in the lathe chuck. To hold firmly, the crystal must be heated above the melting-point of the shellac; this can be done safely by flashing it with a gas flame. The inside of the cup is then ground to its final diameter and the bottom made flat by using carborundum powder upon the end of a brass rod which is a little less in diameter than the cavity and whose end is squared off, the rod being best held in the hand. The *On Laboratory Arts, pp. 187-189. Section 5. — Construction of the Bomb. ip small hole is drilled through the bottom of the cup by the aid of a small diamond set in the end of a steel or brass rod. The diamond must, of course, be a little larger than the rod to give clearance for the latter. To stai-t the hole the T-rest is used, but afterwards the rod is supported only by the hand. The tool must be withdrawn and moistened very frequently. The hole may be run half-way through from either end. It is afterwards expanded to its proper size by the aid of a small brass or steel rod and some carborundum. To form the little V-shaped ridges on the ends of the cup, each of the end surfaces, except at the middle where the ridge is to be, is ground down with carborundum. The projecting portion left in the center is then turned into a sharp ridge by means of a diamond set in the end of a steel rod. This tool is held in the hand and supported on the T-rest just as the ordinary hand tool is used on metal. To support the cup while work is being done on the lower end it is best to fasten in the chuck a piece of brass rod somewhat smaller than the internal diameter of the cup, square off its end, turn a little groove in it which will correspond to the ridge at the bottom of the cup, and then shellac the cup on, so that the ridge comes in the groove. This mode of support insures getting the ridges, as they should be, in parallel planes and centrally located with ref- erence to the axis of the cup. The operation of polishing is best carried out by means of different grades of corundum powder, using finally oxide of tin. These are applied wet on the end of a soft piece of wood. In making such a cup an ordinary mechanician, after a little practice on the different operations, will spend perhaps twelve or fifteen hours. The thickness of the brass compensating washer (Z, fig. 1) can be cal- culated from the known coefficients of expansion of the quartz-crystal and of the brass and steel used. That used in our bomb was 5.1 mm. in thick- ness. Of the two gold washers the upper one is made to fit tightly on the electrode rod, while the hole in the lower one is made to correspond with that in the bottom of the bomb. To keep the lower gold washer from touching the electrode rod, and to keep the latter from touching the steel shell, the following device was employed: The middle part of the steel rod is made about 0.5 mm. smaller in diameter than the hole in the crystal. Three thin strips of mica, each about 2 cm. long and 2 mm. wide, are inserted in the space left between the electrode rod and the crystal, so that the ends of these mica pieces project perhaps 1 cm. below the cup. The mica strips are cut so wide that they have to be pushed into place. They serve to hold the rod in the crystal and keep the lower gold washer in place. The cup can now be grasped by its edge with a pair of tweezers and the electrode rod pushed through the hole in the bottom of the bomb. It is then bolted down. It is next tested to make sure that there is no short circuit between the electrode and the bomb ; and finally, to make sure that the joint is tight, the bomb is connected once more to the pump. 20 Conductivity of Aqueous Solutions. — Part II. If, after the bomb has been in use for some time, it is necessary to remove the lower electrode, it may be done in the following way : The nut N can not be unscrewed, but enough of it can be removed with saw and file so that the remainder will slip through the hole in the brass washer. A light direct blow with the hammer on the end of the electrode rod is then always sufficient to start it out. The brass remaining in the threads of the electrode rod is easily rernoved with any pointed tool, and the elec- trode is ready to use again. The cover B is made slightly concave to allow the air bubbles, which might otherwise collect under it, to escape into the electrode chamber above. To line the cover a round disk of platinum-iridium alloy contain- ing 15 per cent iridium is taken, and the two tubes, T^ and T^, are soldered to this with pure gold. This alloy is used rather than pure platinum on account of its greater hardness, which prevents the gold ring from cutting into it. In the development of the bomb, the tube T^ has probably caused more trouble than any other part. This is due in part to the fact that at high temperatures the pressure is sufficient to force water through the lining at any unsupported spot. If the tube was made of heavy metal, and especially when it was made of the 2 per cent alloy, it was itself capable, owing to its small diameter, of withstanding the pressure without expanding enough to come into perfect contact with the steel at all points ; as a result, the bomb would leak at such points. Or, owing to the greater difficulty in mechanically expanding the small tube to meet the shell, the fit would be so poor at the start that the hydraulic pressure would tear it. Our earlier work here was done with the 2 per cent alloy before we fully realized the great difference in ductility between this and pure platinum. Because of its extreme ductility gold was then tried. This worked beautifully at first, but finally failed because the 22-carat gold solder employed in making the tube disintegrated under the action of the hot water. Recourse was then had to pure platinum, which completely solved the difficulty. The plati- num tube is first expanded by driving in some plugs of cotton with the help of a hammer and a brass rod almost as large as the inside of the tube. Seamless tubing might be advantageously used here, but we used a tube made of sheet platinum soldered with pure gold, and this proved to be entirely satisfactory. The small tube T^ is conveniently made by rolling up tightly some thin sheet platinum and then flowing gold in to fill the spaces between the con- volutions. This gold is fed in from the outside, while the whole tube is kept hot in a large blast-lamp flame. Care must be taken not to use too much gold ; otherwise a drop may form inside the tube, and its removal by Section 5. — Construction of the Bomb. 21 drilling is extremely difficult. Owing to capillary forces, no gold will go to the space inside until the smaller spaces between the convolutions are all filled, so that there is no danger so long as too much gold is not em- ployed. In this, as in all other operations when gold is used in soldering platinum, the piece should be kept hot no longer than is absolutely neces- sary, because the gold rapidly alloys with the platinum, and the resulting alloy is more crystalline in structure than either of the constituents and has not their ductility. To make the joint between Tj^ and the lining of the cover stronger, the tube is reinforced above this point, as shown by the drawing. This was necessary in our earlier apparatus before the lining was screwed down to the cover, but is probably not necessary in the later form. As the upper end of the tube T^ is to act as a valve-seat, and as there- fore there will be a good deal of downward pressure at this point, the tube has to be well expanded into the conical cavity in the steel at V (fig. 1). Because of this, and of the further fact that the valve-seat should be as soft as possible, it is better to make the upper end of Ti of solid gold, bor- ing it out later. This is done as follows : The tube is first packed full of asbestos, to prevent gold from getting into it. A band of thin platinum foil is next wound tightly around the upper end and bound on by means of a platinum wire. This band is then pushed partly off of the end of the tube, so as to make a small projecting tube; and pure gold is melted into this until it is full. The platinum foil on the outside of the gold is now filed off. Both tubes are now attached to the cover lining and inserted in place in the cover. Holding the lower end of T^ on an anvil, the soft gold, projecting perhaps 3 mm. above the steel at V , is compressed with a rivet- ing hammer. The asbestos is now drawn out of the tube, and a hole is drilled down through the gold to meet the hole in the platinum. The valve-seat at the start is of the form shown in fig. 1, and the slight- est pressure on the steel bicycle ball serves to force the ball down into the soft gold tube enough to make the joint tight. But after this process has been repeated a few times the bearing surface of the ball on the gold becomes so large that the pressure which can be obtained by tightening the screw K with the fingers is not sufficient to make the joint tight. The valve-seat can be easily brought back to its original condition, however, by filling the depression, which the ball has made, with soft dental gold and opening the hole again with a scratch awl or a drill. The filling is most conveniently accomplished with a little "moss fiber" gold, using the regular dental tool. Of course the top should always be left concave, so that the ball will of itself roll to the center. Time is saved in the end by putting the valve-seat in order each time ; for, if this is done, there will 23 Conductivity of Aqueous Solutions. — Part II. never be a leak at this point. It is also better to use a fresh steel ball each time. The screw K should fit well, but still turn easily with the fingers ; for, if there were much friction here, it would be impossible to tell how much of the force employed in screwing it down was being communicated to the ball and how much was wasted in friction in the screw. Smearing a little vaseline on the screw prevents air from leaking in while the bomb is being evacuated. The edge of the lining is fastened to the cover by eight steel screws, in the same way as the flange of the lining of the body of the bomb is secured, the only difference being that it is not necessary at the top to recess the edge of the platinum. Care must, of course, be taken that the screws in the top do not come opposite those in the lower part when the top is put on. Two reference marks enable the experimenter to bring the cover always into the same position with respect to the bottom. The cover lining is forced into place and tested, just as was the lining of the lower part of the bomb, by means of the Cailletet pump, making the pump connection with a metal piece like that shown in fig. 6, which takes the place of the lower part of the bomb. The construction of the auxiliary electrode is simi- lar to that of the lower one ; it will be evident from fig. 7. The part a has to be made just as small as is consistent with making the joint tight on the end of the crystal. The platinum covering consists of a little plati- num box similar to that used on the lower electrode, a short piece of tubing b and a piece of platinum wire c. The gold packing-rings are made as follows : A piece of gold wire about 3 mm. shorter than the circumference of the finished ring is cut off and the ends fused together in a small oxy-gas flame. (The ends of the wire were originally filed flat and then soldered with coin gold; but this method besides being much more laborious had the disadvantage of bringing base metal into the gold.) The joint made in this way is slightly thicker thsn the rest of the ring, but not enough so to do any harm. The ring is then annealed and placed on a cast-iron spreader. By pushing a tapered brass plug into this spreader, it is expanded and the ring stretched. By placing a reference mark on the tapered plug, the ring can be stretched to just the same size every time. It, of course, comes off perfectly round. ^P 1 Fig 6. Pj ■ a. XT Fie 7 Section 6- — Method of Procedure. 23 and after reannealing is ready for use. Each ring is used but once; but after a number have been used they are melted down and made into fresh wire. The total weight of platinum used in our bomb is about 185 grams. This, together with the fine construction work involved, makes the initial cost considerable, but the platinum, of course, retains the larger part of its value. We have estimated that the cost of reproducing such a bomb, including the labor of a machinist and all the materials except the plati- num, is about 125. Before adopting the sheet-platinum lining, attempts were made to pro- duce a satisfactory platinum plate on the inner surface of the bomb by the electrolytic process described by Langbein ;* but although a firmly adhering deposit was obtained, it was found not to be dense enough to protect the surface beneath from attack and the liquid from consequent contamination. 6. PROCEDURE FOR THE CONDUCTIVITY MEASUREMENTS. In making a set of conductivity determinations, the valve-seat at the top of the tube, T^ (fig. 1), is first put in order by putting in a gold filling, as has already been described in section 5. Then any loose particles of graphite or dirt adhering to the flange and cover in the neighborhood of the gold packing-ring are removed with absorbent cotton saturated with benzene, and the screw thread on the lower part is cleaned in the same manner. Both the upper and lower parts are now rinsed thoroughly with good water, using the fine stream from a wash bottle to remove more effectually any loose particles of graphite which may have got into the bomb upon previously opening it. By this means, too, water can be forced through the fine tube, T^. If the solution to be investigated is a dilute one, the rinsing must be very thorough. Finally the bomb is rinsed out with some of the solution, and as much as possible of this is then shaken out. The bomb is then ready for use. Suppose now it is desired to make a series of measurements at the tem- peratures up to 381°. An amount of solution which will almost, but not quite, fill the bomb at this temperature is measured in from a pipette pre- viously graduated to contain this amount, as will be described in section 7. A gold packing-ring is annealed and cleaned by heating it in the flame of a burner, and it is placed in the groove. The cover is then put in place, taking care not to disturb the ring. The thread in the large nut is next washed out with benzene, to get rid of any solid substance which may have condensed there in a previous heating. With a piece of cloth or *Langbein's Electro-Deposition of Metals, 378 (1903). 2^ Conductivity of Aqueous Solutions. — Part II. absorbent cotton, a lot of finely powdered graphite is then rubbed into the thread and upon the surface which bears on the brass compensating washer. The nut is now screwed on by hand, care being taken not to dis- turb the cover; otherwise it might be raised slightly, so that particles of graphite would enter the bomb. The apparatus is next transported care- fully to the large wrench, and the nut is tightened up. The air pressure is then reduced to about 2 cm. by connecting the small tube with a Rich- ards water pump, the valve is screwed down, the lead- wires bolted on, and the bomb is ready for the measurements. The conductivity is first measured at 26°. To hasten the equalization of the temperatures, the cold bomb was usually introduced after bringing the bath to about 30°. The other vapor baths are heated up meanwhile. The bomb is then immersed in the 140° bath, whereupon the conduc- tivity increases very rapidly. The minimum in the telephone is at first greatly disturbed by the boiling of the solution, which takes place strongly at the lower electrode, owing to the fact that this is at the start, because of its position, the hottest part of the bomb. But as the temperature of the solution approaches that of the bath the disturbance decreases, and finally ceases altogether. When the temperature has become almost constant, which is indicated by the constancy of the conductivity, the bomb is removed from the bath, shaken, and returned as quickly as possible. To shake it while hot, a piece of asbestos cloth, with a piece of woolen cloth outside, is used. If the shaking is omitted, the measured conductivity may be too high by as much as 0.5 per cent. This was found to be due to the following facts : At 140° there is still a considerable vapor space left in the bomb, the entire cover being above the liquid surface. During the first part of the heating the xylene vapor is condensed so rapidly by the bomb that it extends up only for a little distance above the bottom of the bomb, leaving the upper part completely out of it. This causes an evaporation of pure water and a condensation of it all over the colder cover, leaving the solution too concentrated. If the bomb is shaken after reaching the temperature of the bath and quickly returned, the same action does not repeat itself, since the top is now as hot as the bottom. The bridge readings are now continued (usually for about 30 minutes) till one perfectly constant for 10 to 15 minutes is obtained. The bomb is then transferred to the naphthalene bath. Shaking was found to have no effect at this temperature, owing, doubtless, to the fact that the liquid level has then risen almost to the cover, so that large drops can not adhere to the latter, and to the fact that the surface tension has diminished, so that less water is held clinging to the walls of the narrow chamber in the cover. Section 6. — Method of Procedure. z^ The bomb is next brought into the 281° bath. It is now necessary to keep constant watch of the conductivity between the upper auxiliary elec- trode and the walls of the bomb, so as to be sure that too much solution has not been put into the bomb. The reasons for putting in solution enough at the start to so nearly fill the bomb at the highest temperature are first, to reduce the vapor space at all the temperatures as much as pos- sible, since a correction has to be made for the amount of solvent in this space; and secondly, to see that the bomb is absolutely tight even at the highest temperature, when the solution is in contact with the upper elec- trode. This latter is important, since a leak, if it took place above the liquid level, would cause a loss of pure solvent and a consequent increase in the concentration of the solution. After completing the measurements at 281°, the bomb is returned to the 218° bath, then to the 140° bath, and finally it is brought back to 26°. In going from a higher temperature to a lower much time is saved by cooling the bomb, in front of a fan outside the bath, to a temperature which is at least as low as that next desired; for while heating in a vapor bath is rapid, the cooling in it of a hotter body is very slow. During the first half of the experiment, where the bomb is introduced each time into a hotter bath, stirring inside the bomb takes place of itself, it being accomplished by the rising vapor bubbles and the rapid convection currents caused by the bottom of the bomb being so much hotter than the top during the heat- ing. During the second half it is necessary to provide for this by shaking the bomb before putting it into each bath. How much shaking is neces- sary can be determined by repeating the operation and seeing whether the conductivity has been affected by it. The advantages derived from cooling the bomb down through the same series of temperatures and again taking measurements are that these fur- nish a check on the accuracy of the preceding ones, and especially that they show whether or not there has been any contamination, and if so, between what temperatures it took place and to how much it amounts. The bomb is opened as soon as the experiment is completed, since other- wise there may be trouble in getting the cover off because of the strong adhesion of the gold packing-ring to the platinum lining below. This effect increases with use, since a small amount of gold from the ring adheres to the platinum each time, and subsequent rings will adhere more firmly to this gold than they would to a clean platinum surface. The effect can easily be reduced, however, as soon as it grows troublesome, by rub- bing the platinum cover, where it comes in contact with the ring, with a burnisher and by marking in the groove with a lead pencil. The trace of graphite which adheres to the surface is very effective. 26 Conductiinty of Aqueous Solutions. — Part II. When the bomb is not in use, good water is left standing in the lower part. The cover is inverted and the upper chamber similarly kept filled with water. If for the next experiment a more dilute solution is to be employed, the bomb must first be heated with good water to perhaps 218° for some little time. No amount of rinsing or soaking out at ordinary temperatures will answer the purpose. There is on this account a great saving of time effected by beginning with the most dilute solution to be investigated, and afterwards measuring those more and more concentrated. Our measurements at 306° were carried out, for the most part, after complete experiments up to 381° had been made, so that they usually con- sisted merely of measurements at 26°, 306°, and again at 26° 7. PROCEDURE FOR THE SPECIFIC- VOLUME MEASUREMENTS. To determine the specific volume of a solution at any temperature, such an amount of solution is weighed into the bomb as will bring the liquid level up onto the auxiliary electrode at that temperature. This amount was determined by successive heatings with increasing volumes of solution. A pipette of the form represented by fig. 8 was made for each of the temperatures 218°, 281°, and 306°. The stem is gradu- ated between a and b, and the capacity up to these points is roughly determined by weighing. The volume of the pipette \ is made such that for water or dilute solutions it v^^ill deliver the right amount into the bomb when filled up to the point b. For more concentrated solutions the expansion is less, so that more of the solution must be used. The graduations on the •^ pipette serve only as an indication of how much solution to take. . , The exact amount used is obtained by weighing the pipette filled and then again after discharging. During the weighing the tip is covered with a small test tube c, which is held on by the rubber band d. The bomb is first dried out by rinsing it with alcohol and ether. The residue left by these solvents upon evaporation is sufficient to affect the conductivity of the diluter solutions employed, so that no attempt was made to determine the conductivity of such solutions at the same time as their specific volume. The solution is boiled to expel the air. This increases the concentration slightly ; but this is of no conse- quence if, as was usually the case, the experiment was made solely to deter- mine the specific volume. If it was also to serve for conductivity measure- ments, the solution was boiled gently in a tall platinum vessel which was weighed with its contents before and after boiling. This gave the loss of solvent during the operation. Knowing this and the amount of solution \ Section 8. — Standardization of the Apparatus. 2j originally present in the cylinder, the final concentration is easily calcu- lated. After weighing the solution in from the pipette, the bomb is closed, and the air pressure reduced to 2 cm. Upon heating, careful watch is kept of the readings with the auxiliary electrode to make sure that too much solution has not been put in. After the conductivity of the upper chamber has been constant long enough to show conclusively that the temperature has become stationary and that the bomb is absolutely tight (even the slightest leak being of course indicated by a constant decrease in the con- ductivity of the upper chamber), the conductivities between the walls of the bomb and both the upper and lower electrodes are measured carefully, and the temperature of the bath is observed. The experiment is then complete. The ratio of these two conductivities is calculated, and the correspond- ing volume is obtained by interpolation from a plot obtained as described in section 8. This volume, corrected for the expansion of the bomb and then divided by the weight of solution in the bomb, gives the specific vol- ume of that solution at the temperature in question, and this quantity divided by the specific volume of the solution at 4° gives the volume of that quantity of the solution that would at 4° occupy one cubic centimeter, this quantity being most convenient in subsequent computations. 8. STANDARDIZATION OF THE APPARATUS. THERMOMETERS. These were calibrated by the method recommended by Crafts,* first for irregularities of bore and then at the fixed points 0°, 100°, 218°, and 306°. For the last two temperatures the vapors of boiling naphthalene and of benzophenone were used. These substances were obtained from Kahlbaum, and were purified in the manner suggested by Crafts, until their melting-points came within his limits. The form and dimensions of the vapor bath used in estabhshing the 218° and 306° points were essen- tially those given by him. To reduce the temperatures lying between the fixed points to the gas scale. Crafts' corrections for French glass were also used, our thermometers being of the same make as those used by him. The values adopted for the boiling-points of the naphthalene and benzo- phenone on the hydrogen-gas scale were, however, those recently obtained by Jaquerod and Wassmer (J. chim. phys., 2, 72; 1904). At the begin- ning every temperature measurement was followed by a lag ice-reading; but this was found to be unnecessary, since the thermometers showed no lag. The ice-reading was, however, taken frequently, to make sure that the zero did not change from another cause — evaporation of mercury *Am. Chem. J., 5, 307-338 (1883-84). 28 Conductivity of Aqueous Solutions. — Part II. from the bulb below and condensation in the chamber above. This effect was not apparent even after long use at temperatures up to 280°; but above this the zero would fall perhaps 0.1° from two or three days' use. When in use at 306°, instead of taking an ice-reading the thermometer was first placed in the benzophenone heater and then in the calibrating apparatus containing perfectly pure benzophenone. The difference in reading (usually amounting to 0.1° to 0.3°) was deducted from the true boiling-point of benzophenone at the observed barometric pressure. Two thermometers were calibrated in this way, and in actual use their corrected readings were always found to agree satisfactorily with each other. SLIDE-WIRE BRIDGE AND RESISTANCE COILS. The slide wire was calibrated by the method of Strouhal and Barus.* The resistance coils were calibrated by comparison with a standard bridge of the Massachusetts Institute of Technology. THE CONDUCTANCE-CAPACITY. In order to reduce the observed to specific conductances, the conduct- ance-capacity or so-called " cell-constant "f was determined in the usual manner, by measuring in the bomb solutions of known conductance. For this purpose the measurements at 36° of the solutions of both potassium and sodium chlorides, which were afterward studied at higher tempera- tures, were employed, the mean of the most reliable of them being taken. These data are given in section 13. THE VOLUME OF THE SOLUTION IN THE BOMB AND THE CORRESPONDING CONDUCTANCE-RATIO. It was stated above that the volume of the solution at any time in the bomb was determined by measuring the ratio of the conductances between the walls of the bomb and the lower and upper electrodes respectively. This ratio will hereafter be called the conductance-ratio. Its value is, of course, independent of the nature of the solution in the bomb, and is deter- mined fully by its height in the narrow chamber, and therefore by its vol- ume. To find the values corresponding to different volumes, we proceed as follows : The bomb is first dried by rinsing it with alcohol and ether. *Wied. Ann., 10, 326 (1880). See also Kohlrausch and Holborn, LeitvermoKen der Elektrolyte, 45 (1898). ature. fThe term cell-constant is inappropriate, since the value varies with the teniper- ucure. We shall adopt the expression conductance-capacity, which seems fairlv descriptive, since the quantity may be defined as the specific conductance of a solu- tion which, when placed in the vessel, gives rise to an actual conductance unity. Section 8. — Standardization of the Apparatus. zg Some 0.03 normal potassium chloride solution* is then boiled to free it from air, and, right after cooling, enough of this to fill the bottom part of the bomb to within 1 or 2 mm. of the flange is weighed in from a pipette. The mouth of the pipette is kept under the surface to diminish the absorp- tion of air. The cover is next put on and screwed down, care being taken not to tip the bomb enough to get any of the solution into the mouth of the capillary tube. By means of the water pump the air pressure in the bomb is reduced to about 2 cm., and the valve is then closed. If the air is not removed from the solution at the start, it comes out rapidly upon reducing the pressure and spatters some of the solution up into the tube, thus allowing it to be swept out by the air current. The lead wires are now bolted on and the bomb is placed in the liquid xylene bath, serving ordinarily for the 26° measurements, and the temper- ature of the latter is raised by means of the heating coil. The liquid level in the bomb is at the start about 3 mm. below the point of the auxiliary elec- trode, so that the resistance of the upper cell is shown by the conductivity apparatus to be infinite; but upon heating, the level rises and finally touches the electrode, whereupon the resistance suddenly sinks to perhaps 1,000 ohms. The temperature of the bath (perhaps about 130°) is now held constant until the solution in the bomb has also attained it, as will be indicated by the resistance of the lower and, far more sensitively, by that of the upper cell becoming constant. Both these resistances are then noted, and the temperature is measured. The temperature is now raised by steps of three or four degrees until that ratio of the conductances is reached which corresponds to the bomb being almost completely full. This limiting ratio can be determined cold at any time by measuring the resistance of the lower cell and then invert- ing the bomb and measuring that of the upper cell. Finally, the conduct- ance-ratios are plotted as abscissas and the corresponding volumes as ordinates, whereby a straight line is obtained. The computation of the volumes is made with the help of the following data : Zepernick and Tammannf have found that equal volumes of a 0.52 normal potassium chloride solution and of water at 0° upon heating from that temperature to 140° become diflferent from each other by only 0.1 per cent. It is therefore perfectly safe to assume that the expansion of the 0.02 normal potassium chloride solution used by us is the same as that of pure water. From Hirn'sJ results the specific volume of water at the *The reasons for taking this solution instead of pure water are that it makes the conductance at the upper electrode high enough to give a good minimum, and that the solution is so strong that contamination can not possibly make any trouble. tZ. phys. Chem., 16, 665 (1895). JG. A. Hirn, Ann. chim. phys., (4), 10, 33 (1897). His series of observations covers the range of temperature up to 180°. Between 110° and 143° his values differ from those found by Zepernick and Tammann by only 0.03 per cent. JO Conductivity of Aqueous Solutions. — Part II. temperature in question, but under a pressure of 14.8 atmospheres, may be obtained. At 135°, the mean temperature of the calibration experiments, the vapor pressure is 3.1 atmospheres. Hirn's result should then be reduced to this pressure. The coefficient of compressibility of water has been investigated by Pagliani and Vicentini* up to 100°. By plotting their values and extrapolating, 0.000048 is found for the coefficient at 135°, or for the fractional decrease in volume per atmosphere pressure. Hirn's value should then be increased by 0.000048 X (14.8 — 3.1) X 100 = 0.056 per cent. Multiplying the value so obtained by the weight of solution employed and by the specific gravity of the cold solution referred to water at the same temperature, the volume corresponding to the observed conductance- ratio is obtained. 9. PREPARATION OF THE SUBSTANCES AND SOLUTIONS. The sodium chloride used was purified by precipitation with hydro- chloric acid gas. It was then washed with hydrochloric acid, dried, and finally ignited until decrepitation ceased. The potassium chloride was precipitated twice with hydrochloric acid gas, crystallized from hot water, dried, and finally ignited. Solutions were made up, by weighing out the salts, so as to be almost exactly 0.1 and 0.01 normal at 4°. The solutions of smaller concentra- tion were made by diluting the 0.01 normal one with the help of two grad- uated flasks. The equivalent weights used are as follows : K = 39.14, Na = 33.05, CI = 35.46. All weighings were reduced to a vacuum. The water used throughout this investigation was prepared by redis- tilling ordinary distilled water to which alkaline permanganate solution was added from a steam- jacketed copper still with a tin condenser. The first quarter of the distillate was rejected, and the following portions were condensed hot (between 60° and 90°). The water had a specific conduc- tance of (0.7 to 1.0) X 10-" reciprocal ohms. 10. DISCUSSION OF THE SYSTEMATIC ERRORS AND THEIR CORRECTION. ERRORS AFFECTING THE SPECIFIC-VOLUME VALUES. (1) In calculating the specific- volume, the volume of the bomb was directly determined at about 135°, as described in section 8, and the expansion of the metal from this point to the temperatures of the experi- ments was corrected for Andrews,! working with "soft" cast steel, which corresponds to the material from which the bomb was constructed, found *Landolt-B6rnstein-Meyerhoffer, Tabellen, 60 (1905). fProc. Roy. Soc, 43, 299 (1887). Section lo. — Discussion of Errors and Corrections. ji the mean coefficient of cubical expansion between 100° and 300° to be 0.0000450 ; and this value was adopted for the corrections. The difference between his steel and that used in the bomb can hardly be great enough to cause an appreciable difference in the coefficient of expansion, since his values for two steels as different as Bessemer steel with 0.15 per cent com- bined carbon, and cast steel with 0.45 per cent, differ by only 6 per cent ; and an error of even 6 per cent in the coefficient of expansion would pro- duce a maximum error, even at 306°, of only 0.05 per cent in the specific volume. (2) The quartz-crystal cup expands upon heating, thus diminishing the volume of the bomb occupied by the solution. The correction for this, even at 306°, amounts to only — 0.03 per cent. (3) The bomb expands owing to the pressure within. At 306°, where this correction is greatest, the vapor pressure plus the air pressure may be estimated at 100 atmospheres. Assuming that the modulus of elasticity of the steel is 17,372 kgm. per sq. mm., which is the value found by Pisato* at 300°, the volume correction due to this cause is -f 0.025 per cent. This is opposite in sign and essentially equal to the preceding correction ; they therefore eliminate each other. (4) The volume of the tube T^ is only 0.07 c.cm. or 0.06 per cent of the whole volume of the bomb. It is therefore so small that no irregularities in the extent to which it is filled with solution could much affect the result. (5) The volume of the bomb depends somewhat on the extent to which the large nut is tightened up and the gold packing-ring compressed. Four of the gold rings which had been used were chosen at random, and the mean thickness of each was calculated from measurements made at eight equidistant points with a micrometer caliper. The average deviation from the mean thickness of these rings was such as to affect the volume of the bomb by only 0.02 per cent. So this source of error can be unhesitatingly disregarded, especially as each final specific -volume value is the mean of the values obtained from several independent experiments. (6) The bomb is never completely filled with liquid, the vapor space amounting, on an average, to about 1 c.cm. or 0.8 per cent of the total volume of the bomb (about 124 c.cm.). A certain fraction of the water is therefore vaporized, and the specific volume appears too small by a corresponding amount. The specific volume of the vapor is not yet known above 200°. By extrapolation, however, from the values up to 200°, the specific volume of the vapor at 218° is found to be seventy-five times that of the liquid. From this it follows that at 218° the correction is only rir + tV' or about 0.01 per cent. Such a calculation is not possible at the higher temperatures, 281° and 306°; but that no considerable error *Nuovo Cimento (3), 4, 152 (1878). 32 Conductivity of Aqueous Solutions. — Part II. arises from this source was shown by direct experiments. For example, when two or more specific-volume determinations were made, the amount of solution taken in the different experiments was purposely varied, so that the vapor space should vary from about 1.8 c.cm. to 1 c.cm. If, now, a considerable amount of the water were present in the vapor space, the specific-volume values obtained would, of course, be larger the smaller that space. As a matter of fact, however, the values obtained with the 1 c.cm. vapor space were as often smaller as they were larger than those obtained with the 1.8 c.cm. vapor space. In other words, no difference greater than the variable experimental error was observed. The error due to this source is therefore probably less than 0.1 per cent. (7) The temperature measurements may be regarded as accurate to within 0.2° ; and this of itself introduces an uncertainty of only 0.07 per cent in the worst case, that of the 306° values. That the bomb and its con- tents actually attained the temperature of the surrounding vapor is shown by the fact that the extremely sensitive reading of the upper electrode remained constant indefinitely after it had once become so ; and by the fact that there could not be a continuous loss of heat of appreciable magnitude from the bomb to the surroundings, since upon the sides the bomb was protected against radiation and cold convection-currents by the iron shield with the vapor outside, and since above there was always a layer of vapor 10 cm. in height, and since the dropping back of condensed liquid onto the bomb was prevented by the mica shield; moreover, the copper lead-wires were only 1.3 mm. in diameter and passed through the upper layer of vapor before emerging. (8) Another possible source of error might be the gathering of vapor bubbles on the under surface of the cover, whereby the apparent volume of the liquid would be increased. That this did not occur was shown by removing the bomb from the heater, shaking vigorously, immediately replacing it, and taking conductivity readings as soon as the temperature had again become constant, whereby the same readings were obtained as before the shaking. (9) The air was not entirely removed from the bomb at the start, and, as the solution expands, and the temperature rises, the air pressure increases. Assuming that the preliminary boiling had removed all of the air from the solution in the beginning, and that there is no solubility of the air in the liquid at the high temperatures, its pressure can be calculated by the gas laws. At the temperatures of 318°, 281°, and 306°, it would thus amount to about 1, 2, and 2.5 atmospheres respectively. The effect of these air pressures on the specific-volume values can not be calculated, since the compressibility at these temperatures is not known ; but for these small pressures it is undoubtedly less than the errors of observation. Section lo. — Discussion of Errors and Corrections. jj (10) If the vapor above the solution had an appreciable conductance it would make the conductance between the upper electrode and the bomb appear too great. But this is not the case, as is shown by the fact that unless the liquid is in contact with the electrode there is no measurable conductance here, even at 306° with a 0.1 normal potassium chloride solu- tion. We can at present assign only an upper limit to the conductance of the vapor ; but it certainly does not exceed -^Tj-^^ajj part of that of the solution. ERRORS AFFECTING THE CONDUCTANCE VALUES. (1) All the errors in the values of the specific volume have an effect of the same magnitude upon those of the equivalent conductance, with the important exception of that due to the amount of solvent in the vapor Space at the two highest temperatures, 281° and 306°. No error arises from this last source for the reason that, owing to the increase in concen- tration of the solution, the specific conductance increases in the same pro- portion as the volume diminishes ; for at 281° and 306° (but not at 140° and 218°) the quantity of liquid in the bomb was the same in the two series of measurements. (2) The conductance-capacity might be expected to vary with the height of the liquid level in the bomb, but direct experiment showed that for the range of the liquid level in our measurements the effect of this was less than the error of observation. The smallest amount of solution employed in any of the experiments was first introduced into the bomb and the con- ductance measured at 26°. Then more of the same solution was intro- duced until the liquid was in contact with the whole cover ; but the resist- ance was not measurably changed. Mr. A. C. Melcher has shown (see section 36, Part IV) that even much larger variations in the quantity of solution have no effect. (3) The conductance-capacity changes with the temperature owing to two causes: first, the expansion of the quartz-crystal cup; and, secondly, that of the bomb itself. A direct experimental investigation of the effect on the conductance of such changes in the dimensions of the cup and bomb has been made by Mr. A. C. Melcher and is described in section 36, Part IV. The corrections for the conductance-capacity have been based on his results. The relative values at the different temperatures are given in section 13. (4) The eft'ect of the pressure on the conductance-capacity is entirely negligible. For at 306° the radius is increased by the pressure 0.01 per cent, and this affects the conductance-capacity by even less. (5) The resistance of the lead-wires has to be deducted from the meas- ured resistance of the bomb; and, since a portion of the leads is subjected 34 Conductivity of Aqueous Solutions. — Part II. to the temperature of the bath, this correction is different for different temperatures. This resistance may be considered as made up of three parts : i?i, the constant resistance of the heavy leads ; R^, the resistance of the small leading-in wires, L^ and L^ ; and R^, that of the steel electrode rod. i?i and R^ were measured at room temperature. For the other tem- peratures /?2 was calculated from its value at room temperature. R^ was calculated from its dimensions and the specific resistance of steel. The maximum value (at 306°) of the total resistance of the lead-wires was 0.061 ohms. (6) In the case of the more dilute solutions it was necessary to correct for the conductance of the water used. To do this, some water prepared in the same way and of the same conductance cold as that used for making up the solutions was put into the bomb, and just such a set of experiments was made with it as had been made with the solutions. Then for any tem- perature the conductance of the water, measured at that same temperature and under the same conditions, was deducted from that of the solution. This at the same time corrects for contamination, since, with a dilute, neutral-salt solution, there is no apparent reason why the contamination should not be the same as for water. For the most dilute solution used, 0.0005 normal, the maximum correction (at 306°) amounts to 1.9 per cent. See also section 14. (7) In the conductivity experiments, the vapor space at 140° and 318° was considerable, so that at these temperatures a correction has to be applied for the vaporized solvent, since the solution is more concentrated than it would otherwise be. This correction was calculated from the known volume of the vapor in the bomb and its specific volume, using for the latter the data of Zeuner* which go up to 200°, and extrapolating for the 318° value. The correction amounts to + 0.05 per cent at 140° and + 0.18 per cent at 318°. As explained above, it is not required in the case of the 381° and 306° values. (8) The temperature measurement at 26° is certainly more accurate than the work requires. Above this, the temperature reading is probably correct to 0.2°. Most of the uncertainty in the equivalent conductance values introduced by this possible error finds expression in the specific- volume values, and this has already been considered. Besides this there is the much smaller effect on the observed resistance of the bomb. The total uncertainty in the equivalent conductance arises from both these sources; that due to 0.3° is in the worst case (at 318°) 0.09 per cent, and where, as has usually been the case, several experiments are made and the mean taken, this effect tends to be eliminated. *Landolt-B6rnstein-Meyerhoffer, Tabellen, 62 (1905). Section ii. — The Specific-Volume Data. 55 II. THE SPECIFIC -VOLUME DATA. All of the measurements have been included in table 1 (page 36) with the exception of two, which, though agreeing well with the others, were known to be less reliable. The first and second columns are self-explanatory. The third column gives the concentration of the solution at 4°, expressed in milli-equivalents per liter. The fourth column gives the corrected temperature of the measurement. The fifth column gives the number of grams of solution which were weighed into the dry bomb at the start. The sixth column gives the volume, expressed in cubic centimeters, which, at the temperature (135°) at which the bomb was calibrated, corre- sponds to the observed conductance-ratio. This volume was obtained by interpolation from a plot made as described in section 8. The actual vol- ume occupied by the solution at the higher temperature is greater than this by an amount equal to the expansion of the bomb upon heating from 135° to that temperature. The temperature-coefficient of volume expansion of the steel shell of the bomb is assumed to be 0.000038 per degree. The seventh column gives the specific volume of the solution at the tem- perature of observation. It is obtained by dividing the values of the pi-e- ceding column, after correcting them for the expansion of the bomb as just described, by the weight of solution given in the fifth column. The last column gives the ratio of the specific volume at the round tem- peratures 318°, 281°, and 306°, to that of the same solution at 4°. Thus, this ratio shows the volume occupied by that quantity of solution which at 4° has a volume of 1 c.cm. The values are obtained from those of the preceding column by reducing them to these temperatures by means of the temperature-coefficient obtained from our specific-volume values, and then dividing the results by the specific volumes of the solutions at 4°. These specific volumes are as follows : 0.9958 for 0.1 normal, and 0.9996 for 0.01 normal sodium chloride; and 0.9954 for 0.1 normal, and 0.9995 for 0.01 normal potassium chloride.* 12. SUMMARY OF THE SPECIFIC -VOLUME VALUES. The final results are brought together in table 2 (page 36). The value at 140° is that found by Hirnf for pure water reduced from the higher pressure which he employed to the vapor-pressure. *These values were computed from the densities given by Kohlrausch and Hall- wachs (Wied. Ann., 50, 123, 1893) for NaCl at 18°, and from that given by Kohl- rausch (Leitvermogen der Elektrolyte, 76) for a normal KCl solution at 18°, under the assumptions that the change in density is proportional to the concentration and that the expansion is the same between 4° and 18° for these solutions as for water, tHirn, Ann. chim phys. (4), 10, 32 (1867). 36 Conductivity of Aqueous Solutions. — Part II. Table 1. — The specific-volume data. Date. Substance. Milli- equivalents per liter. Temper- ature. Weight of solution. Volume un- corrected. Specific volume. Specific volume ratio. 1902 Mar. 31 . Apr. 2 .. Apr. 3 .. May 2 .. Apr. 14 . . Apr. 14 . . Apr. 18 . . Apr. 29 . . May 1 . . June 19 . 1903 Mar. 11 . Mar. 27 . Feb. 20 . . Jan. 17 .. Mar. 31 . Feb. 17 . . Feb. 18 . . Jan. 30 .. Feb. 10 . . Feb. 16 . . *Feb. 16 . NaCl Mean. . 2 216.4 216.8 217.5 104.16 104.58 103.44 122.75 123.58 122.18 1.1831 1.1863 1.1859 218°/4°. 1.1858 1.1885 1.1868 1.1870 NaCl NaCl Mean. . 100 217.6 103.52 121.79 1.1862 1.1869 2 280.5 280.6 280.6 92.11 92.97 92.65 122.08 123.51 122.94 1.3343 1.3374 1.3359 281° '4°. 1.3358 1.3387 1.3371 1.3372 NaCl Mean. . 100 280.7 280.2 281.3 92.83 93.27 98.34 122.07 122.37 122.85 1.3237 1.3207 1.3248 1.3302 1.3290 1.3287 1.3293 NaCl Mean. . 2 305.7 305.2 85.40 85.35 121.82 121.30 1.4373 1.4318 306°/4°. 1.4385 1.4352 1.4368 NaCl NaCl Mean. . 10 306.1 85.69 122.14 1.4362 1.4362 100 304.6 304.6 86.39 87.01 120.94 121.92 1.4106 1.4117 1.4226 1.4237 1.4232 KCl Mean. . 10 304.1 305.4 85.61 85.76 121.24 122.01 1.4270 1.4335 1.4360 1.4367 1.4363 KCI Mean. . 100 304.3 305.7 304.7 304.7 86.75 86.78 86.41 86.41 121.56 122.05 121.29 121.24 1.4119 1.4171 1.4143 1.4137 1.4258 1.4248 1.4264 1.4258 1.4257 *Same solution as in preceding experiment, after cooling, shaking, and reheating. Table 2.~Ratio of the specific volume at various temperatures to that at 4°. Substance. Equivalent concentration at 4°. Specific-volume ratio. 26°. 140°. 218°. 281°. 306°. NaCl KCl 0.002 0.01 0.1 0.01 0.1 1.0032 1.0803 1.1870 1.1869 1.3372 1.3293 1.4368 1.4362 1.4232 1.4363 1.4257 Section 12. — Summary of Specific-Volume Values. 57 The results with the 0.002 normal solution may be regarded as com- pletely identical with those that would be obtained with pure water; for this solution contains only about 0.01 per cent of salt ; and, moreover, the experiments themselves show that there is no difiference between the specific-volume ratio of the 0.003 and 0.01 normal solutions, and that the difiference between the latter and that of the 0.1 normal solution is some- what less than 1 per cent, which indicates that the order of magnitude of the difference between pure water and the 0.002 normal solution is 0.02 per cent. The specific volume of water is therefore 1.187 at 218°, 1.337 at 381°, and 1.437 at 306°. It is, according to our estimate of the possible errors, almost certain that these values are not in error by as much as 0.3 per cent, and it is probable that the error does not exceed half this amount. Previous determinations of the specific volume of water at high temperatures have been made by Hirn up to 180°, by Waterston* up to 320°, and by Ramsay and Youngf up to 270°. The values obtained by interpolation from the older results of Waterston are 1.194 at 218°, 1.355 at 281°, and 1.454 at 306°, which are seen to be considerably higher than ours. Ramsay and Young, however, found 1.188 at 218° in substantial agreement with our value. Attention may also be called to the facts that the 0.1 normal solutions between 218° and 306° expand appreciably less than pure water, but that the difference between the solutions of the two salts scarcely exceeds the experimental error. 13. THE CONDUCTANCE-CAPACITY OF THE APPARATUS. The conductance-capacity was calculated from the conductance meas- urements at 26°, using for the specific conductances of the 0.1 and 0.01 normal potassium chloride solutions the standard values of Kohlrausch, Holborn, and Diesselhorst,^ and for the other solutions the values at 18° of Kohlrausch and Maltby,|| and the temperature-coefficients of Deguisne.§ The quartz-crystal cup which was used for the first half of the meas- urements (cell i) was accidentally broken, and a new one had to be substituted for the rest of the work. After making three experiments with the new cup, the platinum lining of the lower part of the bomb had to be removed and repaired, and this operation changed the conductance-capacity. The term cell iia will be used to characterize the bomb as it was in these first three experiments with the new cup, and the *Phil. Mag. (4) 26, 124 (1863). tPhil. Trans. (A), 183, 109 (1892). tWied. Ann., 64, 440 and 451 (1898). llWissensch. Abhandlungen phys.-techn. Reichsanstalt, 3, 210 (1900). §Dissertation, Strassburg (1895) ; Kohlrausch and Holborn, Leitvermogen der Elektrolyte, 199. 38 Conductivity of Aqueous Solutions. — Part II. term cell ii as it was in all subsequent work. With these exceptions, the conductance-capacity calculated from measurements made at widely dif- ferent periods did not vary throughout the work. Even when the elec- trode was removed because of a leak, and then replaced, it did not make any measurable difference, as was, indeed, to be expected, since the value is so largely determined by the dimensions of the quartz cup. The values of the conductance-capacity, with the solutions from which they were derived, are given in table 3. The unit of conductance employed here and throughout this publication is the reciprocal ohm. Table 3. — Conductance-capacity at z6° . Cell I. Cell II. Substance. Milli- equivalents per liter. Conductance- capacity. Substance. Milli- equivalents per liter. Conductance- capacity. KCl NaCl KCl NaCl 100 100 10 2 2 0.8294 0.8288 0.8280 0.8280 0.8317 KOI NaCl 100 10 2 2 0.9853 0.9845 0.9850 0.9840 Mean of first two values 0.9849 Mean of first three values 0.8287 Cell IIj. NaCl 100 0.9949 The original data from which these were calculated are all given in tables 5 and 6. Each value is the mean of all of the values calculated from all of the experiments on the solution in question at 26°. The values derived from the 0.002' normal solutions are not included in the means, because, owing to the higher dilution, they are probably not so reliable as the others. They are given here, especially to show that our conductance measurements were not affected either by polarization or by unsymmetry in the telephone; for had this been the case, our capacity values calculated from these solutions would not have agreed with those derived from the 0.1 normal solutions. As explained in section 10, the conductance-capacity changes with the temperature ; the percentage corrections to be applied at the different temperatures of the experiments to the values of it at 26° are as follows : — 0.23 at 140° ; — 0.41 at 218° ; — 0.56 at 281° ; and — 0.58 at 306°. Sections 14-15. — Water Correction and Conductivity Data. jp 14. THE WATER CORRECTION. The conductance of the water at the various temperatures of the experi- ments was subtracted from the measured conductance of the solution. Two experiments, the data of which are given in table 4, served as a basis for the correction. For a fuller discussion of this correction see section 10. The last two lines give the percentage corrections to be applied at the various temperatures to the observed conductances in the case of a 0.002 normal sodium chloride solution. They are given so as to show the order of magnitude of these corrections. The correction decreases of course in the same proportion as the specific conductance of the solution increases. Table 4. — Observed conductance (X10°) of water in the bomb. Date. Cell No. 26°. 140°. 218°. 281°. 306°. Initial. Final. Initial. Final. Initial. Final. May 14, 1903. Feb. 28, 1903. Percentage ( corrections I II I II 0.85 1.02 0.2s 0.38 1.25 1.67 0.41 0.63 3.57 o!33 4.55 o!42 6.1 0.41 6.5 0.43 7.3 0.45 7.1 o!53 15. THE CONDUCTIVITY DATA. Table 5 (pp. 40, 41) contains the conductivity data for the various solu- tions. The first four columns require no explanation further than the state- ment that the concentration is expressed in milli-equivalents per liter as has been done throughout this series of articles unless otherwise noted. The fifth column gives the concentration at the temperature of the measure- ment, corrected in the case of the 140° and 218° values for the solvent in the vapor space. The correction is made as explained in section 10, and amounts to + 0.05 per cent at 140° and + 0.18 per cent at 218°. The sixth column contains the observed resistances of the bomb, expressed in ohms, after correcting for errors in the resistance coils and slide wire, and deducting the resistance of the lead-wires. The seventh column gives the equivalent conductance obtained by dividing the conductance-capacity for the given temperature by the concentration at t° (given in the fifth col- umn) and by the resistance (given in the sixth column) after correcting it for the water, and by multiplying the result by 10^. 40 Conductivity of Aqueous Solutions. — Part II. Table 5. — Conductivity data for sodium chloride. Cell No. tration at 4°. Tempera- Iiirc, P. Concen- tration at^. Equivalent conductance. 1902 June 23 0.4995 June 25 0.4995 June 26 1903 Mar. 18 1902 May 8 . May 9 . May 10 1903 Mar. 3 1902 May 15 May 16 II II 0.4995 0.4992 2.018 1.998 1.998 1.995 9.990 9.990 25.91 140.6 218.6 281.1 218.8 141.9 25.91 25.91 141.2 218.9 281.1 219.1 142.2 25.91 25.91 280.8 219.2 139.2 25.91 26.00 306.2 26.00 25.91 280.9 25.91 25.91 280.9 25.91 138.8 217.3 25.91 25.91 139.9 217.9 281.0 217.9 140.1 25.91 26.00 306.6 26.00 25.92 138.8 218.5 25.91 139.0 218.0 0.4979 0.4624 0.4212 0.3733 0.4210 0.4617 0.4979 0.4979 0.4621 0.4213 0.3733 0.4213 0.4616 0.4979 0.4979 0.3736 0.4208 0.4630 0.4979 0.4987 0.3472 0.4987 2.012 1.509 2.012 1.991 1.494 1.991 1.852 1.685 1.991 1.991 1.850 1.686 1.495 1.686 1.850 1.991 1.989 1.386 1.989 9.967 9.274 8.438 9.967 9.271 8.440 12945 3564 2565 2333 2571 3538 12835 12932 3554 2573 2333 2566 3494 12614 12921 2333 2565 3586 12782 15305 2732 15163 3293.0 604.0 3277 3326 608.3 3314 927 669.6 3313 3322 923.8 669.3 608.9 669.0 921.0 3310.8 3926 720.5 3909 687.62 194.35 141.54 688.10 194.09 141.30 127.18 496.1 753.6 932.9 751.9 498.8 127.67 127.31 497.8 751.1 933.4 752.6 505.1 129.84 127.42 932.7 754.0 490.8 128.15 127.05 1012.4 127.02 124.76 899.9 125.18 124.76 902.8 125.05 497.4 728.4 125.09 124.91 482.2 728.4 901.6 728.7 483.3 125.18 125.65 975.6 125.87 120.92 458.7 690.9 120.83 459.6 692.0 Section i§. — The Conductivity Data. Table 5. — Conductivity data for sodium chloride — Continued. 41 Cell Concen- Tempera- Concen- Equivalent Date. No. tration at 4°. ture, P. tration at/°. Resistance. conductance. 1902 May 20 I 9.990 25.91 139.3 9.967 9.267 687.99 193.20 120.85 461.8 218.0 8.440 141.70 690.0 283.1 7.441 131.62 841.4 218.0 8.440 141.86 690.0 139.9 9.261 193.59 461.2 25.91 9.967 688.28 130.80 1903 Feb. 20 II 9.977 ,306.1 26.00 6.944 9.945 156.37 803.6 901.9 123.34 Feb. 21 II 9.977 305.8 6.950 156.50 900.3 1902 Apr. 29 I 102.75 25.91 280.7 102.42 77.33 74.55 15.823 108.54 673.5 139.6 95.20 21.568 403.7 217.4 86.80 16.278 584.1 25.91 102.42 74.52 108.59 Apr. 30 I 103.11 25.91 138.5 103.78 95.65 74.25 31.550 108.60 401.2 217.4 87.13 16.217 584.1 May 1 I 101.53 25.91 380. 2 101.18 76.49 75.13 15.905 109.03 677.4 218.4 85.63 16.418 587.1 139.1 94.15 21.810 402.7 25.91 101.18 75.12 109.03 Jlay 2 I 101.48 25.91 217.5 101.14 85.56 75.35 16.534 108.75 583.8 139.8 93.95 21.787 404.0 June 18 I 99.90 25.91 99.57 76.44 108.88 140.2 92.48 22.018 406.1 June 19 I 99.90 25.91 99.57 76.38 109.10 140.3 92.48 21.926 407.8 281.3 75.09 16.236 676.7 218.2 84.38 16.701 586.4 141.2 92.41 21.965 407.4 25.91 99.57 76.23 109.19 1903 Jan. 15 Ila 99.90 25.94 305.1 99.58 70.39 91.90 30.35 108.71 690.7 25.94 99.58 91.73 108.93 Jan. 17 Ila 99.90 99.90 25.94 304.6 99,58 70,51 91.73 30.30 108.93 691.3 25.94 99.58 91.72 108.93 42 Conductivity of Aqueous Solutions. — Part II. Table 6. — Conductivity data for potassium chloride. 1903 Mar. 20 1902 Aug. 20 Aug. 25 1903 Mar. 2 Feb. 17 Feb. 18 Feb. 19 Mar. 28 1902 Aug. 28 Aug. 29 Sept 2 Sept. 27 1903 Jan. 30 Feb. 10 Feb. 13 Feb. 16 Cell No. II II Concen- tration at 4°. Tempera- ture. i°. 0.4999 2.001 2.001 1.997 10.04 10.04 10.04 10.04 100.14 100.14 100.14 100.14 99.92 99.92 99.92 99.92 26.00 305.5 26.00 25.91 140.2 218.0 281.5 218.1 140.3 25.91 25.91 140.0 218.6 281.0 218.9 140.4 25.91 26.00 306.0 26.00 304.1 305.4 25.96 25.96 26.00 25.91 141.2 220.8 281.9 220.8 141.2 25.91 141.6 25.91 141.2 217.8 141.8 25.91 280.7 304.3 305.7 25.94 25.94 304.7 Concen- tration at<°. 0.4983 0.3484 0.4983 1.994 1.853 1.689 1.494 1.689 1.853 1.994 1.994 1.853 1.687 1.496 1.686 1.852 1.994 1.991 1.390 1.991 7.006 6.977 9.972 9.972 9.972 99.72 92.56 84.04 74.22 84.04 92.56 99.72 92.52 99.72 92.54 84.45 92.48 99.72 74.43 70.46 70.15 99.60 99.60 70.36 12981 2611 12763 2790.4 828.0 618.9 574.0 619.3 824.7 2778.5 2785.6 824.8 616.1 573.6 617.2 820.8 2726.8 3308.6 685.8 3298.0 148.58 148.94 675.0 681.8 685.1 63.17 19.760 15.360 15.223 15.341 19.701 63.30 19.724 63.30 19.783 15.406 19.735 63.04 15.160 19.094 19.068 75.30 75.30 19.043 Equivalent conductance. 150.32 1056.5 151.70 148.56 537.4 786.8 957.1 786.2 539.4 149.04 148.82 539.4 791.1 956.4 790.0 542.1 151.87 149.02 1022.2 149.18 940.9 942.4 146.31 144.87 144.18 131.56 452.1 639.4 729.3 640.2 453.5 131.29 453.1 131.15 451.7 634.3 453.1 131.83 730.3 728.0 732.3 131.34 131.34 731.8 Section i6. — Summary of Equivalent Conductances. 43 16. SUMMARY OF THE EQUIVALENT CONDUCTANCE VALUES REDUCED TO ROUND TEMPERATURES AND CONCENTRATIONS. The separate conductance values given in tables 5 and G were all cor- rected so as to correspond to the uniform temperatures of 26°, 140°, 318°, 281°, and 306° by means of temperature-coefficients obtained by plotting those values. The so-corrected equivalent conductances are summarized in the following table. The concentration in table 7 is expressed in milli- Table 7. — Equivalent conductance at round temperatures. SODIUM CHLORIDE. Concen- 26°. 140°. 218°. 281°. 306°. at4°. Initial. Final. Initial. Final. Initial. Final. 1902 June 23.. 0.4995 127.48 127.97 494.2 492.6 751.5 749.1 9.33.0 June 25. . 0.4995 127.61 130.14 493.9 497.9 748.0 748.8 933.0 June 26. . 0.4995 127.72 128.45 493.5 749.9 933.2 1903 Mill-. 18.. Mean . . 1902 0.4992 127.05 127.02 1011.5 127.46 .^il28.85/ |127.02i 494.0 494.7 749.7 748.3 933.1 1011.5 May 8. . 2.018 125.05 125.47 900.1 May 9.. 1.998 125.05 125.38 483.3 730.5 903. Oi 1 May 10.. 1.998 125.20 125.47 482.6 483.1 728.7 739.0 901.5 1903 1 Mar. 3.. Mean.. 1902 1.1995 125.65 125.87 973.9 125.24 »il25.44| /I25.87i 482.6 483.2 728.7 729.8 902.2 973.9 May 15.. 9.990 121.16 462.4 689.7 May 16.. 9.990 121.10 462.6 692.1 May 20. . 9.990 121.12 121.07 464.0 461.6 690.1 690.1 836.6 1903 Feb. 20. . 9.977 901.4 Feb. 21.. Mean.. 1003 9.977 900.5 121.11 462.6 690.5 836.6 901.0 Apr. 29.. 102.75 108.77 108.82 403.8 585.2 673.7 Apr. 30. . 103.11 108.83 405.1 585.2 May 1.. 101.53 109.26 109.26 405.0 586.2 678.1 May 2.. 101.48 108.98 404.5 584.7 June 18.. 99.90 109.11 405.7 June 19. . 99.90 109.33 109.42 407.1 404.4 585.8 676.1 1903 Jan. 15.. 99.90 108.87 109.09 691.0 Jan. 17.. 99.90 109.09 Jan. 17.. Mean. . 99.90 109.09 691.6 109.07 405.1 585.4 676.0 691.3 *These two means refer to the experiments carried to 2S1*' and to 306°, respectively. 44 Conductivity of Aqueous Solutions. — Part II. Table 7.— Equivalent conductance at round temperatures — Continued. POTASSIUM CHLORIDE. Date. Concen- tration at 4°. 26°. 140°. 218°. 281°. 306°. Initial. Final. Initial. Final. Initial. Final, 1903 Mar. 20. . Mean . 1902-03 Aug. 20.. Aug. 25.. Mar. 2.. Mean. . 1903 Feb. 17.. Feb. 18.. Feb. 19.. Mar. 28.. Mean. . 1902 Aug. 28.. Aug. 29. . Sept. 2. . Sept. 27. . 1903 Jan. 30.. Feb. 10.. Feb. 13.. Feb. 16.. Mean.. 0.4999 150.32 151.70 1057.6 150.32 151.70 1057.6 2.001 2.001 1.997 148.87 149.13 149.02 149.35 152.18 149.18 536.7 539.4 538.4 540.7 786.9 789.4 786.0 787.4 955.8 966.4 1622! 6 149.01 *S150.77/ I149.18S 538.0 539.6 788.2 786.7 956.1 1022.0 10.04 10.04 10.04 10.04 144! 87 144.18 146! 42 941.9 943.5 145.16 ^ 942.7 100.14 100.14 100.14 100.14 99.92 99.92 99.92 99.92 131.81 131.54 131.40 132.08 131! 51 131.51 448.9 448.9 448.0 450.3 448.4 633.6 634 ! 7 634.4 729.4 730.4 726.5 732.3 730.7 131.64 448.9 634.2 729.9 729.8 *These two means refer to the experiments carried to 281** and to 306°, respectively. equivalents per liter at 4°. In the columns headed "Initial" are given the equivalent conductances obtained from the measurement at the tempera- ture in question before going to the higher temperatures ; while in the col- umns headed " Final" are given the equivalent conductances obtained after returning to the temperature in question from the higher ones. From a comparison of the separate initial values at any temperature and concen- tration the degree of agreement of the determinations made at different times, and often with different solutions, will be seen. A comparison of the initial and final values in the separate experiments shows the contami- nation that resulted from the heating. In the cases of the 10 and 100 milli-normal solutions where the contamination is insignificant, both the initial and final values have been included in deriving the mean; in the other cases, the means of the initial values and of the final values have been taken separately. Table 8 contains a summary of best values derived from the means in table 7. The general mean of the initial and final values has been directly Section i6. — Summary of Equivalent Conductances. 45 transferred in the cases of the 100 milli-normal and (except at 306°) of the 10 milH-normal solutions. In the other cases we have adopted the mean of the initial values after correcting it for contamination w^hen this amounted to more than 0.25 per cent, as shown by the differences between the initial and final values at 2G°. This contamination-correction is based on the experience that when a solution has once been heated to the highest tem- perature of any experiment it undergoes no further change of importance Table 8. — Best values of equivalent conductance at round temperatures. Tempera- ture, t°. Sodium chloride. Potassium chloride. Conccntra- Equivalent Concentra- Equivalent ' !ion at t°. conductance. tion at t°. conductance. 0.5 107.18 0.5 128.11 18 ' 2.0 105.55 2.0 126.31 10.0 101.95 10.0 122.43 I 100.0 92.02 100.0 112.03 0.4C3 491.5 1.85 535.0 140 1.85 482.0 93.0 449.0 9.26 462.5 95.2 405.0 0.420 745 1.68 782 218 ■ 1.68 8.43 737 690 84.4 634 , 86.6 585 .... f 0.373 925 1.49 949 281 J 1.48 900 74.3 730 7.47 836 77.6 676 .... 0.346 1011 0.347 1051 306 1.38 973 1.38 1022 6.93 895 6.96 937 70.2 691 70.2 730 either upon continued heating at that temperature or upon cooling and reheating. Therefore the difference in initial and final values at 26° cor- responds to the change that had already taken place in the solution when the measurement at the highest temperature was made. Since, however, the conductance of the contaminating substance, if it be a base or acid, would have a smaller temperature-coefficient than that of the salt, it seemed best to apply a percentage correction equal to only two-thirds of this differ- ence at 2(5°.* Instead of reproducing our 36° values in table 8, we have inserted the more accurate ones of Kohlrausch and Maltby at 18°. f ♦Mathematically expressetJ the fractional correction in general at any temperature t is Am (Init — Aai(Fin) At (Inil) — A, (Fin) At )' 3 \ Aj, the highest temperature of each series of experiments. fWissensch. Abhandl, phys.-techn. Reichsanstalt, 3, 210 (1900) the last term dropping out at 46 Conductivity of Aqueous Solutions. — Part II. In order to compare the conductivity values at different temperatures, it is desirable to correct those directly measured for the change in concen- tration produced by the expansion when a given solution is heated. The values in table 8, which, owing to this expansion, refer at different tem- peratures to somewhat different concentrations, as is there indicated, have been reduced to the nearest round concentrations, by a graphic interpola- tion with the help of the nearly linear function — = -— -j- K{CA.)''-^ (See A Aq section 17.) The so-reduced values are presented in table 9. In the subsequent stages of these researches various other measure- ments of the conductivity of sodium and potassium chloride solutions have been made by other experimenters, namely, by A. C. Melcher, by G. W. Eastman, and by H. C. Cooper. This has been done partly as a control and partly in order to complete this first series of measurements. The details and original data of these experiments will be presented in the later articles of this series;* but in order to simplify and shorten the discus- sion of the results we have included all of their final values, together with our own, in table 9. Our values are indicated by adding the letters N-C to the data, those of A. C. Melcher by the letter M, of G. W. Eastman by the letter E, and of H. C. Cooper by the letters Cp. The best final values which we have derived by combining all these data, a double weight being usually assigned to the later determinations, are printed in black type in the table. The values at 18° are those of Kohlrausch and Maltby. The values at 0° for potassium chloride are means derived from the closely concordant determinations of Whethamf and of Kahlenberg.J All the other data in the first table for potassium chloride were obtained by G. W. Eastman in this laboratory. The values given in parentheses for zero concentration were obtained by graphic extrapolation with the help of the empirical formula — = -^ /^(CA)™, as described in section 17. Aq a In this table, as in all those containing final values throughout this publi- cation, the concentration is expressed in milli-equivalents per liter, using as atomic weights the values given by the International Commission for 1905 ; the temperature is expressed on the hydrogen-gas scale, using for the reduction to this scale at 318°, 381°, and 306° the values found for the boiling-points of naphthalene and benzophenone by Jaquerod and Wass- mer ; and the equivalent conductance is expressed in reciprocal ohms and refers to a concentration at the temperature under which it stands equal to the value given opposite to it in the first column. *See section 41, Part IV, and section 54, Part V. tZ. phys. Chem., 33, 351 (1900). jj. Phys. Chem., 5, 348 (1901). Section i6. — Summary of Equivalent Conductances. Table 9. — Final values of the equivalent conductance. 47 SODIUM CHLORIDE. Concen- tration. 18°. 100°. 140°. 156°. 218°. 281°. 306°. 0.0 109.0 862 500 555 760 970 1080 0.5 •• 355.5 Cp. 491 N-C. 545 Cp. 743 N-C. 738 Cp. 922 N-C. 1003 N- C. 0.5 107 2 855.5 49i 645 740 922 1003 2.0 •■ 349.0 B. 349.0 Cp. 481 N-C: 534 Cp. 723 N-C. 722 Cp. 895 N-C: 959 N- 954 M. C. 2.0 105 6 849.0 481 584 723 895 955 10.0 335!5Cp. 461 N-C; 511 Cp. 685 N-C. 685 M. 684 Cp. 821 N-C. 820 M. 870 N- 857 M. c. 10.0 102 6 835.5 461 511 685 820 880 80.0 411 N-C. 590 N-C. 674 N-C. 676 N- c. 301.0 E. 4.50.5 E. 591 M. 674 M. 682 M. 80.0 93 5 801.0 411 450.5 500 674 680 100.0 •• 296! OB. 403.5N-C. 441 . 5 E. .... .... 100.0 92 296.0 403.5 441.5 .... 1 POTASSIUM CHLORIDE. Concen- 0° 18°. 25°. 50°. 75°. 100°. 128°. tration. 0.0 81.4 180.1 (152.1) (232.5) (321.5) 414 (519) 0.5 80.5 128.1 .... .... .... 2.0 79.6 126.3 146.4 .... .... 393.0 10.0 77.5 122.4 141.5 215.3 295.2 377.0 470.0 80.0 72.8 113.5 .... . . • • .... 341.5 .... 100.0 71.5 112.0 129.0 194.5 264.6 336.0 415.0 Concen- tration. 140°. 156°. 218°. 281°. 306°. 0.0 565 625 825 1005 1120 0.5 1044 N-C. 2.0 534 N-C. 588 E. 779 N- C. 980 N-C. 1008 N-C. 10.0 .... 560 B. 741 M. 874 M. 909 M. 912 N-C. 10.0 .... 560 741 874 910 80.0 455 N-C. 637 N- C. 724 N-C. 716 N-C. 489 E. 640 M. 722 M. 722 M. 80.0 455 498 638 723 720 100.0 446.5 N-C. 489.5 E. 48 Conductivity of Aqueous Solutions. — Part II. An examination of table 9 shows that the results obtained independently by the various experimenters in this laboratory with different sets of ap- paratus and different solutions agree in almost all cases within 0.2 to 0.3 per cent, except at the temperature of 306°, but that at this temperature there are several deviations of nearly 1 per cent. Except at this highest temperature the agreement is entirely satisfactory and indicates a cor- responding precision of the results ; and even at 306° it is probable that the final values adopted are not in error by more than 0.3 per cent, since the later measurements made in larger number and after more experience by ]\Ir. A. C. Melcher are probably more accurate than our own. 17. CHANGE OF EQUIVALENT CONDUCTANCE WITH THE CONCENTRATION. It is a well-known fact that the mass-action law does not express even approximately the change with the concentration of the ionization of salts and strong acids and bases, when this, in accordance with the familiar h)-pothesis of the ionic theory, is calculated from the conductance ratio A/Aq. This has led to the proposal of numerous other functions,* which have for their purpose an accurate representation of the experimental values of the equivalent conductance and the ionization values deduced therefrom. The extended discussion of the matter has not yet led to any conclusion, so far as the theoretical explanation of the phenomenon is concerned. There have, however, been discovered some simple empirical formulas which at ordinary temperatures express the observed results satisfactorily. Those which contain only a single arbitrary constantf have the follow- ing form when expressed in terms of the equivalent conductance (A) at any concentration C and the limiting conductance A^ at zero concentra- tion: •^" ~ '^ = K (Kohlrausch) ~fy^ = K (Barmwater) :^y=^ = K (van't Hoff ) \~a ^ ^ (Rudolphi) *Compare Kohlrausch, Wied. Ann., 26, 200 (1885) ; 50, 394 (1893) ; MacGregory, ibid, 51, 133 (1894) ; Barmwater, Z. phys. Chem., 28, 134, 428 (1899) ; Sabat, ibid., 41, 224 (1902); Muller, Compt. rend., 128, 505 (1899); Rudolphi, Z. phys. Chem., 17, 885 (1895) ; van't Hoff, ibid., 18, 300 (1895) ; Kohlrausch, ibid., 18, 663 (1895) ; Storch, ibid., 19, 13 (1896) ; Bancroft, ibid., 31, 188 (1899) ; Jahn, ibid., 37, 499 (1901) ; 41, 265, 288 (1902) ; Nernst, ibid., 38, 493 (1901) ; Bousfield, ibid., 53, 263 (1905) ; Kohlrausch and Maltby, Wissensch. Abhandl. phys.-techn. Reichsanstalt, 3, 219 (1900) ; Kohlrausch, Sitzungsber., preus. Akad., 44, 1002 (1900) ; Kohlrausch and Steinwehr, ibid., 1902, 581; Kohlrausch and Griineisen, ibid., 1904, 1215. tKohlrausch and Maltby (loc. cit., p. 219) and Kohlrausch and Griineisen (loc. cit.) find that the formula K — A„ = KCi applies closely to the results with uni-univalent, uni-bivalent, and bi-bivalent salts between 0.002 and 0.0001 normal, but that large deviations exist at higher concentrations, even at 0.01 normal. Section 17. — Effect of Concentration on Conductance. 49 It seemed therefore to be of especial interest to test the applicabiHty of these formulas at the widely different temperatures emplo)-ed in our experiments. When such a test is made by direct substitution the results are in a high degree dependent on the values of A^ employed, since in dilute solutions A,-, — A is a relatively small quantity; yet in several instances authors have not given sufficient consideration to this matter. The most satisfactory method of procedure seems to us to be the elimina- tion of the A(, value, which can not be determined with sufficient accuracy by extrapolation, bj' writing the functions in the following form : A = A„ — i^ C* (Kohlrausch) A = A^ — K A^ C* (Barmwater) A = Ao — if A3 O (van't Hoff ) A = A,, — K A^ C* (Rudolphi) and then plotting the values of A along one coordinate axis and those of the C-A function constituting the last term (that is. O, A* C*, etc.) along the other axis. If the function in question holds, the points will of course lie upon a straight line; and by comparing, in the case of the different functions, the deviations of the separate points from the best representa- tive straight line that can be drawn, a measure of the degree of applica- bility of each function is obtained. All our complete series of measure- ments and those of Kohlrausch and Maltby on the same salts at 18° have been studied in this way, a plot on a very large scale being employed. The straight lines were drawn in every case so as to represent most closely the points for the concentrations 100 or 80, 10, and 2 milli- normal, and the average of the percentage deviations of the observed A values at these three points taken. These averages for the two functions are given in the following table under C* and (Ca)*, respectively. Table 10. — Mean percentage deviations of the observed values of the equivalent conductance from those calculated by the cube-root functions. Sodium chloride. Potassium chloride. Temper- ature. ci (CA)i d (c.vu 18 0.1 0.15 0.05 0.05 100 0.05 0.1 0.1 0.05 140 0.05 0.1 156 0.1 0.15 0.15 0.05 218 0.15 0.3 0.2 0.3 281 0.45 0.35 0.05 0.1 306 0.4 0.4 0.45 0.3 It will be seen that the deviations from either function are insignificant up to 156°, but that they become considerable at the higher temperatures. It may be of interest to state also the percentage deviations of our straight line corresponding to the Kohlrausch function from the points repre- ^0 Conductivity of Aqueous Solutions. — Part II. senting the conductances of sodium and potassium chloride at 18° in the still more dilute solutions investigated by Kohlrausch and Maltby. These deviations are — 0.53 and — 0.42 per cent, respectively, in case of the 0.0001 normal solutions, and — 0.36 and — 0.25 per cent, respectively, in that of the 0.0002 normal solutions. Thus this function does not satis- factorily represent the results at very low concentrations, and seems there- fore unsuitable for obtaining the value (Ao) at zero concentration. Aloreover, this function, as well as that of Barmwater, does not seem to admit of any theoretical interpretations, since it does not even correspond to any functional relation between the concentrations of the ions and un-ionized molecules. The fact that the van't Hoff equation does not satisfactorily express the results with many salts* at 18° and 25° has led to the suggestion by Storch and later by Bancroft that a general expression of the form A„ — A = i(:A"C«-^ be employed, the exponent n being varied as required by the results with different salts. An equation of this general form has the advantage that it does express the concentrations of the ions and un-ionized substance as a function of each other. This becomes obvious when the function is written in the form C(Ao — A) = K(AC)", which is equivalent to C(l— y) = const. X (Cy)", where y is the conductance ratio (A/Ao) or the fraction of the salt ionized. That such an expres- sion with three arbitrary constants (assuming that Ao is to be deter- mined with the help of the function itself) can be made to express the conductivity fairly accurately through a considerable range of concen- tration is obvious. It is nevertheless of interest to determine what values of the exponent n must be used for different salts and for the same salts at different temperatures. For this purpose it is best to write the equation in the form A A„ and to plot the values of — against those of (CA)"-^ the exponent being given successively different values (in the neighborhood of 0.5) until the points fall as nearly as possible on a straight line. We have done this with the final values for sodium and potassium chloride given in table 9. The values of the exponent n so found at various temperatures are given in table 11. It was usually possible to determine them within 0.02. It will be seen that the exponent varies but little with the temperature, and that the results do not correspond at all closely at any temperature with the mass-action law, which requires the exponent 2. *See Kohlrausch and Maltby, loc. cit., p. 222. Section ly. — Effect of Concentration on Conductance. 57 Table l\.~Values of the exponent n in the function C(A„ — A) =^(CA.)n Substance. 0°. 18°. 100°. 140°. 156°. 218°. 281°. 306°. KCl NaCl 1.50 1.42 1.43 1.40 1.48 1.48 1.40 1.50 1.48 1.50 1.50 1.47 1.48 1.46 This form of function seems to us to furnish the best means of deter- mining the value of A^, at any rate in cases where a series of accurate measurements at very small concentrations is not available; we have therefore employed this method generally throughout this series of inves- tigations. The values of Ao given in table 9 (except those at 18° which were derived by Kohlrausch and Maltby) were obtained in this way by graphic extrapolation upon the plots just referred to. It is interesting to compare the A, values to which this method leads with those derived by Kohlrausch and his co-workers at 18° by appli- cation of the function Ao — A = KC^ to his own conductivity-values at very small concentrations (0.1 to 2 milli-normal). We have made the necessary calculations for seven salts of two different types with the following results. The table also contains the results obtained by Kohl- rausch by applying the function A^ — A = ifC*A«' at concentrations between 0.1 and 100 milli-normal. KCl. NaCl. KNO3. AgNOa. Ea(N03)2 K2SO4. CaCla. A„byA„-A=A'(CA)"*. KhsK — A = KC^AK.. A„by A„-A = A'C' 130.6 130.1 1S9.9 109.8 109.0 108.9 136.3 136.5 126.4 115.7 115.8 115.8 117.0 117.7 117.0 134.7 133.5 133.5 119.0 117.5 116.7 The values of A^ obtained from the conductances at moderate con- centrations either by the Storch function or the Kohlrausch function Ao — A ^KC^AP are seen to be usually somewhat higher than those derived from the conductances at very low concentrations; but the differences are not as a rule very important, being less than 1 per cent, except in the last two cases. *Assuming n — l=0A2 for KCl and NaCl, 0.50 for KNO3, 0.52 for AgNOs, 0,55 for Ba(N03)2, 0.45 for K2SO4, and 0.40 for CaCli, which are the values which give a most nearly linear function between 3 and 50 milli-normal. With K2SO4, however, no value of the exponent gave a fully satisfactory expression of the conductance values. Incidentally it is of interest to note that the conductance value at 100 milli-normal was greater than that required by the assumed function by the following percentage amounts: 0.36 for KCl, 0.00 for NaCl, 0.06 for AgNOs, 0.00 for Ba(N0s)2, 0.4 for K2SO4, and 0.3 for CaClj. 52 Conductivity of Aqueous Solutions. — P(Wt II. 18. CHANGE OF THE EQUIVALENT CONDUCTANCE WITH THE TEMPERATURE. We shall in this section confine our considerations almost wholly to the effect of temperature on the conductance (A„) extrapolated for zero concentration; for at higher concentrations the equivalent conductance of the salt is the product of two factors — the degree of ionization of the salt and the equivalent conductance of its ions; and the first of these factors is best discussed separately, as will be done in section 19. Attention may first be called to the fact that the limiting conductances of the two salts approach equality as the temperature increases ; thus the ratio of Ao(Naci) to Ao(KCi) has the following values at the various temper- atures : 18° 0.84 100° 0.87 140° 0.88 156° 0.89 218° 0.92 281° 0.96 0.96 The percentage difference in the migration-velocities of the potassium ion and sodium ion, therefore, becomes less, the higher the temperature. In order to show more clearly the character of the relation between migration-velocity and temperature we have calculated the mean temper- ature-coefficients (AAo/Af) for the successive temperature-intervals, and these were found to be as follows : 0-18 18-50 18-100 50-100 100-156 156-218 218-281 281-306 KCl NaCl 2.70 3.20 3.46 3.09 3.63 3.77 3.44 3.23 3.31 2.86 3.33 4.60 4.40 It will be seen that up to about 156° the temperature-coefficient of the conductance values extrapolated for zero concentration increases steadily, and then, between 156° and 281°, decreases markedly in the case of potas- sium chloride and remains nearly constant in the case of sodium chloride, while above 281° a pronounced increase again takes place with both salts. It is also of interest to compare the fractional change in equivalent conductance with that in the viscosity of the water ; for the former is doubt- less more closely related to the latter than to any other simple physical property. The viscosity (t;) of water has been measured by several experimenters at temperatures below 100° and by de Haas at 124°, 142°, and 153°.* In the table on the next page are given in the same columns the ratio (Ao)t2: (Ao)ti for potassium chloride and i?ti:i?t2 for water for a number of consecutive pairs of temperature. The values of the viscosity -q *See Landolt-Bornstein-Meyerhoffer, Physigalisch-chemische Tabellen, p 76. de Haas' values are 0.00223 at 124°, 0.00193 at 142°, and 0.00181 at 153° Section ig. — Ionization Values. 53 used up to 100° are those of Thorpe and Rodger and for 138° and 156° the values were interpolated from the data of de Haas. (2=18 (l=0 (a=50 (i=18 fe=75 «l=50 fe=100 h= 75 fa=128 <1=100 fa=lS6 • July 25 .... II 3.31 10.4 37.9 48.0 .... .... July 27 1 II 2.25 11.4 27.1 29.0 .... 1905 Feb. 15 .... II 2.04 5.5 48.8 52.7 .... Feb. 16 Slean II II 2.04 7.3 51.7 56.7 .... .... .... 2.40 8.6 44.7 48.9 1 .... 36. VARIATION OF THE CONDUCTANCE-CAPACITY WITH THE TEMPERATURE. The following measurements and computations were made in order to determine what variation in the conductance-capacity of the bomb is caused by the change in the diameter and length of the electrode cup or of the small electrode and in the diameter of the bomb itself owing to the expansion upon heating. The apparatus used to determine the variation of the conductance when the electrode was placed within the quartz cup was an imitation of the bomb, consisting of an outer cylindrical brass vessel, a cup composed of a glass tube with a brass electrode permanently fixed at the bottom of the tube with rosin, and a piece of insulating material (the "red fiber'' of trade) separating the cup from the bottom of the vessel, and allowing the electrode rod to pass through it. Combinations of three such electrode cups of diameters 1.31, 1.50, and 1.59 cm. and of two brass vessels of diameters 4.22 and 4.54 cm. were investigated. Mercury was used to change the efifective height of the cup, the change being determined by Section 36. — Change in Conductance-capacity. 79 introducing weighed portions of mercury into the cup and measuring by a cathetometer the height of its surface above the electrode and below the top of the cup. The heights of the mercury in the cup were plotted against the weights of mercury, the points being found to lie on a straight line; and by means of these plots, the effective height of the cup in the succeeding experiments was derived from the weight of mercury intro- duced. The relative conductance at various lieights was then determined by measuring that of a 0.01 normal sodium chloride solution at 18° in the apparatus, which was made up of the three electrode cups in succession and one of the brass cylinders, successive portions of mercury being added. The effective heights of the cup were first plotted against the conduct- ances. The diameters of the three cups were then plotted against the conductances obtained for various definite heights from the first plot. From these plots, the ratio of the fractional change in conductance (Sl/l) to that in height {hh/K) for a given diameter or to that in diameter (Sd/d) for a given height could be found. The results so derived for a series of heights and diameters expressed in centimeters are given in table 8l/l 15. The columns headed i show the values of the ratio ^-^ and those Sh/h ^r /i headed 11, the values of the ratio . Table 15. — Change in conductance-capacity with the dimensions f the electrode cup. Height. Diameter. 1.30 1.40 1.50 1.60 I. II. I. II. I II. I. II. 1.0 0.70 1.92 0.72 1.80 0.72 ' 1.72 0.72 1.64 1.2 0.71 1.79 0.74 1.76 0.73 1.75 0.73 1 1.72 1.4 0.73 1.66 0.77 1.73 0.76 1.80 0.74 ■■ 1.71 1.6 0.75 1.54 0.79 1.70 0.79 1 1.82 0.75 i 1.80 1.8 0.80 1.47 0.80 1.60 0.80 i 1.92 0.76 ' 1.88 2.0 0.88 1.60 0.81 1.64 0.80 ! 1.87 0.78 2.04 2.2 0.95 1.75 0.88 1.67 0.82 1.91 0.81 : 2.00 The apparatus for detennining the variation of the conductance when no cup was used was made up as follows. The top of the main body of the bomb was covered with a brass disk. Through the center of this disk was inserted a hollow rod of vulcanite of the length and diameter of the quartz cylinder supporting the lower electrode in the bomb itself. Through this vulcanite tube a brass rod was inserted, which could be forced down successively so as to produce an electrode of varying length. The con- 8o Conductivity of Aqueous Solutions. — Part IV. ductance of a 0.01 normal sodium chloride solution between this electrode and the sides of the bomb was determined. Brass electrodes of three dif- ferent diameters (0.475, 0.72, and 0.95 cm.) were used. The lengths of the electrode were plotted against the conductances for the three diameters and the diameters of the electrode against the conduct- ances for the different lengths. From these plots, the ratio of the frac- tional change in conductance to that in length for a given diameter or to that in diameter for a given length can be computed. The values of the ratios so derived for a series of lengths and diameters are given in table Sl/l , 8l/l 16, those of -—jY in the columns headed i and those of jrr, in the columns headed ii. U/l U/d Table 16. — Change in conductance-capacity with the dimensions of the electrode. Length. Diameter. 0.5 0.7 0.9 \. n. 1. II. I. II. 0.5 1.0 1.5 2.0 2.5 3.0 0.65 0.3 0.2 0.15 0.1 0.7 0.65 0.55 0.5 0.55 0.55 0.6 0.3 0.2 0.1 0.1 0.95 0.8 0.7 0.7 0.7 0.7 6!55 0.3 0.2 0.1 0.1 1.05 0.95 0.9 0.9 0.9 0.9 The variation in the conductance due to a change in diameter of the large cylindrical vessel was determined in the presence and absence of a cup by measuring the conductance of a 0.01 normal sodium chloride solu- tion between the small electrode and brass cylinders (diameters of 3.66, 3.35, 3.39, and 1.75 cm.) placed successively inside of the outer cylinder. The effect of the increase of diameter of the bomb which would occur even up to 400° on the conductance-capacity was less than 0.1 per cent. The linear expansion coefficients (dl/lodt) used in computing the change in conductance-capacity of the bombs were as follows : dili^d, Remarks. Platinum-iridium electrodes Quartz (length) Quartz (diameter) Steel 8.9 X 10-° 9 X 10-° 16 X 10-° 13 X 10-° Fizeau, Compt.Rend., 68,1125(1869). Randall, Phys. Rev., 20, 10 (1905). Benoit, Trav. et mem. Bur. Int.Poids et Mes., 6, 190 (1888). Le Chate- lier,Compt.Rend., 108,1046(1889) . See section 21, Part III. Section 3/. — Speciftc-volume Data. Table 17. — Specitic volume — Data and final values. Si Date. Salt. Milli- cquiva- lents per liter at 4°. Temper- ature, Weight of solution. Volume uncor- rected. Specific volume at 1°. Specific volume at 4°. Specific volume ratio. 1904 Feb. 25.. Feb. 25.. Mar. 24. . Apr. 13.. Apr. 28.. Mar. 29. . Mar. 29. . Mar 30.. Mean . . AgNO, AgNO, K,SO^ Ba(N03), MgSO, NaCl i L 25 100 100 100 100 10 10 10 155.6 155.8 156.6 155.5 156.2 218.2 218.3 218.4 108.61 111.36 110.19 110.35 110.09 100.83 100.77 100.93 118.31 119.94 119.64 119.38 119.52 118.80 118.77 118.98 1.0917 1.0794 1.0881 1.0849 1.0880 1.1837 1.1841 1.1843 0.9963 0.9861 0.9933 0.9899 0.9939 0.9996 156°/4° 1.0963 1.0948 1.0948 1.0957 1.0944 218°;4° 1.1837 1.1839 1.1840 j 1.1839 Mar. 25.. Mar. 28.. Feb. 18.. Feb. 23.. Feb. 24.. Mean . . KCl KCl ■AgNO,- 10 100 25 25 25 218.4 218.0 218.6 217.6 216.8 100.80 101.57 101.31 101.06 101.21 118.79 1.1839 118.96 : 1.1766 119.14 1.1814 118.65 1.1791 118.73 i 1.1785 1 0.9995 0.9954 0.9963 1.1838 1.1830 1.1846 1.1846 1.1850 1.1847 Feb. 4... Feb. 5... Apr. 16.. Mean . . AgN03-! 100 100 100 218.1 218.1 217.3 101.96 102.65 102.48 118.26 119.08 118.70 1.1653 1.1654 1.1636 0.9861 t ( n 1.1815 1.1816 1.1814 1.1815 Mar. 18. . Mar. 21.. Mean . . j K,S04 j 50 50 217.7 218.5 100.96 101.24 118.48 118.98 1.1790 1.1807 0.9967 1.1835 1.1836 1.1836 Mar. 22.. Mar. 23.. Mean . . j K,SO, j 100 100 218.4 218.1 101.28 101.22 118.27 118.13 1.1732 1.1724 0.9933 1.1802 1.1801 1.1803 1.1821 1.1813 Apr. 121 Apr, 13 J Mean . . Ba(N03).j 100 100 217.3 217.5 101.92 102.31 118.59 119.04 1.1689 1.1689 0.9899 j 1.1820 Apr. 28.. May 2... 1905 Oct. 1... Oct 2... Nov. 20.. Sept 29.'. Sept 29. . Mean . . MgSO^ MgSO, NaCl KOI AgNOs 1 KoSO, j 100 200 100 100 50 50 50 218.2 218.4 305.6 305.7 306.0 305.5 305.5 103.89 102.68 85.61 85.57 85.38 84.97 85.11 120.27 119.26 119.97 119.85 119.62 119.62 119.93 1.1743 1.1671 1.4153 1.4145 1.4149 1.4317 1.4237 0.9939 0.9880 0.9958 0.9954 0.9929 0.9967 1.1812 1.1808 306°;4° 1.4328 1.4322 1.4352 1.4284 1 1.4394 . 1.4389 ; Sept 30.. Sept 30.. Mean . . K,SO, 1 100 100 305.7 305.4 85.92 85.67 120.25 119.77 1.4130 1.4122 0.9933 « 1.4237 ; 1.4243 1.4240 Oct 2.\ Oct 12; Mean . Ba(N03),! 50 50 305.2 305.5 85.28 85.04 119.. 59 119.31 1.4165 1.4174 0.99.50 1.4271 1.4265 1.4268 ' 82 Conductivity of Aqueous Solutions. — Part IV. 37. THE SPECIFIC-VOLUME DATA. The results of the specific-volume measurements are given in table 17. The first four columns need no further explanation. The fifth column gives the number of grams of solution which were weighed into the dry bomb at the start. The sixth column gives the volume expressed in cubic centimeters which, at the temperature of 100° (at which the volume of the bomb was determined) corresponds to the observed ratio of the conductances at the upper and lower electrodes. This volume was obtained by interpolation from a plot made as described in section 8, Part II. The actual volume occupied by the solution at the higher temperature is greater than this by an amount equal to the expansion of the bomb upon heating from 100° to that temperature. The temperature-coefficient of volume expansion of the steel shell of the bomb is assumed to be 0.000038 per degree, upon the basis of determinations made by R. B. Sosman in this laboratory. The seventh column gives the specific volume of the solu- tion at the temperature of observation. It is obtained by dividing the values of the preceding column, after correcting them for the expansion of the bomb as just described, by the weight of solution g^ven in the fifth column. The eighth column gives the values of the specific volumes at 4° of the various solutions used. The last column gives the ratio of the specific volume at the round temperatures 318°, 281°, and 306°, to that of the same solution at 4°. Thus, this ratio shows the volume occupied by that quantity of solution which at 4° has a volume of 1 c.cm. The values are obtained from those of the preceding column by reducing them to these temperatures by means of the temperature-coefficient obtained from our specific-volume values, and then dividing the results by the specific volumes of the solutions at 4°. 38. SUMMARY OF THE SPECIFIC-VOLUME VALUES. The final values of the ratio of the specific volume at various tempera- tures to that at 4° are summarized in table 18. For comparison the values obtained by Noyes and Coolidge (section 12, Part II) for a 2 milli-normal solution of sodium chloride, which are substantially identical with those of pure water, are given in the table within parentheses. For the 100 milli-normal solution of this substance they found 1.187 at 218° in fair agreement with our value and 1.423 at 306° in complete agreement with our value. A comparison of values for the different 50 milli-normal solu- tions shows that these all expand considerably less than water itself, the ratio being 1.425 - 1.429 instead of 1.437 at 306°. Up to 218° the expan- sions of even the 100 milli-normal solutions of all the different salts are substantially equal (ratio 1.180-1.182) ; but at 306° the ratios for silver nitrate and barium nitrate, the salts of the metals with high atomic weights, are somewhat smaller than those for the other three salts, being 1.426 instead of 1.429 at 50 milli-normal. Section jp. — The Conductivity Data. 8s Table IS.—Ratio of specific volume at various temperatures to that at 4°. Salt. Concentra- tion at 4°. Specific volume ratio. 156°. 218°. 306°. NaCI KCl AgNO„. . . K,SO,.. . . Ba(N03)=. MgSO^. . . 2 10 100 10 100 25 50 100 50 100 50 100 100 1.096 1.095 'i!695 1.096 1.094 (1.187) 1.184 1.184 1.182 1.185 1.182 1.184 1.180 1.182 1.181 (1.437) 1.423 1.423 1.435 1.42*9 1.434 1.427 39. THE CONDUCTIVITY DATA. Table 19 contains the conductivity data obtained in the separate experi- ments. The first column contains the date; the second, the cell-number which by reference to section 32 shows the modification of the conduc- tivity-vessel used ; the third, the concentration at -1° in milH-equivalents per liter, the international atomic v^^eights for 1905 being employed, and the fourth, the true temperature (^°) of the measurement upon the hydrogen- gas scale. The fifth gives the concentration at the temperature of the measurement obtained from that at 4° by dividing it by the appropriate specific volume ratio taken directly from table 18 or derived from the values there given by linear interpolation and by correcting it (at 281° and 306°) for the solvent in the vapor-space as described in section 34. The sixth column contains the actual conductance in reciprocal ohms of the solution in the bomb, which was obtained by correcting the observed conductance for the resistance of the lead-wires and for errors in the resistance coils and sHde wire. The seventh column gives the corresponding conductance-capacity of the vessel, determined as described in sections 35 and 36 ; when no number or quotation mark is inserted it is to be under- stood that the value used was the same as that given for the same temper- ature in the preceding experiment. The eighth column gives the equiva- lent conductance in reciprocal ohms, which was computed by subtracting from the actual conductance X 10' (given in the sixth column) that of the water (as given in section 35), multiplying the remainder by the con- ductance-capacity (given in the seventh column), and dividing by the concentration at t° (given in the fifth column). 84 Conductivity of Aqueous Solutions. — Part IV. Table 19. — The conductivity data. SODIUM CHLORIDE. Date. Cell Concentra- Tempera- Concentra- Conduct- Conductance Equivalent No. tion at 4°. ture, t°. tion at i°. ance X 106. capacity. conductance. 1905 Mar. 25. . . II 2.000 18.00 1.997 712.8 0.3974 105.71 305.3 1.397 4,631.5 0.2965 970.3 18.00 1.997 721.8 0.3974 106.22 Nov. 13... IV 2.006 18.00 2.004 174.3 1.3181 105.5 99.93 1.924 554.9 1.3163 349.1 18.00 2.004 174.4 1.2181 105.5 1904 Mar. 31... I 10.013 18.00 10.000 1,139.4 0.8960 103.02 318.3 8.433 6,533.2 ** 692.1 18.00 10.000 1,140.8 " 103.01 July 1... II 10.020 18.00 10.007 3,325.4 0.3070 101.96 217.6 8.446 18,973 0.3064 687.3 18.00 10.007 3,333.. 3 0.3070 103.13 1905 Mar. 15... II 10.027 18.00 10.014 3,433.9 0.3974 101.91 280.4 7.543 31,130 0.2966 838.6 306.0 7.000 30,818 0.2965 879.8 18.00 10.014 3,435.2 0.2974 101.89 Mar. 17... II 10.009 18.00 9.996 3,439.4 101.96 280.2 7.534 21,250 834.8 305.8 6.989 20,943 886.4 18.00 9.996 3.461.9 102.86 Mar. 21... II 10.021 18.00 10.009 3,432.9 101.93 279.5 7.554 21,332 831.5 306.0 3.994 20,900 884.0 18.00 10.009 3,473.0 103.07 Mar. 23... II 10.015 18.00 10.002 3,429.8 101.94 280.5 7.539 21,217 834.0 306.0 6.989 20,871 883.4 18.00 10.002 3,439.8 102.14 Mar. 29... II 9.974 18.00 9.961 3,419.6 103.02 376.5 7.571 21,119 835.5 305.6 6.971 30,844 884.5 18.00 9.961 3,433.0 103.07 April 25.. II 10.017 18.00 10.004 3,459.6 6! 2950 101.94 381.1 7.534 31,460 0.2943 837.4 305.5 7.003 31,145 0.3941 886.1 18.00 10.004 3,463.2 0.3950 101.98 1904 April 1 .. I 100.13 18.00 100.00 10,284 0.8960 92.14 318.1 84.35 55,365 " 588.2 18.00 100.00 10,290 t< 92.18 1905 Sept. 26.. III 100.13 18.00 100.00 8,045.7 1.1446 92.08 318.2 75.64 45,147 1.1381 679.0 305.6 70.60 43,105 1.1375 694.2 18.00 100.00 8,058.6 1.1446 92.22 Oct. 1 ... III 100.17 18.00 100.04 8,073.3 1.1411 92.07 218.3 75.63 45,371 1.1346 679.1 305.6 70.56 43,149 1.1340 693.3 18.00 100.04 8,091.3 1.1411 98.34 Nov. 28.. IV 100.02 18.00 99.88 7,540 1.2181 91.94 100.00 95.89 33,403 1.3162 296.8 140.0 92.59 30,817 1.2153 404.5 156.0 91.10 33,411 1.2148 445.5 18.00 99.88 7,546 1.2181 92.01 Section 59. — The Conductivity Data. 85 Table 19. — The conductivity data — Continued. POTASSIUM CHLORIDE. Dace. CtU Concentra- Tempera- Concentra- Conduct- [Conductance Equivalent No. tion at 4°. ture, t°. tion at i°- ance X 10«. capacity. conductance. 1904 Mar. 25 . . I 10.015 18.00 10.003 1,366.9 0.8960 122.38 218.4 8.433 7,048.2 " 748.0 18.00 10.003 1,371.8 '*( 133.68 1905 Mar. 13 . . II 10.021 18.00 10.008 4,122.3 0.2974 122.40 306.1 6.990 32,105 0.3965 935.6 Mar. 14. . . II 10.031 18.00 10.008 4,121.8 0.2974 122.40 380.6 7.510 22,550 0.2966 888.9 18.00 10.008 4,124.0 0.3974 133.41 AprU 24.. II 10.008 18.00 9.995 4,150.6 0.3950 122.45 281.3 7.512 23,750 0.3943 888.4 305.8 6.989 22,285 0.3941 935.2 18.00 9.995 4,154.7 0.3950 122.51 1904 Mar. 28 . . I 100.13 18.00 100.00 13,498 0.8960 111.98 218.0 84.36 60,049 ** 637.7 18.00 100.00 13,522 *' 112.18 1905 Sept. 27.. III 100.12 18.00 99.99 9,779.9 1.1446 111.95 Oct. 2 .. III 100.20 18.00 100.06 9,818.3 1.1411 111.97 281.4 75.61 48,338 1.1346 725.0 305.7 70.55 45,815 1.1340 736.1 18.00 100.06 9.840.5 1.1411 112.20 Oct. 27 .. III 100.04 18.00 99.91 9,947.2 1.1252 112.03 281.4 75.42 49,193 1.1187 729.9 18.00 99.91 9,978.0 1.1252 112.35 Nov. 18 . . IV 2.002 18.00 2.000 208.2 1.2181 136.4 25.00 1.997 240.7 1.2179 146.4 100.00 1.920 623.1 1.2162 393.3 140.0 1.854 818.4 1.2152 534.2 156.0 1.824 888.3 1.2148 589.1 18.00 2.000 208.5 126.2 Nov. 21 . . IV 9.996 18.00 9.982 1,003.6 122.4 25.00 9.967 1,158.6 141.5 50.00 9.879 1,747.6 1.2174 215.3 75.00 9.746 2,366.3 1.2168 295.4 100.00 9.583 3,978.8 377.7 128.0 9.355 3,633.4 1.3155 471.8 155.9 9.104 4,219.4 562.7 18.00 9.982 1,004.5 122.5 Nov. 20 . . IV 19.993 18.00 19.963 1,968.9 120.1 25.00 19.933 3,271.1 138.8 50.02 19.756 3,415.3 310.4 100.00 19.165 5,803.8 368.3 18.00 19.963 1,968.3 130.1 Nov. 25... IV 100.01 18.00 99.87 9,185 113.0 35.00 99.73 10,562 129.0 50.00 98.83 15,810 194.7 75.02 97.51 31,345 265.1 100.00 95.88 36,546 336.7 128.0 93.60 32,123 417.1 140.0 92.58 34,370 449.7 156.0 91.09 36,957 492.8 18.00 99.87 9,183 112.0 86 Conductivity of Aqueous Solutions. — Part IV. Table 19. — The conductivity data — Continued. SILVER NITRATE. j Date. Cell Concentra- Tempera- Concentra- Conduct- Conductance Equivalent No. tion at 4°. lure, t°. tion at t°. ance X 10«. capacity. conductance. 1904 Feb. 16... I 1.999 18.00 1.997 250.20 0.8974 112.03 99.67 1.917 752.45 '*" 350.7 155.4 1.822 1,083.7 ** 530.9 217.6 1.685 1,363.0 " 720.9 155.5 1.832 1,092.7 *' 534.5 99.69 1.917 759.36 *' 352.6 18.00 1.997 254.52 ** 113.35 Feb. 17... I 1.999 18.00 1.997 350.34 113.14 99.97 1.916 755.07 352.0 155.7 1.821 1,087.4 533.8 218.3 1.684 1,362.4 721.4 i 155.8 1.821 1,091.4 534.0 99.97 1.916 761.50 353.8 1 18.00 1.997 253.50 112.89 June 27... II 2.002 18.00 1.999 733.31 o!3076 112.35 1 99.88 1.919 2,199.9 0.3068 305.3 ^ 155.5 1.834 3,182.6 0.3066 532.3 217.8 1.687 4,039.8 0.3064 739.0 155.6 1.824 3,201.4 0.3066 534.6 99.88 1.919 3,221.8 0.3068 352.8 18.00 1.999 743.17 0.3070 113.18 1905 May 19... II 2.000 18.00 1.997 782.9 0.3884 112.63 280.3 1.503 4,719.9 0.3876 894.2 304.8 1.399 4,692.6 0.3875 953.9 18.00 1.997 817.3 0.2884 117.31 May 22 .. II 1.996 18.00 1.994 479.9 112.38 280.8 1.499 4,707.0 894.8 i ; 305.5 1.394 4,666.4 952.4 18.00 1.994 805.2 115.75 May 23... II 1.999 18.00 1.996 478.8 113.10 1 281.0 1.500 4,699.0 892.8 305.5 1.395 4,665.7 951.4 18.00 1.996 803.0 115.30 July 11.. II 2.004 18.00 2.002 774.83 oisois 112.32 305.7 1.398 4,662.9 0.3904 956.0 18.00 2.003 820.75 0.3913 118.20 April 14. . . I 13.481 18.00 13.47 1,497.5 0.8958 107.55 99.84 11.97 4,476.5 " 334.9 155.7 11.37 6,393.9 " 503.1 217.5 10.53 7,893.9 " 671.0 155.7 11.37 6,396.4 " 503.3 99.81 11.97 4,480.5 " 335.0 18.00 13.47 1,501.3 (4 107.72 1905 May 24... II 12.497 18.00 12.48 4,635.7 0.2884 107.09 281.2 9.38 26,096 0.2876 797.8 305.7 8.72 25,334 0.2875 832.1 18.00 12.48 4,663.8 0.2884 107.58 May 25... II 12.497 18.00 12.48 4,635.7 107.09 281.2 9.38 26,104 798.4 305.7 8.73 35,333 833.3 18.00 12.48 4,651.8 107.30 Section jp. — The Conductivity Data. 87 Table 19. — Tlie conductivity data — Continued. SILVER NITRATE. Cell No. Concentra- tion at 4°, 1904 Jan. 27. Jan. 28 Feb. 1.. Feb. 2. Feb. 18 2-1.98 Feb. 23.. Feb. 24.. Feb. 25.. April 15. 24.98 24.98 24.98 24.98 24.98 24.98 24.98 49.89 Tempera- ture, t°. 18.00 100.00 154.9 218.0 155.3 100.07 18.00 18.00 100.55 156.2 218.6 156.5 100.45 18.00 18.00 99.38 154.8 216.6 155.1 99.29 18.00 18.00 100.20 156.4 218.1 156.6 100.09 18.00 18.00 100.31 156.4 218.6 156.2 100.27 18.00 99.73 18.00 155.4 217.5 155.4 99.66 18.00 18.00 216.8 18.00 18.00 155.6 18.00 18.00 100.04 156.3 218.0 155.7 99.92 18.00 Concentra- tion at t°. 24.95 23.95 22.78 21.07 22.78 23.95 24.95 24.95 23.94 22.75 21.08 22.74 23.94 24.95 24.95 23.96 22.78 21.11 22.77 23.96 24.95 24.95 23.94 22.75 21.07 22.73 23.94 24.95 24.95 23.94 22.74 21.05 22.75 23.94 24.95 23.95 24.95 22.77 21.09 22.77 23.95 24.95 24.95 21.11 24.95 24.95 22.76 24.95 49.83 47.83 45.42 42.13 45.45 47.83 49.83 Conduct- ance X 10«. 2,898 8,609 12,200 14,978 12,221 8,637 2,928 2,893 8,629 12,247 15,005 12,283 8,673 2,917 2,893 8,553 12,168 14,932 12,189 8,566 2,905 2,895 8,611 12,250 14,981 12,331 8,666 2,923 2,892 8,617 12,254 14,970 12,245 8,641 2,906 8,581 3,890 12,331 14,964 12,336 8,613 2,908 2,893 14,936 2,918 2,892 12,197 2,900 5,574.1 16,456 23,342 28,113 23,237 16,465 5,584 Conductance capacity. 0.8974 0.8958 Equivalent conductance. 104.22 332.5 480.4 637.4 481.1 323.5 105.22 104.03 323.4 483.0 639.1 484.5 324.9 104.83 104.04 320.3 479.1 634.3 480.1 330.6 104.43 104.13 322.7 483.2 637.7 486.1 334.6 105.06 104.01 322.9 483.3 637.6 482.8 323.6 104.44 321.4 103.94 481.9 636.3 482.0 322.4 104.51 104.04 634.8 104.86 103.99 480.6 104.23 100.19 308.2 458.2 597.5 457.6 308.2 100.33 88 Conductivity of Aqueous Solutions. — Part IV. Table 19. — The conductivity data — Continued. SILVER NITRATE. | Date. Cell Concentra- Tempera- Concentra- Conduct- Conductance Equivalent No. tion at 4°. ture. 1°. tion at t°. ance X 10«. capacity. conductance. 1905 Nov. 16... Ill 49.94 18.00 49.87 4,450.8 1.1253 100.42 Nov. 17... III 18.00 49.87 4,453.6 1.1252 100.45 305.0 35.33 21,912 1.1187 695.0 380.3 37.80 33,179 1.1181 685.5 18.00 49.87 4,455.9 1.1252 100.48 Nov. 18... III 49.93 18.00 49.86 4,451.2 100.45 380.9 37.68 33,156 687.1 306.0 35.08 31,820 695.0 i 18.00 49.86 4,440.1 100.16 1904 1 Feb. 4. . . I 99.93 18.00 99.79 10,519 0.8974 94.59 100.31 95.77 30,915 (( 289.7 157.3 90.77 43,459 " 439.1 318.1 84.56 51,677 " 548.3 157.7 90.74 43,571 " 430.4 100.15 95.77 30,937 '* 289.7 18.00 99.79 10,543 " 94.80 Feb. 5... I 99.93 18.00 99.79 10,519 94.59 100.14 95.77 30,894 289.4 158.5 90.74 43,548 430.6 218.1 84.56 51,680 548.4 159.3 90.56 43,956 , 435.5 100.15 95.77 30,949 289.9 18.00 99.79 10,546 94.82 Feb. 35... I 99.92 18.00 99.79 10,518 94.58 155.8 91.02 43,236 426.3 18.00 99.79 10,537 94.65 Apr. 16 .. I 100.01 18.00 99.88 10,568 0.8958 94.77 99.55 95.91 30,908 " 388.7 155.4 91.14 43,323 425.7 317.5 84.73 51,840 " 547.9 155.4 91.14 43,358 " 436.1 99.67 95.89 30,999 " 389.5 18.00 99.88 10,583 " 94.90 1905 Nov. 21 . . III 99.85 18.00 99.73 8,433.8 1.1253 95.16 281.0 75.71 (41,911) 1.1187 (619.0) Nov. 23... III 306.0 70.55 (39,154) 1.1181 (620.1) POTASSIU M SULPHAT E. 1904 Mar. 14 . . I 3.001 18.00 1.998 278.39 0.8967 124.58 100.00 1.918 863.04 " 401.8 155.9 1.822 1,336.0 " 605.6 317.8 1.686 1,515.0 ** 801.4 155.8 1.833 1,240.7 '* 606.7 1 99.95 1.918 864.30 " 401.3 i 18.00 1.998 280.08 " 124.63 Mar. 15 . . I 1.999 18.00 1.996 377.73 124.41 99.88 1.916 858.74 400.3 155.7 1.831 1,236.8 606.2 217.6 1.685 1,515.0 801.3 155.6 1.821 1,237.0 605.2 99.81 1.916 859.27 399.4 18.00 1.996 278.50 124.07 Section jp. — The Conductivity Data. 89 Table 19 — The conductivity data — Continued. POTASSIUM SULPHATE-Continued. | Date. Cell Concentra- Tempera- Concentra- Conduct- Conductance Equivalent No. tion at 4°. ture, t°. tion at t°. ance X 108. capacity. conductance. 1905 Apr. 3 .. II 2.001 18.00 1.999 845.9 0.3974 125.42 277.2 1.516 4,737.3 0.3966 916.0 305.4 1.399 4,417.8 0.2965 933.7 18.00 1.999 849.9 0.2974 125.33 Apr. 4 . . II 2.001 18.00 1.999 843.6 134.94 377.3 1.515 4,748.8 920.5 305.4 1.398 4,426.3 929.1 18.00 1.999 847.7 125.00 Apr. 21 .. II 1.999 18.00 1.996 847.0 0.2950 124.76 280.5 1.502 4,780.5 0.3942 927.2 305.0 1.398 4,470.1 0.3941 930.5 18.00 1.996 853.2 0.3950 124.87 July 13 . . II 3.001 18.00 1.998 859.7 0.3913 125.03 281.1 1.503 4,858.6 0.2905 930.7 305.6 1.397 4,471.3 0.3904 919.4 18.00 1.998 895.6 0.2913 129.33 July 13... II 2.003 18.00 2.000 857.6 124.44 281.0 1.504 4,852.2 928.3 305.5 1.397 4,480.9 920.2 18.00 2.000 880.3 126.98 Mar. 16 . . I 12.505 18.00 12.490 1,588.5 0.8967 114.00 99.86 11.989 4,815.8 " 359.9 156.1 11.388 6,755.4 *' 531.5 217.8 10.547 7,880.8 " 669.2 156.3 11.387 6,761.8 " 531.9 99.88 11.989 4,819.5 " 360.0 18.00 13.490 1,591.6 *' 114.10 Mar. 17 . . I 12.508 18.00 13.490 1,590.5 114.13 100.38 11.985 4,844.3 362.2 156.7 11.381 6,782.9 534.0 218.4 10.543 7,895.8 671.0 156.7 11.381 6,788.9 534.3 100.30 11.985 4,845.2 362.1 18.00 13.490 1,593.6 114.17 1905 Apr. 6 . . II 12.503 18.00 13.487 4,799.6 0.2972 114.14 Apr. 10 .. II 12.493 18.00 13.477 4,800.3 0.2965 114.02 375.5 9.507 22,460 0.2954 696.3 304.9 8.753 19,463 0.2953 655.0 18.00 12.477 4,811.9 0.2962 114.03 Apr. 12 .. II 12.493 18.00 12.476 4,807.7 0.2962 114.07 375.6 9.503 22,528 0.3951 698.0 305.1 8.746 19,496 0.2950 656.0 380.6 9.394 22,293 0.2951 698.6 18.00 13.476 4,818.8 0.2959 114.08 Apr. 13 .. II 13.490 18.00 13.473 4,813.0 0.2959 114.10 280.7 9.392 33,281 0.2948 697.7 305.3 8.744 19,523 0.2947 656.4 18.00 12.473 4,817.5 0.2956 113.97 May 1 .. II 12.497 18.00 12.481 4,841.0 0.3951 114.37 381.2 9.388 22,314 0.3940 694.0 305.3 8.748 19,531 0.2939 654.4 18.00 12.481 4,845.5 0.2948 114.35 90 Conductivity of Aqueous Solutions. — Part IV. Table 19. — The conductivity data — Continued. POTASSIUM SULPHATE— Continued. j Date. Cell Concentra- Tempera- Concentra- Conduct- Conductance Equivalent No. tion at 4°. ture, t°. tion at t°. ance X 106. capacity. conductance. 1904 Mar. 18 . . I 50.05 18.00 49.99 5,688.3 0.8967 102.03 99.90 47.98 16,775 313.4 156.4 45.56 22,861 449.8 217.7 42.29 25,376 537.7 156.4 45.56 22,861 449.7 99.69 47.99 16,744 312.7 18.00 49.99 5,696.4 102.14 Mar. 21 . . I 50.00 18.00 49.94 5,684.4 102.05 100.36 47.92 16,827 314.8 157.4 45.47 22,968 452.9 218.5 42.24 25,389 539.0 157.7 45.45 23,009 453.8 100.34 47.92 16,829 314.8 18.00 49.94 5,688.9 102.11 1905 Sept. 29 . . III 50.122 18.00 50.06 4,462.1 1.1446 102.02 281.4 37.71 17,482 1.1373 526.9 305.5 35.15 14,940 1.1367 482.6 18.00 50.06 4,480.7 1.1438 102.33 Sept. 29 . . III 50.042 18.00 49.98 4,459.9 1.1438 102.06 281.3 37.65 17,444 1.1364 526.1 305.5 35.10 14,883 1.1358 481.3 18.00 49.98 4,475.9 1.1429 102.31 1904 Mar. 22 .. I 100.13 18.00 100.00 10,601 0.8967 95.05 100.24 95.97 30,878 288.5 156.3 91.16 41,466 407.8 218.4 84.79 45,076 477.3 156.2 91.17 41,450 407.6 100.09 95.97 30,844 288.1 18.00 100.00 10,601 95.04 Mar. 23 . . I 100.16 18.00 100.03 10,605 95.06 99.89 96.01 30,844 288.0 156.0 91.21 41,447 407.4 218.2 84.84 45,151 477.7 156.0 91.21 41,456 407.5 100.02 96.01 30,862 288.2 18.00 100.03 10,605 95.05 1905 Sept. 30 . . III 100.03 18.00 99.90 8,301.5 1.1429 94.97 281.3 75.48 30,237 1.1355 454.7 305.7 70.39 25,513 1.1349 411.1 18.00 99.90 8,313.3 1.1420 95.01 Sept. 30 . . III 100.07 18.00 99.94 8,302.2 1.1420 94.86 281.3 75.53 30,215 1.1346 453.7 305.4 70.52 25,561 1.1340 410.8 18.00 99.94 8,311.9 1.1411 94.88 Section jp. — The Conductivity Data. 91 Table 19. — The conductivity data — Continued. BARIUM NITRATE. I Date. Cell Concentra- Tempera- Concentra- Conduct- Conductance Equivalent No. tion at 4°. ture, t°. tion at t°- ance X 10». capacity. conductance. 1904 Apr. 7 . . I 1.999 18.00 1.996 244.93 0.8960 109.52 99.89 1.916 756.83 " 353.1 155.7 1.821 1,102.2 " 539.1 217.7 1.685 1,363.4 " 719.9 155.7 1.831 1,100.3 " 537.3 99.87 1.916 758.02 " 350.7 18.00 1.996 245.43 " 109.05 Apr. 8 . . I 1.999 18.00 1.996 344.93 109.55 100.14 1.916 758.79 353.3 156.4 1.820 1,101.7 539.4 218.2 1.684 1,371.3 724.7 156.4 1.830 1,103.3 539.4 100.07 1.916 759.83 352.4 18.00 1.996 345.83 109.26 1905 May 2 .. II 1.997 18.00 1.993 747.9 0.3947 110.08 281.3 1.496 4,450.0 0.3940 864.3 305.7 1.391 4,210.3 0.2939 877.0 18.00 1.993 752.7 0.2947 110.51 May 3 .. II 2.003 18.00 2.000 748.7 109.83 280.9 1.505 4,471.3 863.7 305.3 1.398 4,345.2 880.2 18.00 2.000 751.7 110.00 1904 Apr. 11 .. I 12.512 18.00 13.50 1,388.7 0.8960 99.48 99.64 13.01 4,239.8 " 316.3 155.6 11.43 6,048.1 " 475.0 217.4 10.56 7,244.3 " 613.8 155.7 11.41 6,051.4 " 474.9 99.64 12.01 4,244.9 " 316.4 18.00 12.50 1,390.2 " 99.47 1905 May 4 . . II 12.512 18.00 12.50 4,223.7 0.2937 99.48 May 5 . . II 12.508 18.00 12.49 4,235.0 0.2937 99.51 281.2 9.428 21,474 0.3919 665.6 305.5 8.779 19,060 0.3918 634.0 18.00 12.49 4,283.5 0.2927 100.23 May 8 .. II 12.496 18.00 12.49 4,347.6 0.2927 99.48 281.0 9.433 31,532 0.2909 664.8 305.1 8.790 19,133 0.2908 633.1 18.00 12.49 4,275.3 0.2917 99.73 1904 Apr. 12 .. I 50.05 18.00 49.98 4,853.4 0.8960 86.97 99.60 47.98 14,714 " 274.6 155.4 45.60 20,540 *' 403.3 217.3 43.38 23,730 " 502.3 155.3 45.60 30,533 '* 403.1 99.49 47.98 14,708 " 274.5 18.00 49.98 4,855.5 ** 87.03 Oct. 2 .. III 50.09 18.00 50.03 3,813.6 1.1411 86.95 281.2 37.77 16,908 1.1333 507.0 305.3 35.25 14,445 1.1337 463.8 Oct. 3 .. III 50.16 18.00 50.09 3,831.3 1.1398 86.93 Oct. 3 .. III 18.00 50.09 3,838.7 1.1385 87.00 92 Conductivity of Aqueous Solutions. — Part IV. Table 19. — The conductivity data — Continued. BARIUM NITRATE— Continued. j Date. Cell Concentra- Tempera- Concentra- Conduct- Conductance Equivalent No. tion at 4°. ture, t°. tion at t°. ance X 108. capacity. conductance. 1904 Oct 4 .. Ill 50.17 18.00 50.11 3,827.7 1.1372 86.85 Oct. 5 .. III 18.00 50.11 3,836.0 1.1359 86.94 280.8 37.86 17,191 1.1284 512.0 Oct. 12 .. III 50.19 18.00 50.12 3,845.9 1.1349 87.08 281.2 37.86 17,086 1.1272 508.6 305.5 35.29 14,597 1.1266 465.5 18.00 50.12 3,817.9 1.1337 86.29 Oct. 22 .. III 50.09 18.00 50.02 3,860.1 1.1274 86.97 305.5 35.22 14,703 1.1190 466.7 18.00 50.02 3,885.6 1.1261 87.41 Oct 20 .. III 78.72 18.00 78.62 5,696.4 1.1320 82.03 281.0 59.53 24,606 1.1247 465.6 305.1 55.60 21,025 1.1241 424.7 18.00 78.62 5,670.2 1.1312 81.56 Oct. 25 .. III 78.73 18.00 78.63 5,726.4 1.1261 82.02 281.2 59.51 24,742 1.1187 464.8 305.7 55.52 21,120 1.1181 425.2 18.00 78.63 5,705.9 1.1252 81.63 Apr. 12 .. I 100.07 18.00 99.95 8,830.1 0.8960 79.14 99.50 95.97 26,789 " 250.1 155.3 91.22 37,027 •* 363.6 217.3 84.83 42,075 " 444.7 18.00 99.95 8,832.4 *' 79.14 Apr. 13 .. I 100.00 18.00 99.87 8,819.1 79.11 99.80 95.87 26,850 250.9 155.5 91.07 37,079 364.5 217.5 84.68 42,012 444.8 155.5 91.07 37,179 364.5 99.77 95.88 26,846 250.8 18.00 99.87 8,821.4 79.11 1905 Oct 14 .. III 100.34 18.00 100.21 6,995.4 1.1337 79.14 281.3 75.97 29,526 1.1263 437.3 18.00 100.21 6,693.0 1.1328 75.60 Oct 17 .. III 100.40 18.00 100.28 7,004.0 1.1328 79.12 280.9 76.12 29,763 1.1255 439.8 18.00 100.28 7,019.0 1.1320 79.21 MAGNESI UM SULPHA- PE. 1904 June 28 . . II 1.982 18.00 1.979 611.07 0.3070 94.43 100.07 1.900 1,894.2 0.3068 304.4 155.7 1.805 2,280.7 0.3066 384.7 217.7 1.670 1,537.5 0.3064 277.6 155.9 1.805 2,290.4 0.3066 385.6 100.05 1.900 1,907.3 0.3068 305.7 18.00 1.979 614.67 0.3070 94.55 June 28 . . II 2.168 18.00 2.105 661.16 93.41 100.12 2.078 2,045.2 300.5 155.9 1.975 2,440.7 376.4 217.8 1.827 1,628.8 269.1 155.9 1.975 2,457.6 378.3 100.12 2.078 2,056.6 301.4 18.00 2.165 665.82 93.68 Section jp. — The Conductivity Data. Table 19. — The conductivity data — Continued. 93 MAGNESIUM SULPHATE— Continued. Cell No. Concentra- tion at 4°- 1904 May 6 Apr. 25 . . Apr. 26 . . Apr. 28 . . Apr. 28 . . Apr. 27 .. May 2 . . May 3 . . 12.529 26.16 52.83 99.93 99.93 106.83 195.96 350.9 Tempera- ture, i^. 18.00 100.14 156.7 219.3 156.7 100.11 18.00 18.00 99.55 155.7 217.8 155.6 99.49 18.00 18.00 99.70 155.8 218.0 155.8 99.84 18.00 18.00 100.07 156.5 218.6 18.00 18.00 156.4 18.00 18.00 100.05 156.5 218.6 156.5 100.03 18.00 18.00 100.09 156.7 218.8 156.3 100.11 18.00 18.00 100.31 156.5 218.8 156.6 18.00 Concentra- tion at t°. 12.51 12.01 11.41 10.55 11.41 12.01 12.51 26.13 25.09 23.84 22.09 23.84 25.09 26.13 52.76 50.65 48.13 44.62 48.13 50.65 52.76 99.81 95.79 90.98 84.62 99.81 99.81 90.99 99.81 106.69 102.40 97.26 90.42 97.26 102.40 106.69 195.71 187.83 178.36 166.49 178.44 187.82 195.71 350.4 336.2 319.4 319.4 350.4 Conduct- ance X 106. Conductance capacity. 1,032.6 2,877.8 2,951.7 1,629.3 2,953.4 2,881.0 1,035.3 1,880.9 5,026.7 4,961.8 2,678.7 4,964.7 5,026.9 1,882.9 3,324.2 8,581.5 8,186.0 4,342.7 8,190.7 8,590.4 3,332.8 5,552.4 14,017 13,088 7,015.0 5,568.5 5,552.4 13,109 5,555.0 5,851.1 14,739 13,754 7,340.5 13,766 14,766 5,869.2 9,467.9 23,561 21,896 11,384 21,955 23,619 9,485.9 15,044 37,372 35,115 35,115 15.075 0.8954 Equivalent conductance. 73.83 214.4 231.4 137.7 231.4 214.4 73.91 64.41 179.2 186.2 108.3 186.2 179.3 64.44 56.40 151.7 152.2 87.0 152.3 151.8 56.52 49.81 131.0 128.8 74.1 49.92 49.81 129.0 49.82 49.10 128.9 126.6 72.6 126.7 129.1 49.23 43.31 112.3 109.9 61.2 110.3 112.5 43.40 38.44 99.53 98.46 98.46 38.51 94 Conductivity of Aqueous Solutions. — Part IV. In regard to these experiments a few remarks of a special character may be added. In the case of silver nitrate it was observed, when the bomb was rinsed with absolute alcohol and ether and the adhering portion of the latter solvent allowed to evaporate, that there was, even at 218°, a rapid progressive decrease in the conductance of the solution and that this was due to an extensive reduction of the salt. In fact, in two experi- ments, one at 218° and one at 306°, it was found upon cooling and open- ing the bomb that it was entirely coated with a crystalline deposit of metal- lic silver, and that the solution contained no silver and no acid whatever, giving no precipitate with hydrochloric acid and no color change with lit- mus. Since the minute quantity of organic matter present could not pos- sibly cause this reduction, it is evident that the decomposition when once started goes on spontaneously, the reaction being apparently catalyzed by the metallic silver. This remarkable phenomenon was not observed when the bomb was rinsed with pure water and quickly dried at 100°, or when rinsed with the solution, except in the last experiments at 281° and 306° made with the strongest (100 milli-normal) solution; in these cases a slow decrease in conductance occurred, and the conductivity-values given are therefore less reliable than usual ; yet since they have been corrected upon the basis of measurements of the rate of change they are probably not in error by more than 1 per cent. In the case of the 100 milli-normal barium nitrate solution at 306° a steady decrease in conductance was also observed, but, since upon return- ing to 18° the conductance was found to be the same as before the heating, the observed change was doubtless due to the gradual separation of the salt itself or of a basic derivative of it from the solution. We did not therefore obtain reliable measurements at this concentration at 306°, but in place of them we investigated at that temperature a somewhat more dilute solution (80 milli-normal) in which the change, though noticeable, was so slow as to introduce no important error. In the experiments with magnesium sulphate a similar decrease in conductance was observed with the 350 milli-normal solution at 218° and even with an 80 milli-normal solution at 306°. In the former case a white crystalline deposit was found in the bomb upon cooling and opening it without shaking, and the solution was found by titration to contain con- siderable acid. On account of the large hydrolysis and the separation of a solid phase, even in fairly dilute solution, no attempt was made to carry the measurements above 218°. Section 40. — Summary of Equivalent Conductances. 95 40. SUMMARY OF THE EQUIVALENT-CONDUCTANCE VALUES. The separate conductance values given in table 19 were all corrected so as to correspond to the uniform temperatures of 18°, 100°, 156°, 218°, 381°, and 306° by means of temperature-coefficients obtained by plotting those values. The so-corrected equivalent conductances are summarized in table 20. The concentration is expressed in milli-equivalents per liter at 4°. In the columns headed "Initial" are given the equivalent conductances obtained from the measurement at the temperature in question before going to the higher temperatures ; while in the columns headed " Final" are given the equivalent conductances obtained after returning to the tempera- ture in question from the higher ones. From a comparison of the separate initial values at any temperature and concentration the degree of agree- ment of determinations made at different times, and often v^fith differ- ent solutions, will be seen. A comparison of the initial and final values in the separate experiments shows the contamination that resulted from the heating. Table 20. — Equivalent conductance at round temperatures. SODIUM CHLORIDE. Date. Concentra- tion at 4°. IS 100°. 218°. 281° 306°. Initial. Final. 1905 Mar. 25 .. 2.000 105.71 106.22 972 Nov. 13 .. 2.006 105.5 105.5 349.3 1904 Mar. 31 .. 10.013 103.03 102.01 691.3 July 1 .. Meau . . 1905 10.020 101.96 102.13 688.4 10.017 101.99 103.07 689.9 Mar. 15 .. 10.027 101.91 101.89 830.0 879.8 Mar. 17 .. 10.009 101.96 102.86 836.7 886.8 Mar. 21 .. 10.021 101.93 103.07 835.1 884.0 Mar. 23 .. 10.015 101.94 103.14 835.2 883.4 Mar. 29 .. 9.974 103.03 103.07 836.3 885.4 Apr. 23 .. Mean . . 1904 10.017 101.94 101.98 837.3 887.2 884.5 10.010 101.95 103.33 835.1 Apr. 1 .. 100.13 92.14 92.18 588.0 1905 Sept. 26 .. 100.13 92.08 92.22 678.7 694.4 Oct. 1 .. Mean . . 100.17 92.08 92.34 678.7 693.5 100.15 93.08 92.28 678.7 694.0 156° Nov. 28 .. 100.02 91.94 93.01 296.8 445.5 p6 Conductivity of Aqueous Solutions. — Part IV. Table 20. — Equivalent conductance at round temperatures — Continued. POTASSIUM CHLORIDE. 18°. Date. Concentra- tion at 4°. 218°. 281°. . Initial. Final. 1904 Mar. 25. . 10.015 122.38 122.68 746.8 1905 Mar. 13.. 10.021 122.40 935.4 Mar. 14.. 10.021 122.40 122.41 889.8 Apr. 24.. 10.008 122.45 122.51 887.6 935.6 Mean . 10.016 122.42 122.46 888.7 935.5 1904 Mar. 28.. 100.13 111.98 112.18 637.7 1905 Sept 27. . 100.13 111.97 Oct. 2. . 100.20 111.97 112.20 724.5 736.2 Oct. 9.. 100.17 112.03 Oct. 27.. 100.04 112.03 112.35 729.4 Mean . 100.13 112.00 112.27 727.0 736.2 Concentra- tion at 4°. 18°. 25°. 50°. 75°. 100°. 128°. 1905 Nov. 18.. Nov. 21.. Nov. 20. . Nov. 25.. 2.002 9.996 19.992 100.01 126.4 122.4 120.1 112.0 126.2 122.5 120.1 112.0 146.4 141.5 138.8 129.0 215.3 210.4 194.7 295.4 265.1 393.3 377.7 368.3 336.7 471.8 417.1 534.2 449.7 589.1 563.0 492.8 Section 40. — Summary of Equivalent Conductances. p/ Table 30. — Equivalent conductance at round temperatures — Continued. SILVER NITRATE. Date. Concen- tration at 4°. 18°. -00°. .56°. 218°. 281°. 306°. Initial. Final. Initial Final. Initial Final. 1904 Feb. 16 Feb. 17 June 27 Mean 1905 May 19 May 22 May 23 July 11 Mean 1904 April 14 1905 May 24 May 25 Mean 1904 Jan. 27 Jan. 38 Feb. 1 Feb. 2 Feb. 18 Feb. 23 Feb. 34 Feb. 25 Mean 1904 Apr. 15 1905 Nov. 16 Nov. 17 Nov. 18 Mean 1904 Feb. 4 Feb. 5 Feb. 25 April 16 Mean Nov. 21 Nov. 23 1.999 1.999 2.002 112.03 113.14 112.25 113.35 113.89 113.18 351.7 352.1 350.7 353.5 353.9 353.3 533.0 533.9 534.0 536.3 7?,9, . n 534.7 720.6 536.0739.6 2.000 112.14 113.14 351.5 353.6 533.61535.7 724.1 2.003 1.999 2.002 2.004 112.62 112.38 113.10 112.33 117.31 115.75 115.30 118.20 896.1 895.3 893.8 957.0 953.7 952.7 956.8 2.002 112.29 116.64 894.7 955.1 12.481 12.497 12.497 107.55 107.09 107.09 107.72 107.58 107.30 335.3 335.5 504.0 504.1 672.2 797.6 798.3 831.9 832.1 12.497 107.09 107.44 797.9 833.0 24.98 24.98 24.98 24.98 24.98 34.98 24.98 24.98 104.32 104.03 104.04 104.13 104.01 103.94 104.04 103.99 105.22 104.83 104.43 105.06 104.44 104.51 104.86 104.23 323.5 321.8 322.1 322.2 322.0 322.2 333.3 323.6 322.7 324.3 322.8 323.4 483.4 482.5 482.3 482.1 482.2 483.5 482.8 637.4 483.0 638.0 482.5 637.0 484.5 482.3 483.6 637.5 636.5 637.3 636.8 481.7 24.98 104.05 104.70 322.1 323.3 482.5 483.1 637.3 49.89 49.94 49.94 49.93 100.19 100.42 100.45 100.45 100.33 308.1 308.4 457.4 4.18 . 4 597.5 100.48 100.16 685.5 687.1 694.3 695.0 49.94 100.44 686.3 694.8 99.92 99.92 99.93 100.01 94.59 94.59 94.58 94.77 94.80 94.83 94.65 94.90 289.3 289.1 289.4 289.6 425 9 Aofi.a 548.1 548.2 424 4 i'^l 1 436.8 437.2 289.6 390.1 427.6 548.9 99.94 94.64 94.79 289.3 389.7 426.1 427.0,548.4 1 99.85 95.16 (619.) (620.) 1 i pS Conductivity of Aqueous Solutions. — Part IV. Table 20. — Equivalent conductance at round temperatures — Continued. POTASSIUM SULPHATE. Concen- tration at 4°. 18°. 100". 156°. 218°. 281°- 306° Date. Initial. Final. Initial. Final. Initial. Final. 1904 2.001 1.999 124.58 124.41 124.63 124.07 401.8 400.7 401.4 400.1 606.0 607.2 607.4 606.6 802.0 802.4 Mar. 14 Mar 15 2.000 124.50 124.35 401.3 400.8 606.6 607.0 802.2 919.8 924.3 927.7 930.6 928.3 1905 April 3 April 4 April 21 July 12 July 12 Mean 2.001 2.001 1.999 2.001 2.003 125.42 124.94 124.76 125.03 124.44 125.22 125.00 124.87 129.33 126.98 933.3 928.7 929.9 919.2 919.9 2.001 124.92 126.28 926.1 926.2 1904 Mar. 16 Mar. 17 12.503 12.508 114.00 114.13 114.10 114.17 360.3 361.0 360.4 361.1 531.2 532.0 531.3 532.3 669.5 670.4 Mean 12.506 114.07 114.14 360.7 360.8 531.6 531.8 670.0 1905 April 6 April 10 April 12 April 13 May 1..-.. 12.503 12.493 12.492 12.490 12.497 114.13 114.02 114.07 114.10 114.37 114.03 114.08 113.97 114.25 696.2 698.0 697.7 694.0 652.8 654.2 654.6 653.0 Mean 12.495 114.14 114.08 696.5 653.7 1904 Mar. 18 Mar. 21 50.05 50.00 102.03 102.05 102.14 102.11 313.7 313.9 313.5 313.9 449.0 450.1 448.9 450.4 537.9 538.6 Mean 50.03 102.04 102.13 313.8 313.7 449.6 449.7 538.3 1905 Sept. 29 Sept. 29 50.12 50.04 102.02 102.06 102.33 102.31 527.3 526.4 481.6 480.3 Mean 50.08 102.04 102.32 526.8 481.0 1904 Mar. 22 Mar. 23 100.13 100.16 95.05 95.06 95.04 95.05 288.0 288.0 287.9 288.1 407.3 407.4 407.3 407.5 477.0 477.6 Mean 100.15 95.06 95.05 288.0 288.0 407.4 407.4 477.3 1905 Sept. 30 Sept. 30 100.03 100.07 94.97 94.86 95.01 94.88 455.1 454.1 410.5 409.6 100.05 94.92 94.94 454.6 410.0 1 BARIUM NITRATE. 1904 April 7 . April 8. Mean . 1905 May 2. May 3. Mean . 1904 April 11. 1.999 1.999 1.999 1.997 2.003 2.000 12.512 109.52 109.55 109.54 110.08 109.83 109.95 99.48 109.05 109.26 109.16 110.51 110.00 110.26 99.47 352.5 352.7 352.6 317.4 351.1 352.2 351.7 317.5 540.1 538.2 539.2 476.1 538.2 538.2 720.7 724.2 538.2 475.7 722.5 614.9 863.8 877.0 863.8 880.1 863.81 878.6 T Section 40. — Summary of Equivalent Conductances. pp Table 20. — Equivalent conductance at round temperatures — Continued. BARIUM NITRATE. Concen- tration at 4°. 18°. 100°. 156°. 218°. 281°. Initial. Final. Initial Final. Initial Final. 306°. 1905 May 4 May 5 May 8 12.512 13.508 13.496 99.48 99.51 99.48 100.23 99.73 665.6 664.7 633.2 631.7 Mean 12.. 504 99.49 99.98 665.1 632.5 1904 April 12 50.05 50.09 50.16 50.17 50.19 50.09 86.97 86.95 86.93 87.00 86.85 86.94 87.08 86.97 87.02 275 . 5 375.6 404.6 404.6 502.9 1905 Oct. 2 507.3 462.2 Oct. 3 Oct. 3 Oct. 4 Oct. 5 511.8 508.8 Oct. 13 86.29 87.41 464.5 Oct. 22 465.7 Mean 86.96 609.3 464.1 Oct. 20 78.72 78.73 82.03 82.03 81.56 81.63 " " — 465.6 465.0 422.9 Oct. 25 424.6 Mean 78.73 83.03 465.3 433.8 1904 April 12 100.07 100.00 79.14 79.11 79.14 79.11 251.2 351.3 351.3 364.8 365.4 365.4 445.1 445.1 i April 13 Mean 100.04 79.13 79.13 75.60 79.31 251.3 251.3 365.1 365.4 445.1 1 1905 Oct. 14 100.34 100.40 100.37 79.14 79.12 79.13 437 e! Oct. 17 439.61 .. Mean 438 6 MAGNESIUM SULPHATE. 1904 June 28 .Tune 28 Corrected values . . May 6 Corrected values . . Apr. 25 Corrected values. . Apr. 26 Corrected values. . Apr. 38 Apr. 28 Apr. 27 Corrected values. . May 3 May 3 tration at 4°. 1.982 2.168 2.000 12.529 12.500 26.16 25.00 52.83 50.00 99.93 99.93 106.83 100.00 195.96 350.9 94.43 93.41 94.3 94.56 93.68 73 . S3 73.9 73.91 64.41 64. f 64.44 56.40 56.8 49.81 49.81 49.10 43.31 38.44 56.53 49.93 49.83 48.23 43.40 38.51 100°. Initial. 304.3 300.3 304.0 214.2 314.3 179.6 180.7 151.9 153.1 131.0 138.9 131.0 112.3 99.7 305.6 301.2 214.3 179.7 151.9 139.1 112.4 384.7 376.4 384.0 231.4 231.5 185.9 187.0 1.51.9 385.6 378.3 231.4 185.9 153.0 136.9 218°. 276.5 268.4 275.7 140.0 140.1 107.4 108.0 86.5 87.1 74.4 73.9 74.4 61.6 100 Conductivity of Aqueous Solutions. — Part IV. Table 21 contains a summary of best values derived from the means in table 20. The means of only the initial values have been taken and these have been corrected for the contamination upon heating in the man- ner described in section 16, Part II. Table 21. — Best values of the equivalent conductance at round temperatures. Temperature Sodium chloride. Potassium ctiloride. silver nitrate. (t°) Concentration Equivalent Concentration Equivalent Concentration Equivalent at<°. conductance. Mt°. conductance. at(° conductance. 18 2.000 105.6 2.000 126.4 1.998 112.2 10.00 102.0 10.00 122.4 12.48 107.2 100.0 92.0 100.0 112.0 24.95 49.86 99.8 104.0 100.2 94.6 100 1.924 349.3 1.920 393.3 1.916 351.0 95.9 296.8 9.58 377.7 11.97 335.0 95.9 336.7 23.95 47.83 95.8 321.5 308.0 289.0 156 91.1 445.5 1.824 589 1.821 532 9.10 563 11.37 504 91.1 493 22.75 45.43 91.0 481.0 457.0 426.0 218 8.44 690 8.44 746 1.685 720 84.4 588 84.4 637 10.52 21.07 43.13 84.6 672 635 597 548 281 7.53 834 7.51 889 1.500 877 75.7 678 75.6 726 9.38 37.70 75.7 796 685 (616) 306 1.394 972 6.99 935 1.394 937 6.99 883 70.5 735 8.71 830 70.5 694 35.10 70.6 693 (617) Section 40. — Summary of Equivalent Conductances. loi Table Zl.~Best values of equivalent conductance at round tetnperatures— Continued. Potassium chloride. Temperature Potassium chloride. Temperature in Concentration Equivalent ((°) Concentration Equivalent at<°. conductance. at<°. conductance. 25 1.997 146.4 75° 9.75 295.4 9.97 141.5 97.5 265.1 19.9; 138.8 99.7 129.0 50 9.88 215.3 128° 9.36 471.8 19.76 210.4 93.6 417.1 98.8 194.7 Temperature Potassium sulphate. Barium nitrate. Magnesi im sulphate. ((°) Concentration Equivalent Concentration Equivalent Concentration Equivalent at(°. conductance. at(°. conductance. at(°. conductance. 18 1.998 124.8 1.996 109.7 1.998 94.3 12.48 114.1 12.51 99.5 12.49 73.9 50.00 102.0 50.07 87.0 34.98 64.8 100.0 95.0 78.6 82.0 49.95 56.8 100.1 79.1 99.9 195.7 350.4 49.8 43.3 38.45 100 1.918 401.5 1.916 353.0 1.919 304.0 11.99 360.5 12.01 317.5 11.99 214.3 47.95 313.5 47.98 375.5 23.98 180.7 96.0 288.0 95.9 251.0 47.97 95.9 187.8 336.3 153.1 131.0 113.3 99.7 156 1.821 607 1.831 539 1.833 384.0 11.39 532 11.41 476.0 11.39 331.5 45.56 449.5 45.58 404.5 33.77 187.0 91.2 407.5 91.1 365.5 45.55 91.1 178.5 319.5 153.1 129.0 110.3 98.7 218 1.685 802 1.685 723 1.685 375.7 10.55 670 10.55 615 10.53 140.1 42.27 538 42.24 503 21.07 108.0 84.8 477.5 84.7 445.0 42.13 84.3 166.7 87.1 74.4 61.6 281 1.503 920 1.501 863 9.39 697 9.43 664 37.71 526 37.85 509 75.6 454.5 59.5 76.0 465.5 438.5 306 1.395 920 1.392 877 8.73 654 8.77 631 35.07 480.5 35.19 464 70.36 410.0 55.5 434 103 Conductivity of Aqueous Solutions. — Part IV. 41. EQUIVALENT-CONDUCTANCE VALUES AT ROUND CONCENTRATIONS. The conductance values in table 31 which refer to different concentra- tions at different temperatures have been reduced to a uniform round con- centration by graphic interpolation with the help of the linear function — z= 1- K(Ca)"' discussed in section 17. The so-reduced values are A Ao presented in table 22, except those for sodium and potassium chlorides, which have already been summarized in table 9, section 16. As these are our final values it may be again stated in explanation of the table, that, as in the preceding tables, the concentration is expressed in milli-equivalents per liter based on the international atomic weights for 1905 referred to oxygen as 16.00 ; that the temperature is the true temperature on the hydrogen-gas scale as derived (at the higher temperatures) from the determinations of Jaquerod and Wassmer of the boiling-points of naphthalene and benzo- phenone; and that the equivalent conductance, which has been corrected for that of the water, is expressed in reciprocal ohms, the absolute conduct- ance-capacity of the conductivity vessel having been derived from Kohl- rausch and Maltby's data for sodium and potassium chloride at 18° and corrected for its change with the temperature. The concentration given in the second column is that at the temperature of the measurement. The conductances at zero concentration were obtained in the cases of silver nitrate, barium nitrate, and potassium sulphate, at 100° and above, by graphic extrapolation upon plots of the function — ^ • 1- K(CA.)'^ A Ao At the higher temperatures the results are doubtless much in error owing to the large extrapolation involved, but they are the best obtainable from the data. At 18° we have inserted for zero concentration the values cal- culated from Kohlrausch's conductance values for the separate ions of the potassium sulphate, barium nitrate, and magnesium sulphate. In the case of magnesium sulphate at the higher temperatures, the method employed for the other salts was inapplicable owing to the large hydrolysis, and there are at present no independent data upon which a fully satisfactory determination of its A(, value can be based. But, in order to give some idea of the relation of its conductivity at the various concentrations to that of the completely ionized salt, we have assumed that, at 100° and above, magnesium and barium ions have the same equivalent conductance and have computed rough A,, values by the relation Ao(Mgso4)=Ao(BaN206)+ A(,(K2S04) — Ao(Kci)- The assumption that chloride-ion and nitrate-ion have the same equivalent conductance is also involved; but this assump- tion is doubtless substantially correct. The so-computed A,, values for magnesium sulphate are given within parentheses in the table. Section 41. — Equivalent Conductance at Round Concentrations. 10^ Table 22. — Final values of the equivalent conductance. AgNOs . KjSO, Ba(N03)2 MgSOi Concen- tration. 2.0 10.0 13.5 20.0 25.0 40.0 50.0 80.0 100.0 2.0 10.0 12.5 40.0 50.0 80.0 100.0 2.0 10.0 13.5 40.0 50.0 80.0 100.0 2.0 10.0 12.5 20.0 25.0 40.0 50.0 80.0 100.0 160.0 200.0 320.0 18°. 115.8 112.2 108.0 107.2 105.1 104.0 101.3 99.9 96.5 94.6 132.8 124.8 115.7 114.1 104.3 103.0 97.3 95.0 116.9 109.7 101.0 99.4 88.7 86.8 81.6 79.1 114.1 94.3 76.1 73.9 67.5 64.8 59.3 56.8 53.0 49.8 45.3 43.1 39.2 367 353 337 334.5 335.5 333.5 311.5 307.5 294.0 389.0 455 401.5 365.0 358.0 320.0 312.0 294.5 286.0 385 353.0 333.0 316.0 380.0 373.5 357.5 349.0 (426) 302 223.5 212.5 190.0 179.0 160.0 151.5 136.0 129.5 116.5 110.5 100.6 570 539 507 487.5 462.6 433.0 715 605 537 455.0 415.0 600 536 481 412 372 (690) 377 241.0 225.0 195.0 180.0 158.0 149.0 133.0 126.0 114.8 109.1 98.7 218°. 780 727 673 639 599 553 1065 806 673 545 483.0 840 715 618 507 449 (1080) 360 143 110.5 88.5 75.2 63.4 281°. 965 877 790 680 614 1460 893 687 519 448.0 1130 838 658 503 430 306°. 1065 935 818 680 604 1725 867 637 466.0 395.5 1300 824 615 448 It is of interest to compare our results at 18° with those previously obtained by Kohlrausch and Steinwehr*, Kohlrausch and Gruneisen,f and (for magnesium sulphate) by Foster.^ All these data at corresponding concentrations have been brought together in table 23. It W\l\ be seen that the results agree within 0.2 per cent in nearly all cases, and within 0.4 per cent without exception. Measurements have been made at 95° in a glass apparatus by Kahlenberg§ with silver nitrate and magnesium sulphate. ♦Kohlrausch und Steinwehr, Sitzungsber. preuss. Akad., 1902, 581. tKohlrausch und Griineisen, Sitzungsber. preuss. Akad., 1904, 1315. tW. Foster, Phys. Rev., 8, 257 (1899). §Kahlenberg, J. Phys. Chem., 5, 349 (1901). 104 Conductivity of Aqueous Solutions. — Part IV. We have reduced his results to 100° by means of our temperature-coeffi- cients at that temperature, and have given them beside our own in the table. It will be seen that the results with silver nitrate are widely diver- gent at all concentrations, and that those with magnesium sulphate are somewhat so except at the higher concentrations, indicating the difficulty of getting reliable results at such high temperatures in glass vessels. Table 23. — Comparison of the conductivity results of different investigators Temper- ature. Concen- tration. Silver nitrate. Barium nitrate. Potassium sulphate. Magnesium sulphate. Noyes and Melcher. Kolil- rausch and Stein- welir.* Noyes and Melclier. Kohl- rauscb and Griin- eisen.t Noyes and Melcher. Kohl- rausch and GrQn- eisen.t Noyes and Melcher Kohl- rausch k Grun- eisen.t Fostert. 18 2.0 10.0 20.0 50.0 100.0 112.2 108.0 99.9 94.6 112.1 107.8 99.5 94.3 109.7 101.0 86.8 79.1 109.5 101.0 86.8 78.9 124.8 115.7 102.0 95.0 124.6 115.8 101.9 94.9 94.3 76.1 67.5 56.8 49.8 94.1 76.2 67.7 56.9 49.7 93.8 76.1 m'.k 49.5 Temperature. Concentration. Silver nitrate. Magnesium sulphate. Noyes and Melcher. KalilenberB.§ Noyes and Melcher. Kahlenberg.^ loa 2.0 10.0 40.0 80.0 100.0 353 337 312 294 289 335 311 282 259 257 302 224 160 136 130 305 221 163 136 130 *Kohlrausch und Steinwehr, Sitzungsber. preuss. Akad., 1902, 581. fKohlrausch und Steinwehr, Sitzungsber. preuss. Akad., 1904, 1215. JW. Foster, Phys. Rev., 8, 257 (1899). §Kahlenberg, J. Phys. Chem. 5, 349, (1901). 42. CHANCiE OF THE EQUIVALENT CONDUCrTANCE WITH THE CONCENTRATION. The empirical law of the variation of the conductance of silver nitrate, potassium sulphate, and barium nitrate with the concentration is shown by table 24, in which the values of the exponent n in the function C(A„ — A) =i?(CA)" are tabulated. Table 24. — Values of the exponent n in the function C(Ao — A^X'(CA)". Substance. 18°. 100°. 156°. 218°. 281°. 306°. AgNOs K2SO4 1.53 1.42 1.50 1.43 1.52 1.42 1.50 1.50 1.42 1.50 1.50 1.43 1.50 1.52 1.42 1.50 1.53 1.42 1.50 Ba(NO»)i, MgSO. Section 42. — Change of Conductance with Concentration. 105 It was shown in table 11, section 17, Part II, that the value of n for sodium and potassium chlorides lies between 1.40 and 1.50 at all tempera- tures, and it will be seen from this table that the same is true also for the tri-ionic salts, potassium sulphate and barium nitrate. This striking fact, which is in utter contrast with the requirements of the mass-action law, according to which the exponent should have the very different values 2 and 3 for these diflferent types of salts does not seem to have been suffi- ciently considered in the discussion of the possible causes of the devia- tions. It is worthy of note also that the exponent has about the same value for the uni-univalent salt silver nitrate, which is very different chemically from the alkali-element chlorides, and that this is also true even for the bibivalent di-ionic salt magnesium sulphate at 18°. For the last salt we have not calculated the exponent at higher temperatures, owing to the large hydrolysis which doubtless exists. Attention may also be called to the constancy throughout the whole range of temperature of the exponent n for eadh individual salt. This seems to indicate that even at the highest temperature the hydrolysis has not in any case become considerable. It should be mentioned, however, that in the case of potassium sulphate it was not possible to determine the value of the exponent nearer than 0.05 unit, owing to the fact that this salt, unlike the others, does not seem to conform completely to any expo- nential function of the type in question. 43. CHANGE OF THE EQUIVALENT CONDUCTANCE WITH THE TEMPERATURE. The effect of temperature on the equivalent conductance values at zero concentration (the Ao values) will be mainly considered in this section. Attention may first be called to the ratios given in table 25 of the Aj, values for silver nitrate, potassium, sulphate, and barium nitrate to those for potassium chloride. Table 25. — Ratio of Ao values to those for potassium chloride. Substance. 18°. 100°. 156°. 218°. 281°. 306°. AgNOa Ki,S04 BaCNOs)^ 0.89 1.02 0.90 0.89 1.10 0.93 0.91 1.14 0.96 0.95 1.29 1.02 0.96 1.45 1.11 0.95 1.54 1.16 It will be seen that with rising temperature the conductance of silver nitrate, like that of sodium chloride (see section 18, Part II), approaches the conductance of potassium chloride, thus furnishing another exempli- fication of the principle that the ratio of the specific velocities of the vari- ous ions approaches unity with rising temperature. io6 Conductivity of Aqueous Solutions. — Part IV. In the cases of the two tri-ionic salts the apparently abnormal phenom- enon is observed that their equivalent conductance, though about equal to or less than that of potassium chloride at 18°, becomes much larger than it at the higher temperatures. The very large values of the ratios at 281° and 306°, especially for potassium sulphate, can not be caused by hydrolysis ; for this would have an opposite effect, owing to the smaller equivalent conductance of the univalent ions thereby produced (for example, of the OH- + HSO4- ions which would replace the 50^= ion) : and at the lower temperatures (218° and below) appreciable hydrolysis does not exist, since the acids and bases involved have been shown by the measurements of Noyes and Eastman (section 97, Part VIII) to be too much ionized to admit of it. The real peculiarity in the results does not, however, con- sist in the large value of the ratio at the higher temperatures, but rather in the approximation of it to unity at the lower ones; for, since a bivalent ion, like Ba-^ or S04= , is in the same electric field, owing to its double charge, acted on by twice as large a force as a univalent ion, it would, provided it met with the same resistance, move with twice the velocity, and therefore have twice the equivalent conductance. The equiv- alent conductance of a completely ionized uni-bivalent salt would therefore approach 1.5 times that of a uni-univalent salt if the specific velocities of the various ions (that is, the velocities under unit electric force) approached equality. An approximation to this limiting value seems to be indicated in the case of potassium sulphate, and a change in the same direction is clearly shown by barium nitrate. That the equivalent conduct- ances of the bivalent ions are so small at ordinary temperatures signifies, of course, a high resistance to their passage through the solution. This may arise from their being much hydrated; and the large increase in velocity with rising temperature may be due to a decrease in the hydration. In order to show more clearly the relation between equivalent conduct- ance and temperature for the individual substances, we have calculated the values of AA„/Af for the successive temperature intervals, and tabu- lated them in table 26, together with those for potassium and sodium chlorides already given in section 18, Part II. Table 26. — Temperature-coefficients of the equivalent conductance at zero concentration. Substance. 18-100°. 100-156°. 156-218°. 218-281°. 281-306°. KCl 3.46 3.09 3.06 3.93 3.27 3.77 3.44 3.62 4.64 3.84 3.23 3.31 3.39 5.64 3.87 2.86 3.33 2.94 6.27 4.44 4.60 4.40 4.00 10.6 7.20 NaCl AgNOa KjSOi Ba(N03)= Section 43.~Change of Conductance with Temperature. 107 It will be seen that silver nitrate has temperature-coefficients which run parallel to those for potassium and sodium chlorides, and which, like the lattef, pass through a maximum value somewhere in the neighborhood of 156°. The coefficients of potassium sulphate and barium nitrate, on the other hand, differ greatly from each other, and increase continuously with rising temperature. With reference to the equivalent conductance values at the higher con- centrations, mention need be made only of the fact that as shown in table 22, those for SO-milH-normal solutions have a maximum value at 281° in the case of silver nitrate, at 218° in the cases of potassium sulphate and barium nitrate, and at 100° in that of magnesium sulphate. This is, of course, due to a compensation of the effect of increasing migration-velocity by that of decreasing ionization. 44. lONIZATlON-VALUES AND THEIR CHANGE WITH THE CONCENTRATION AND TEMPERATURE. In table 27 are given the ratios (multiplied by 100) of the conductances at the various concentrations to that at zero concentration at each tempera- ture. These ratios are at least an approximate measure of the percentage ionization of the substances, in those cases where the hydrolysis is not large and complex or intermediate ions are not formed, and provided the conductances at zero concentration can be regarded as correct. It is not probable that the hydrolysis is large enough at the higher concentrations to seriously vitiate this interpretation of the results, except in the case of magnesium sulphate at 100° and above. No definite information is avail- able in regard to the existence at the higher temperatures of intermediate ions like KSO^ and BaN03+ ; but the facts that transference determina- tions* have shown their absence in any considerable quantity at ordinary temperatures and that the functional relation between concentration and conductivity is identical at all temperatures (as was shown in section 42) make it probable that such ions do not exist in large quantity at the higher temperatures. Aside from these uncertainties in the interpretation of the conductivities at the higher concentrations, there is the possibility of con- siderable inaccuracy in some of the values adopted for zero concentra- tion. This possibility exists especially in the case of magnesium sul- phate at 100° and above, for which the A,, values were derived from those for potassium sulphate and barium nitrate under the assumption that the magnesium and barium ions have equal migration-velocities. It may also exist to some extent in the case of potassium sulphate and barium nitrate ♦See Noyes, Z. phys. Cham., 36, 79 (1901). io8 Conductivity of Aqueous Solutions. — Part IV. at 381° and 306°, owing to the possible effect of hydrolysis. The ioniza- tion-values for magnesium sulphate at 100°, 156°, and 218° are therefore to be regarded only as rough estimates, and those for potassium sulphate and barium nitrate at 281° and 306° as possibly in error by several per cent. Table 27. — The conductance ratio (100 A/Ao) and approximate percentage ionization. Substance. Concen- tration, 18°. 100°. 156°. 218°. 281°. 306°. Silver nitrate 100.0 100.0 100.0 100.0 100.0 1 30.0 2.0 96.9 96.2 94.6 93.2 90.9 37.7 10.0 93.3 91.8 88.8 86.3 81.8 ' ?6.8 20.0 90.8 88.7 85.5 81.9 .... 40.0 87.5 84.9 81.2 76.8 70.5 f 33.8 80.0 83.3 80.2 75.8 70.8 63.7 56.7 100.0 81.7 78.8 .... .... .... Potassium 2.0 94.0 88.4 85 76 61 50 sulphate 10.0 87.2 80.3 75 63 47 37 40.0 78.5 70.3 64 51 36 27 80.0 73.2 64.8 58 45 31 i J3 100.0 71.6 62.3 .... Barium nitrate 2.0 93.8 91.4 89 85 74 f 53 10.0 86.7 83.6 80 74 59 17 40.0 76.2 72.7 69 60 45 : i4 80.0 70.1 66.9 62 53 38 100.0 67.9 64.7 Magnesium 2.0 82.6 70.8 55 24 sulphate 10.0 66.7 52.4 35 13 20.0 59.3 44.6 38 10 40.0 52.0 37.5 23 8 80.0 45.5 31.9 19 7 100.0 43.7 30.4 With respect to the change of ionization with the concentration at any definite temperature, it will suffice to recall that the functional relation must be of a corresponding form to that between equivalent conductance and concentration, which was discussed in section 42, and again to empha- size the remarkable fact that the exponent in that function has nearly the same value for di-ionic and tri-ionic salts, and a value, moreover, which does not vary markedly with the temperature. Thus for the five substances, potassium chloride, sodium chloride, silver nitrate, potassium sulphate, and barium nitrate, at all temperatures between 18° and 306° inclusive, the ionization (y) can be expressed by an equation C(l — y) = const. X (Cy)", in which n has values varying only between 1.40 and 1.52. Assuming that the conductance-ratio may be regarded as at least an approximate measure of the ionization, certain conclusions in regard to the relation of the latter to temperature may be drawn from the results of Section 44. — I onization-values. lOp table 27 considered in connection with those of potassium and sodium chlorides given in table 13 of section 19, Part II. To make these more evident we have brought together in table 28 the values of the percentage ionization as given by the ratio lOOA/Ao for all these substances at a concentration of 0.08 normal. Table 28. — Percentage ionization (IOO7) at 0.08 normal. Substance. 18°. 100°. 156°. 218°. 281°. 306°. NaCl 85.7 87.3 83.3 73.2 70.1 45.5 83.2 83.6 80.2 64.8 66.9 32 81.2 79.7 75.8 58 62 19 77.7 77.3 70.8 45 53 7 70 72 64 31 38 63 64 57 23 (28) KCl AgNOa KjSO, BaCNOa)^ MgSO^ It will be seen from this table that the ionization of the three di-ionic salts, sodium and potassium chlorides and silver nitrate, different as they are chemically, have not very far from the same ionization values through- out the whole range of temperature. The same is true of the two tri- ionic salts, potassium sulphate and barium nitrate. Thus the rule already deduced from the ionization values at ordinary temperatures that salts of the same ionic type have roughly the same degree of ionization also applies at high temperatures. The principle that the ionization of salts at any definite concentration is smaller, the greater the product of the valences of the constituent ions, is an even more pronounced one at the higher temperatures. Thus at 218° the ionization of the uni-univalent salts in 0.08 normal solution is on the average 74 per cent, that of the unibivalent salts about 50 per cent, and that of the single bibivalent salt investigated only 7 per cent. Most striking of all is the fact that the still more definite principle that the un-ionized fraction is directly proportional to the product of the valences of the ions* still holds true approximately when that fraction has become very large as it has at the higher temperatures. Table 29 shows under A the mean values of 100(1 — y) at 0.04 molal (and for the uni- univalent salts at 0.08 molal), and under B the ratios of these values to the product (vjVa) of the valences, for the salts of the three types included in table 28. *In regard to this, see A. A. Noyes, The Physical Properties of Aqueous Salt Solutions in Relation to the Ionic Theory, Congress of Arts and Science, St. Louis Exposition, 4, 320 (1904) ; Technology Quarterly, 17, 303 (1904) ; abstracted in Z. phys. Chem., 52, 634 (1905). no Conductivity of Aqueous Solutions. — Part IV. Table 39. — Un-ionized fraction in relation to valence-product. ^1^2 Mols per liter. 18°. 100°. j 156°. 218°. 281°. " 306°. A B A B A B A B A B A B 1x1 1x1 1x2 2x2 0.04 0.08 0.04 0.04 12 15 28 55 12 15 14 14 15 18 34 68 15 18 17 17 17 21 40 81 17 21 20 20 20 25 51 93 20 25 25 23 25 31 65 25 31 32 31 39 74 31 39 37 It will be seen that the principle continues to hold, especially when the comparison is made at the same equivalent concentration, even when the ionization has become very small ; thus it is only 26 per cent for the uni- bivalent salts at 306° and only 7 per cent for the bibivalent salt (magne- sium sulphate) at 218°. In correspondence with this principle, the rate of decrease of ionization with rising temperature for the individual substances is greater for the unibivalent than for the uni-univalent salts, and is still greater for the bibivalent salt magnesium sulphate. Moreover, the rate of decrease of ionization per degree increases rapidly with rising temperature, especially above 100°. The following values of ( — 10^ Ay /At), which represent the absolute decrease in percentage ionization produced by a rise in tempera- ture of 10°, illustrate these statements. Table 30. — Temperature-coeMcients of ionization ( — 103A7/At). Substance. 18°-100°. 100°-156°. 156°- 218°. 218°-281°. 281°-306°. NaCl 0.30 0.57 0.38 1.05 0.39 0.36 0.52 0.79 1.2 0.9 0.56 0.39 0.81 2.1 1.5 1.30 0.86 1.15 2.2 2.4 3.6 3.1 2.8 3.2 KCl AgNOs K^SO* 45. SUMMARY. In this article have been presented (in table 22, section 41) values for the equivalent conductance of silver nitrate, potassium sulphate, and barium nitrate at six different temperatures lying between 18° and 306° and at concentrations between 0.002 and 0.08 or 0.1 normal. Similar values are given for magnesium sulphate up to still higher concentrations for four different temperatures extending up to 218°. From these by graphic extrapolation have been derived equivalent conductance values for zero concentration, which are proportional to the migration-velocities of the constituent ions. The ratios of the conductance at the various concen- trations to that at zero concentration, which ratios represent approximately Section ^5. — Summary. iii the degree of ionization, have been calculated (see table 27, section 44). Specific volume data for the more concentrated solutions have also been presented (in table 18, section 38). A study of these data has led to the following conclusions : (1) At all temperatures the equivalent conductance (A) and ioniza- tion (7) of the two tri-ionic salts, potassium sulphate and barium nitrate, vary with the concentration according to approximately the same law as do those of silver nitrate and of the other two di-ionic salts, potas- sium and sodium chlorides, previously investigated. For, in the case of all these five salts, in order that functional relations of the form C(Ao — A) = const. X(C"A)" or C(l — y)= const X(Cy)" may express the results, values varying only between 1.40 and 1.52 must be assigned to the exponent n, while according to the mass action law its value should be 2 for di-ionic and 3 for tri-ionic salts. (2) The principle that the relative velocities of different ions acted upon by the same electric force approach equality with rising temperature is strikingly exemplified in the case of the bivalent SO^^ and Ba++ ions. Since bivalent ions owing to their double charge are acted upon by twice the electric force when in the same electric field, their equivalent con- ductance would become twice as great as that of univalent ions when the resistance to their motion through the solution was the same; and in this case the equivalent conductance of a completely ionized salt con- sisting of a univalent and a bivalent ion would become 1.5 times that of a uni-univalent salt. Now, our results show that at 18° the salts potas- sium suphate and barium nitrate have equivalent conductances at zero concentration which are 1.02 and 0.90 times respectively that of potas- sium chloride, but that at 306° the corresponding ratios are 1.54 and 1.16. (3) The ionization values at all temperatures for silver nitrate agree within a few per cent with those previously derived (in Part II) for sodium and potassium chlorides; and the values for potassium sulphate and barium nitrate also agree with each other within a few per cent; thus confirming at high temperatures and for relatively small ionization the rule that most salts of the same ionic type have roughly the same degree of ionization. (4) The ionization of all the salts investigated decreases steadily with rising temperature, the decrease being more rapid the higher the tem- perature and the greater the valences of the ions of the salt. Even where the ionization has become small, as it has at the higher temperatures, the simple principle still holds true approximately that the fraction of the salt un-ionized is proportional to the product of the valences of its ions. Part V. Conductivity and Ionization of Hydrochloric Acid, Acetic Acid, and Sodium Acetate up to 218°. Hydrolysis of Sodium Acetate and Ionization of Water at 218°. By Arthur A. Noyes and Hermon C. Cooper. Part V. CONDUCTIVITY AND IONIZATION OF HYDROCHLORIC ACID, ACETIC ACID, AND SODIUM ACETATE UP TO 218°. HYDROLYSIS OF SODIUM ACETATE AND IONIZATION OF WATER AT 218°. 46. OUTLINE OF THE INVESTIGATION, In Parts II and III of this publication an apparatus and method have been described by which accurate measurements of the electrical conduct- ance of aqueous solutions can be extended up to 306° or higher. This has made it possible to investigate at high temperatures such other physical properties and chemical reactions, as can be studied with the help of conductivity measurements. One of the most interesting of these is the phenomenon of the hydrolysis of salts into free acid and base — a phenomenon which is dependent in large measure on the degree of ioniza- tion of water itself, and from which, when supplemented by determina- tions of the ionization of the acid and base involved, this important quan- tity can be computed. Owing to the fact that the ionization of water in- creases very rapidly with rising temperature while the ionization of most weak acids and bases decreases, the hydrolysis of salts plays at high temperatures a much more prominent part than at ordinary ones and its effect must be taken into consideration even in the case of salts which at the ordinary temperature are not appreciably hydrolyzed. We have therefore undertaken an investigation in this direction. The method employed for determining the hydrolysis is in principle that described first by Walker,* and later, in much more exact form by Bredig.f It consists in measuring the decrease of conductivity produced by adding to the salt solution, in which the salt is partially hydrolyzed, a sufficient quantity of the slightly ionized acid (or base) to reduce the degree of hydrolysis substantially to zero and in computing from this decrease and the previously determined difference in the mobility of the hydroxyl (or hydrogen) ion and the anion (or cathion) of the salt the fraction of the salt hydrolyzed. Thus, in the case of sodium acetate, the conductivity of this salt in its ordinary condition was first measured ; then that of a solution of the salt of the same concentration containing also a considerable proportion of free acetic acid (which was varied in different experiments) was determined. The observed difference (after applying a small correction for the conductivity of the added acid in the presence *Ztschr. phys. Chem., 4, 333 (1889). tZtschr. phys. Chem., 13, 214, 321 (1894). 115 ii6 Conductivity of Aqueous Solutions. — Pa/rt V. of its neutral salt) evidently corresponds to the difference between the conductivity of the sodium hydroxide that exists free in the original solu- tion and that of an equivalent quantity of sodium acetate. From the so- derived degree of hydrolysis and the ionization-constant of the acetic acid, the ionization-constant of water itself can be calculated with the help of the mass-action law, as has been shown by Arrhenius.* The determination of the hydrolysis of the single salt, sodium acetate, and the calculation from it of the ionization of water at any temperature involves, therefore, conductivity measurements of solutions at various concentrations of the following substances: (1) sodium acetate alone; (3) sodium acetate mixed with acetic acid (preferably in varying pro- portions) ; (3) acetic acid; (4) hydrochloric acid; (5) sodium chloride in very dilute solution (the last two being necessary in order to compute the conductivity of completely ionized acetic acid according to the rela- tion Ao(HAc) = A(|(NaAc) -|- A„(Hci) — Ao(NaCi); and (6) sodium hydroxide in dilute solution. These measurements, except those with sodium hy- droxide, have been made at a series of four temperatures, 18°, 100°, 156°, and 218°, by one of us ( H. C. Cooper ), those with sodium chloride at 318° being, in part, however, a repetition of the earlier ones of Noyes and Coolidge. Measurements with sodium hydroxide at the same tempera- tures have been made in this laboratory by Mr. Yogoro Kato ; and these will be described in Part VI. All the data necessary for the calculations are therefore available. Since the measurements with hydrochloric acid and acetic acid are the first ones made with acids at high temperatures, and since those with sodium acetate make possible a comparison of the behavior of this or- ganic salt with that of the inorganic salts previously investigated, the re- sults have a considerable interest of their own; and a large part of this article is devoted to the presentation and discussion of them. Before considering these results, however, the apparatus and method used for the conductivity measurements and the preparation and stand- ardization of the solutions must be described ; and to this description the next two sections will be devoted. 47. APPARATUS AND METHOD OF PROCEDURE. The apparatus used was substantially the same as that employed in the previous investigation of Noyes and Coolidge. (See Part II.) Only the small modifications made in it will be here described in detail. THE CONDUCTIVITY CELLj OR BOMB. The bomb itself was the same one that was used by these investigators. It was used without any modification in the first experiments. Somewhat *Ztschr. phys. Chem,, 5, 17 (1890). Section 4y. — Apparatus and Procedure. iiy later, in attempting to make measurements with dilute sodium acetate and hydrochloric acid at 218°, difficulty was met with in obtaining constant readings, apparently owing to adsorption by the lower electrode. The platinum-black was therefore removed from it (on April 4, 1904) by rub- bing it with cotton and moist pumice. Later (on June 25, 1904), in order to diminish any contaminating influence of the electrode or quartz cup exerted upon the small quantity of liquid within the cup, the cup and the flat electrode within it were removed and replaced by a cylindrical electrode of an iridium-platinum alloy with 15 per cent iridium and an insulating cylinder of quartz.* This electrode was 9.7 mm. high and 7.2 mm. in diameter. It was not found necessary to renew any of the parts of the bomb throughout the course of the work; and very little difficulty was experi- enced from leaks, which occurred only a few times and were then easily remedied. THE CONDUCTIVITY MEASURING APPARATUS. The conductivity was measured with an apparatus of the roller type described by Kohlrausch and Holbornf and furnished by Hartmann and Braun. The resistance coils of 1, 10, 100, 1,000, 10,000 ohms were of manganine. Heavy copper wire leads were used to within a few cm. of the slide wire and the heaters, the end connections being made of heavy flexi- ble leads with brass connectors joining them to the slide wire and to the leads attached to the bomb. The entire lead resistance amounted to only 0.02 ohm. The slide-wire was calibrated by the method of Strouhal and Barus, once just before the conductivity work was begun and again on June 1, 1904, the difference in the two cases, as well as the maximum error, being very slight. The corrections were, however, applied to the conductivity measurements. The resistance coils were compared with standard resist- ances, certified by the Deutsche phys.-technische Reichsanstalt. INDUCTION COILS. Two induction coils were used ; at first a small one of the ordinary form was employed, and afterwards, in order to reduce the effect of ejection of material from the electrodes, a Nernst:): string interrupter was used. The quality of the minimum afforded by this latter interrupter was satisfactory even with bright electrodes. In the case of all the measurements except those with sodium chloride, a commutating switch was introduced between the induction coil and the bridge, and the mean of the two readings taken. ♦Section 27, Part III. fLeitvermogen der Elektrolyte, 1898, p. 43, fig. 37. fKohlrausch and Holbom, Leitvermogen der Elektrolyte, 1898, p. 29. Ii8 Conductivity of Aqueous Solutions. — Part V. HEATERS. The conductivity measurements were made at 18° and approximately 100°, 156°, and 318°. The first of these temperatures was secured with a bath of liquid xylene contained in a well- jacketed metal cylinder. The temperature was regulated by the observer, the bath being heated elec- ti4cally by means of a resistance coil and cooled by a coil of lead pipe, through which cold water was passed. The bath was constantly stirred by a propeller. The temperature could be maintained constant to within 0.01°. The 100° heater was a double-walled copper cylinder heated by steam, similar to that described in section 32, Part IV. The 156° and 218° baths were of the form described in the article by Noyes and Coolidge.* Brombenzene and naphthalene were used as boiling substances, the latter substance proving very satisfactory throughout. The temperature of the brombenzene bath remained constant through sev- eral successive heatings, but in time a slight decomposition necessitated the substitution of fresh liquid. The same shielding devices for securing uniform temperature were employed as in the previous work. THERMOMETERS. Three different thermometers were used in the work — a 0-60° ther- mometer, reading directly to tenths, for the 18° bath, an ordinary Beck- mann style thermometer for the 100° bath, a French mercurial 360° thermometer made by Alvergniat, No. 65650, for the two vapor baths. The 18° point of the first thermometer was determined by comparison with a standard Baudin thermometer. The steam point of the Beckmann ther- mometer was determined each time by introducing the thermometer into a boiling-point testing apparatus of the Regnault type immediately before or after each 100° measurement. The Alvergniat 360° thermometer was similarly calibrated for the 218° point at frequent intervals by immersion in a vapor bath of specially purified naphthalene of the type recommended by Crafts.f For the 156° point the bore was calibrated by the method rec- ommended by Crafts and the value of the scale unit was determined from the interval between the steam and naphthalene points. The temperatures lying between the fixed points were reduced to the gas scale by using Crafts' table of corrections for French glass, our thermometer being of the same make as those used by him. For the boiling point of naphthalene, however, the result more recently obtained by Jaquerod and Wassmer | was adopted. ♦Section 3, Part II. tAm. Chem. J., 5, 307-338 (1883-84). tJ. chim. phys., 2, 72 (1904). Section 48. — Preparation of Substances and Solutions. up METHOD OF PROCEDURE. The procedure was substantially the same as that described by Noyes and Coolidge.* In the case of solutions which were liable to adsorption by the platinum, this effect was largely avoided by allowing the solution to remain in the bomb between the experiments (usually over night) and rinsing the bomb with solution only before introducing a fresh portion for a new experiment. In passing to a diluter solution, the bomb was first steamed out at 318° with the diluter solution instead of with water. In the experiments with a platinized lower electrode, the air pressure within the bomb was reduced at the start to 3 cm. of mercury. In sub- sequent experiments with unplatinized electrodes, the measurement at 18° was made under atmospheric pressure and then the pressure was reduced to about 10 cm. of mercury before going on to the higher temperatures. For each measurement of resistance, three different box resistances were used, generally in the order 100, 110, 111. These series of read- ings were made at 5-minute intervals, and the bomb was kept in the bath until three or more successive series of readings showed no progressive change. In the case of all the solutions which showed any variation in the read- ing, the bomb was removed from the bath, shaken, and returned as quickly as possible, in order to determine whether there was any change in the solution around the electrode. 48. PREPARATION OF THE SUBSTANCES AND SOLUTIONS. For the preparation of sodium chloride, pure commercial salt was twice reprecipitated from saturated solution with hydrochloric acid, filtered, washed, and ignited. Tests for potassium and for sulphate gave negative results. For potassium chloride, a Kahlbaum preparation was purified by reprecipitation from saturated solution in best water by pure hydrochloric acid and subsequent washing and ignition. A flame test showed no so- dium. The potassium chloride and sodium chloride solutions, except the 0.0005 normal sodium chloride solution, were prepared by weighing out a proper quantity of freshly ignited salt (corrected for the buoyancy of the air) and dissolving it in water in a graduated 2,000 or 500 c.cm. flask at 31°, the flask being so calibrated as to contain 3,000 or 500 grams of water at that temperature. The 0.0005 normal sodium chloride solution was made by diluting a 0.002 normal solution by means of a 500 c.cm. and a 2,000 c.cm. flask. Hydrochloric acid was prepared by heating sodium chloride of the same *Section 6, Part II. 120 Conductivity of Aqueous Solutions. — Part V. quality as was used for preparing the sodium chloride solutions with sul- phuric acid and absorbing the hydrochloric acid gas in pure water, after washing it by passing it through a bottle containing a little water. With the help of a specific gravity determination, two liters of approximately 0.1 normal hydrochloric acid were prepared (January 9, 1904) by dilution with pure water. The concentration of this 0.1 normal hydrochloric acid solution was determined by precipitating with silver nitrate and taking the mean of three analyses. One gram of solution was found to give 0.014519 gm. AgCl (a. d.,* 0.07 per cent). Some of the measurements (with tenth normal HCl) were made with a solution diluted from a hydro- chloric acid solution carefully and independently prepared by Mr. Y. Kato. One gram of this latter solution gave 0.019675 gm. AgCl (a. d., 0.03 per cent). For the preparation of pure sodium acetate, about 500 grams of a Kahl- baum sample were crystallized from water, after the salt had been tested with negative results for potassium and the common acids. The salt was partially dried with filter paper. An approximately tenth-normal solution was prepared (March 10, 1904) and analyzed by evaporating it with hy- drochloric acid in a platinum dish, and gently igniting and weighing the residue of sodium chloride. One gram of solution gave on the average, 0.005732 gm. NaCl {a. d., 0.09 per cent). A second solution was similarly prepared June 6, 1904, and analyzed three times, twice immediately after its preparation and again on August 1, 1904. One gram of solution gave (1) 0.005588 gm. (2) 0.005592 gm. (3) 0.005601 gm. NaCl or as the aver- age 0.005594 gm. (a. d., 0.08 per cent). For acetic acid some Kahlbaum "Eisessig" was subjected three times to fractional freezing in a specially devised apparatus, care being taken to exclude moisture. The liquid obtained was then rectified by distillation, about one-tenth being rejected. From the purified substance an approxi- mately tenth-normal acetic acid was prepared (on May 12, 1904). Quali- tative tests for sulphate and chloride gave negative results. The solution was then standardized against a barium hydroxide solution whose strength was determined by titration against two solutions of hydrochloric acid which had been independently standardized by precipitating with silver nitrate and weighing the silver chloride. One gram of solution was found to contain 0.006105 gm. acetic acid (C2H4O2) by titration with one of the solutions and 0.006097 gm. by titration with the other, or, as a mean, 0.006101 gm. acetic acid. The more dilute solutions of hydrochloric acid, sodium acetate and ace- tic acid were prepared by weighing out a definite amount of the stock solu- *a. d. signifies the average deviation of the separate values from the mean. Section 4p. — Errors and their Elimination. 121 tion and either diluting to the mark in a graduated flask or adding a known weight of water. The water used in the preparation of the stock solution had a specific conductance of less than 1.1 X 10""- That used for preparing the more dilute solutions had in almost all cases a specific conductance of 0.75 - 0.95 X 10-". 49. SYSTEMATIC ERRORS AND THEIR ELIMINATION. The possible errors affecting the conductivity values and their elimina- tion or correction have been fully discussed in section 10, Part II. It is therefore necessary only to refer to a few modifications of the corrections applied and to some new difficulties met with in the experiments. VOLATILIZATION OF SOLVENT. The correction for the quantity of solvent in the vapor-space in the bomb was applied in the case of the non-volatile solutes as before, it being calculated from the known volume of the vapor in the bomb and its specific volume interpolated or extrapolated from the data of Zeuner* which extend up to 200°. The correction requires an increase of the con- centration of 0.01 per cent at 100°. 0.03 per cent at 156°, and 0.02 per cent at 218° in the case of our experiments. Although certainly less than the other errors it was always appHed at 156° but not at the other tempera- tures. VOLATILIZATION OF SOLUTE. In the case of the acetic and hydrochloric acid solutions the correction for the vapor-space should also take into account the possible volatility of these solutes. In these cases the total correction for volatilized solvent and solute was experimentally determined at 218° by varying the quantity of solution placed in the bomb and measuring the conductances. From the variations of these with the known variations of vapor-space the cor- rection for the vapor-space existing in the ordinary measurements could be readily calculated. Thus, for three different volumes of a 0.01017 nor- mal acetic acid placed in the bomb, the vapor-spaces and conductances at 2 J 8° were as follows: Vapor-space (cubic centimeters) . . 1.5 11.1 25.4 Specific conductance X 10° 447.3 447.8 448.5 It is evident that since 24 c.cm. of vapor-space cause an increase in the conductance of 0.27 per cent, that produced by the 1.5 c.cm. usually pres- ent would be about 0.02 per cent, which is the magnitude of the correction *Landolt-B6mstein-Meyerhoffer, Tabellen, p. 127 (1905). 122 Conductivity of Aqueous Solutions. — Part V. for the solvent alone, indicating that this solute does not volatilize appre- ciably. The same result was obtained with hydrochloric acid. CONDUCTANCE OF THE WATER. A correction was applied in the case of the two salts (but not in that of the two acids) for the conductance of the impurities in the water. This will be fully described in section 51, in connection with the data upon which it is based. INCONSTANT BRIDGE READINGS. No Special trouble was encountered in the sodium chloride measure- ments. It was observed, however, in working with the diluter hydro- chloric acid solutions that the bridge readings at 18°, and to a less extent at other temperatures, shifted rapidly when the current was kept on, the displacement being generally in the direction of increasing conductivity. The shifting reached a limit in about three minutes, but on discontinuing the current for a minute or two the reading returned to approximately its original value. It was considered likely that this was due to the ejection by the alternating current of solute which had been adsorbed by the lower electrode. It was not permissible to adopt the final reading, since the ef- fect of ejection would be to concentrate the solution within the cup ; and the initial reading could not be accurately determined. It was found that the shifting of the reading was greater, the louder the tone of the induction coil. A Nernst string interrupter, with low vibration frequency, was there- fore substituted for the ordinary induction coil. The total shifting with the string interrupter was much less, and it took place so slowly that no diffi- culty was experienced in making a satisfactory reading. Except at the highest resistances measured the minimum with this interrupter was very good. In working with the sodium acetate and the 0.0005 normal hydrochloric acid solution great difficulty was experienced, when either induction coil was employed, in securing constant readings at 218°, Cell i (see section 50) being then in use. Even after sufficient time had elapsed for the bomb to acquire the temperature of the bath, successive readings made during a half hour exhibited an irregular, somewhat oscillatory shifting through several centimeters on the bridge in the direction of decreased conduc- tivity. If instead of reducing the pressure in the air space originally to 2 cm. of mercury as had been the practice, the air was allowed to remain in the bomb, the direction of shifting was reversed, these tests being made with a 0.01 normal sodium acetate solution. It was not possible to find an intermediate pressure which afforded constant readings. The effect of Section 4p. — Errors and their Elimination. 12^ removing and shaking the bomb in the usual manner was to cause partial reversion towards the original reading, but not to prevent the recurrence of shifting. To see whether the shifting was due to uneven temperature some experiments were made, such as altering the level of the vapor in the bath and the manner of shielding, but with negative results. The removal of the platinum-black from the electrode almost entirely obviated this trouble, however, for the subsequent bridge-readings with sodium acetate and dilute hydrochloric acid at 218° were constant to within 0.2 to 0.3 mm. for a sufficient period. The pressure was reduced to 2 cm. pre- vious to these measurements, as before. The change in reading was ap- parently due either to formation of bubbles on the electrode, or to an ad- sorption effect, but its cause could not be fully determined. The use of a polished lower electrode (in Cell 11) gave rise, however, to a similar difficulty under other conditions, namely, to a shifting of the bridge-reading in the direction of decreased conductance at 18° and to a less extent at higher temperatures. This was found to be due to the formation of bubbles and was obviated at 18° by postponing evacuation of the air space in the bomb till after the measurement at that temperature had been made. As a similar effect was observed to some extent at 100° and 156°, the air pressure was thereafter reduced only to about 12 cm. before the measurements at the three higher temperatures. The subse- quent measurements proceeded satisfactorily, the same method being fol- lowed also after the introduction of the cylindrical electrode (Cell iii). The air pressure that obtains in the bomb at 218°, for the usual volume of liquid, after a reduction of the pressure to 12 cm. at 18°, is only about two atmospheres, which does not affect the conductance to a considerable extent. In order to diminish the adsorption, the rinsing of the bomb with water was omitted in the case of hydrochloric acid, acetic acid, and sodium ace- tate, and a portion of the solution to be measured was left in the cell for some hours previous to the experiment, in order to thoroughly saturate the electrode, a new portion of the same solution being introduced just before the measurements were made. The experiments with sodium acetate were at first conducted with the quartz cup in the bomb. The readings with the solutions of it diluter than tenth-normal were not as constant as with other solutes. It was thought that the inconstancy might be due to a contamination of the solution by its attacking the quartz cup and a consequent concentration of the solution within the cup. This difficulty was apparently obviated (cell iii) by the in- troduction of the new form of electrode and quartz insulator as described in section 47. 12/^ Conductivity of Aqueous Solutions. — Part V. INSTRUMENTAL ERRORS. In working with dilute solutions of hydrochloric acid it was found that commutating the current from the secondary coil gave a difference of reading of 0.1 — 0.4 mm. The coil was tested with known resistances and found to show an asymmetric reading only with the higher resistances, an error of 0.1 per cent or more being involved when the resistance ex- ceeded 5,000 ohms. This error was corrected for, however, by taking double commutated readings in all such cases and finding the mean. It was found that commutating the telephone had no effect even with the highest resistances used. In the measurement of very high resistances (those above 10,000 ohms) the proximity of the induction coil to the bridge was found to have an influence on the reading, if the distance was less than 40 cm. Such prox- imity was therefore avoided. 50. CONDUCTANCE-CAPACITY OF THE APPARATUS. The conductance-capacity was calculated from measurements made in the bomb at 18° of the conductance of various known solutions of potas- sium chloride and sodium chloride and from the values of the equivalent conductance of these salts as given by Kohlrausch and Maltby.* In the course of the work three different values of the conductance- capacity were used, corresponding to the changes made in the lower elec- trode. In all the measurements made prior to April 4, 1904, the bomb was used as it was left by Noyes and Coolidge, in which form it will be designated cell i. On that date the platinizing was mechanically removed from the electrode, which caused a slight change in the capacity, the new value of which (cell ii) was used in connection with all measurements be- tween April 4, and June 25, 1904. The quartz cup was then removed from the bomb and a cylindrical electrode substituted for the flat one. The new conductance capacity (cell iii) then obtained is that used in calculating all the measurements made subsequently to June 25, 1904. The following table shows the actual conductance at 18° of the solutions diminished by that of the water, and the conductance-capacities calculated therefrom. The conductances expressed in reciprocal ohms are given in the table multiplied by 10'. The concentration is expressed in milli-equiv- alents per liter at 18°. The conductance-capacity is, as usual, the factor by which the observed conductance must be multiplied to give the specific conductance. Each of the measurements was made upon separate, freshly prepared solutions. *Wissensch. Abhandlungen phys.-techn. Reichsanstalt, 3, 310 (1900). See also Lan- dolt-Bornstein-Meyerhoffer, Tabellen, p. 744 (1905). Sections 50 and 57. — Conductance-capacity and Water Correction. 12^ Table 31. — Conductance-capacity. — Data and final values. Date. Cell No. Salt. Concentra- tion at 18°. Conduct- ance X 10«. Conductance-capacity. Separate values. Final values. 1903 Nov. 20 1904 Jan. 20 Jan. 21 .Tan. 22 Jan. 22 June 11 June 11 June 11 June 29 June 29 July 12 July 12 July 12 I II III NaCl.... NaCl.... NaCl.... KCl NaCl.... KCl KCl NaCl.... NaCl.... KCl KCl KCl KCl 9.999 9.995 100.52 99.77 99.86 9.990 49.95 9.992 9.993 9.990 4.996 5.002 9.999 1038.1 1039.9 9440 11400 9361 1242.7 5865 1034.0 6856 8233 4194 4197 8246 0.9819 0.9799 0.9800 0.9804 0.9816 0.9842 0.9858 0.9851 0.14860 0.14856 0.14820 0.14827 0.14845 0.9808 0.9850 0.14842 The variation of these vahies of the conductance-capacity with the tem- perature was computed upon the basis and in the manner described in sec- tion 36j Part IV. The percentage corrections to be applied to them at the various temperatures are as follows : Cells I and n Cell in 100° 156° 218° 0.14 — 0.25 — 0.39 0.10 — 0.18 — 0.26 51. THE WATER CORRECTION. CONDUCTANCE OF THE WATER. In order to determine the conductance of the impurities in the water under the conditions of the experiments, water having about the same con- ductance as that used in making up the solutions was placed in the bomb, which had been previously twice heated to 218° with fresh portions of conductivity water to remove adsorbed substance. The conductance was measured at 18° and the bomb was heated in each of the various baths for the length of time usual in the measurements, being finally brought back in the reverse order to 18°. Table 32 contains the results of two such experiments, which served as the basis for the water correction. In the case of the measurements with sodium chloride and sodium ace- tate (both with and without acetic acid added) the mean value here tabu- lated of the conductance of the water corresponding to the same stage of the experiment was subtracted from the measured conductance of the solution (except that in the few cases where the solutions were prepared from water having a specific conductance less than 0.75 or greater than 0.95 X 10"° these corrections were varied in the ratio of that conductance to 0.85 X 10'°, which was the conductance of the water used in the two experiments before its introduction into the bomb). No correction for the impurities in the water was applied to the measured conductances of 126 Conductivity of Aqueous Solutions. — Part V. the hydrochloric acid, since their effect is ordinarily to decrease by an in- definite amount the conductance of a solution of a strong acid rather than to increase it. In the case of acetic acid (and of sodium acetate with ace- tic acid added) the effect of the impurities would depend on their nature: bases {e. g., ammonium hydroxide) and salts {e. g., ammonium carbonate, sodium silicate) would increase the conductance of the solution by an amount equal to or greater than their own conductance, but very weak acids (for example, carbonic or silicic) owing to the reduction of their ionization would scarcely influence it at all. Since the water used was distilled from an alkaline solution (of permanganate) and was scarcely exposed to the atmosphere, it seems most probable that the impurities present are basic or saline; and therefore that it is best to subtract the conductance of the water. It has seemed advisable, however, to apply this correction to the final rather than to the separate values, and to give for comparison both the corrected and uncorrected results. Table 32. — Actual conductance of the water. Conductance X lO^. 18°. 100°. 156°. 218°. 156°. 100°. 18°. Dec. 16, 1903 1.056 0.854 3.07 3.11 5.14 5.45 7.30 7.35 6.00 5.93 4.80 4.28 2.03 1.67 Mar. 12, 1904 Mean 0.955 3.09 5.30 7.32 5.97 4.54 1.85 Specific conductance X 10° 0.937 3.03 5.18 7.15 5.84 4.45 1.82 52. CONDUCTIVITY DATA FOR SODIUM CHLORIDE, HYDROCHLORIC ACID. ACETIC ACID, AND SODIUM ACETATE. The following table contains the direct results of the observations and the equivalent conductances computed from them. The first column gives the date of the experiment ; the second, the cell-number of the conductivity vessel ; the third, the concentration at 4° in milli-equivalents per liter (the number of milli-equivalents being based upon the atomic weights referred to oxygen as 16.000 and the weights being reduced to vacuo) ; the fourth, the temperature on the hydrogen-gas scale at which the conduct- ance was measured; the fifth, the concentration at the temperature ot the measurement, calculated by dividing the concentration at 4° by the ratio of the specific volume of the solution at that temperature to its speci- fic volume at 4°*, and applying the correction at 156° for the vapor space; ♦The specific-volume ratio at 100° and 156° was assumed to be identical with that for pure water. At 100° this value is 1.0432 according to Matthiessen and Rosetti ; at 156° it is 1.0976, interpolated graphically from Hirn's values [Ann chim phys (4), 10, 32 (1867)] at 140.17°, 151.00°, and 160.68° after correcting them to the pres- sures of saturated aqueous vapor with the help of the compression-coefficient of water, derived by extrapolation from the data of Pagliani and Vincentini which extend only to 100° [Landolt-Bornstein-Meyerhoffer, Tabellen 60 (1905)]. Section §2. — The Conductivity Data. 127 the sixth, the measured conductance in reciprocal ohms, multipHed by 10^ and corrected for the instrumental errors (those in the slide wire and the resistance coils) and for the lead resistance; the seventh, the conductance- capacity of the vessel (the values being omitted when identical with those in a preceding experiment) ; the eighth, the equivalent conductance cal- culated from the value of the conductance in the sixth column by applying (in the case of the two salts) the water-correction (see section 51), mul- tiplying by the conductance-capacity in the seventh column, and dividing by the concentration given in the fifth column. Table 33.— The conductivity data. SODIUM CHLORIDE. Cell No. Concentra- tion at 4°. Tempera- ture, t°. Concentra- tion at f. Conduct- ance X 100. Conductance capacity. Equivalent conductance. 1904 Jan. 4. 0.5003 Jan. 5. 0.5003 Jan. 8. 0.5003 Jan. 9. . 1903 Nov. 28 Dec. 17 Dec. 18. 0.5002 2.0009 2.0009 2.0009 18.00 100.26 156.3 222.3 156.5 100.30 18.00 18.00 100.38 157.2 320.7 158.5 100.15 18.00 18.00 99.68 156,15 316.9 156.7 99.57 18.00 18.00 216.6 18.07 218.65 18.00 99.76 157.15 220.8 158.0 99.86 18.00 18.00 100.19 158.8 321.0 160.1 100.29 18.00 0.4996 0.4795 0.4559 0.4190 0.4558 0.4795 0.4996 0.4996 0.4795 0.4555 0.4201 0.4548 0.4796 0.4996 0.4996 0.4797 0.4559 0.4334 0.4556 0.4797 0.4996 0.4996 0.4326 1.9981 1.6850 1.9981 1.9185 1.8215 1.6796 1.8199 1.9184 1.9981 1.9981 1.9174 1.8184 1.6790 1.8160 1.9177 1.9981 55.62 177.62 260.38 331.4 261.36 179.34 .j6.48 55.78 178.03 263.3 334.1 272.4 185.80 59.45 55.94 177.24 260.8 327.0 262.6 179.63 57.28 55.86 325.9 215.81 1,371.9 316.19 686.1 1,009.5 1,268.3 1,016.7 691.1 317.87 315.70 689.0 1,018.8 1,273 . 2 1,030.4 695.4 218. 6i 0.9808 0.9794 0.9783 0.9770 0.9783 0.9794 0.9808 107.34 356.5 547.5 755.5 548.3 357.0 107.30 107.65 357.3 554.3 760.1 573.3 370.3 113.1 107.61 354.3 546.2 736.1 548.6 355.6 108.17 107.46 733.1 105.47 733.2 105.66 348.7 539.4 733.5 543.3 350.5 106.05 105.41 350.3 545.3 736.6 551.9 352.8 106.43 128 Conductivity of Aqueous Solutions. — Part V. Table 33. — The conductivity data — Continued. SODIUM CHLORIDE. Date. Cell No. CoDcentra- lion at 4°. Tempera- ture, <°. Concentra- tion at f. Conduct- ance X 10«. Conductance capacity. Equivalent conductance. 1 2 3 4 5 6 7 8 1903 Nov. 17 Nov. 19 Nov. 20 Nov. 23 1904 Jan. 20 I I I I I 10.013 10.013 10.013 10.013 10.009 18.07 99.72 155.5 218.5 155.75 99.68 18.07 18.07 100.30 18.07 18.07 99.81 155.65 318.6 155.5 18.07 18.00 100.14 157.3 216.9 157.9 100.05 18.00 9.999 9.601 9.130 8.434 9.127 9.601 9.999 9.999 9.597 9.999 9.999 9.600 9.128 8.433 9.130 9.999 9.995 9.594 9.111 8.450 9.104 9.594 9.995 1,041.4 3,388 4,777 5,967 4,786 3,394 1,048.5 1,040.3 3,399 1,040.7 1,041.5 3,393 4,816 5,969 4,777 1,044.8 1,041.5 3,395 4,810 5,936 4,835 3,303 1,041.9 103.04 335.1 511.2 690.1 512.3 335.4 102.63 101.93 336.3 101.97 102.05 335.5 515.5 690.5 511.2 102.27 103.09 336.0 515.8 685.2 517.7 336.6 103.03 HYDROCHLORIC ACID. 1904 Feb. 10 Feb. 13 Feb. 13 Feb. 15 Mar. 15 Mar. 16 I I I I I I 0.4991 0.4996 0.4996 0.4996 0.4443 0.4993 18.00 100.17 158.5 18.00 100.16 158.4 218.6 159.3 100.08 18.00 18.00 18.00 18.00 217.7 18.00 18.00 99.81 156.8 217.9 157.3 99.85 18.00 0.4985 0.4784 0.4538 0.4989 0.4789 0.4542 0.4208 0.4538 0.4789 0.4989 0.4989 0.4989 0.4436 0.3746 0.4436 0.4985 0.4786 0.4546 0.4209 0.4543 0.4786 0.4985 190.77 408.8 497.5 191.09 408.4 494.4 532.4 500.8 408.1 190.53 190.77 190.77 169.04 475.7 168.69 190.15 406.4 493.5 533.1 495.7 408.2 190.15 0.9808 0.9794 0.9783 0.9770 375.4 836.8 1,073.8 375.7 835.4 1,065.0 1,236.2 1,079.6 834.5 374.6 375.0 375.0 373.8 1,240.4 373.0 374.1 831.6 1,063.3 1,237.5 1,067.6 835.3 374.1 Section 52. — The Conductivity Data. Table 33. — The conductivity data — Continued. 129 HYDROCHLORIC ACID. Cell No. 1904 Apr. 8. Apr. 9. Apr. 15. Apr. 16. Feb. 16. Feb. 17. Feb. 18. Feb. 20. Feb. 23. Feb. 24. II II II II Concentra- tion at 4°. 0.4977 0.4977 0.4995 0.4995 1.9997 1.9997 1.9997 9.994 9.994 9.994 Tempera- ture, t°. 18.00 100.05 156.3 218.1 156.3 100.01 18.00 18.00 99.90 156.1 217.9 156.2 99.76 18.00 18.00 99.90 18.00 99.60 217.8 18.00 99.57 156.8 217.6 157.5 99.59 18.00 18.00 99.85 157.8 218.2 157.9 99.87 18.00 18.00 218.7 18.00 18.00 100.34 157.5 218.9 157.8 100.36 18.00 18.00 99.75 156.8 217.8 156.4 99.64 18.00 18.00 217.1 18.00 Concentra- tion at i°. 0.4970 0.4663 0.4534 0.4195 0.4534 0.4662 0.4970 0.4970 0.4771 0.4535 0.4196 0.4535 0.4772 0.4970 0.4988 0.4789 0.4988 0.4790 0.4212 1.9970 1.9176 1.8210 1.6867 1.8197 1.9176 1.9970 1.9970 1.9173 1.8192 1.6856 1.8190 1.9172 1.9970 1.9970 1.6839 1.9970 9.981 9.578 9.094 8.413 9.092 9.578 9.981 9.981 9.583 9.101 8.428 9.105 9.583 9.981 9.981 8.435 9.981 Conduct- ance X 108. Conductance capacity. 189.65 406, 493, 533 494 407 189.79 189.67 406.1 492.7 533.2 493.8 406.1 189.79 190.37 406.9 190.20 406.7 534.0 761.2 1,616.3 1,956.6 2,112.4 1,965.4 1,617.3 761.5 760.5 1,616.6 1,960.8 2,097.3 1,962.4 1,616.0 759.4 760.6 2,106.0 761.2 3,747 7,919 9,514 10,109 9,530 7,924 3,743 3,752 7,904 9,506 10,145 9,473 7,892 3,736 3,748 10,114 3,747 Equivalent conductance. 0.9850 0.9836 0.9825 0.9811 0.9808 0.9794 0.9783 0.9770 375.8 837.9 1,068.5 1,246.7 1,071.1 839.1 376.1 375.9 837.1 1,067.5 1,246.7 1,069.8 837.0 376.1 375.9 835.8 375.6 835.1 1,243.8 373.8 825.5 1,051.2 1,223.3 1,056.8 826.0 374.0 373.5 825.7 1,054.5 1,215.9 1,055.6 825.5 373.0 373.5 1,221.9 374.8 368.2 809.8 1,023.5 1,173.9 1,025.5 810.2 367.8 368.7 807.8 1,021.9 1,176.1 1,017.9 806.6 367.2 369.3 1,171.3 368.2 130 Conductivity of Aqueous Solutions. — Part V. Table 33. — The conductivity data — Continued. HYDROCHLORIC ACID. Date. Cell No. ConccQtra- tion at 4°. Tempera- ture, <°. Concentra- tion at t^. Conduct- ance X 10«. Conductance capacity. Equivalent conductance. 1 2 3 4 5 6 7 8 1904 Mar. 18 Mar. 21 I I 100.66 100.66 18.00 99.78 156.2 217.6 156.2 99.57 18.00 18.00 100.26 157.3 218.7 157.8 100.27 18.00 100.52 96.51 91.73 84.91 91.72 96.53 100.52 100.52 96.48 91.62 84.76 91.57 96.48 100.52 35,910 74,370 87,570 90,450 87,620 74,410 35,950 35,900 74,490 87,740 90,220 87,750 74,560 35,950 350.4 754.7 934.0 1,040.7 934.8 755.0 350.8 350.3 756.2 936.9 1,039.9 937.5 756.9 350.8 SODIUM ACETATE. Apr. 23 : II ! 0.5008 Apr. 26 ! II Apr. 27. Apr. 12. Apr. 20. II II 0.4988 0.5015 1.9903 II 1.9980 18.00 100.36 156.4 218.6 156.5 100.27 18.00 18.00 99.79 156.0 217.8 156.1 99.81 18.00 18.00 100.03 156.3 218.1 156.5 100.05 18.00 18.00 99.51 156.8 155.7 99.60 18.00 18.00 99.50 15S.3 217.3 155.3 99.57 18.00 0.5003 0.4800 0.4563 0.4218 0.4562 0.4800 0.5002 0.4981 0.4782 0.4545 0.4206 0.4545 0.4782 0.4981 0.5008 0.4808 0.4569 0.4227 0.4568 0.4808 0.5008 1.9876 1.9087 1.8124 1.8143 1.9086 1.9876 1.9953 1.9160 1.8222 1.6861 1.8222 1.9160 1.9953 39, 136, 209, 274. 207, 136, 39, 39, 136, 208, 275, 206, 136, 39, 39, 137, 209, 277, 208, 137, 40, 149, 518, 790, 785, 520, 151 151, 521 790 1,036 789, 521, 151, 0.9850 0.9836 0.9825 0.9811 75.82 275.3 441.9 625.7 436.1 272.8 74.83 76.28 275.3 441.4 628.7 436.9 272.4 75.17 75.80 274.2 439.7 637.7 435.7 271.9 75.09 73.77 365.9 425.9 422.0 265.7 74.16 74.57 266.9 424.6 600.3 423.6 266.4 74.30 Section 52. — The Conductivity Data. Table 33. — The conductivity data — Continued. 131 SODIUM ACETATE. Cell No. 1904 Apr. 21. July 14. Mar. 24. Mar. 25. June 10. June 27. July 5. July 6. July 7. July 11. June 16. II III II III III III III III II Concentra- tion at 4°. 1.9980 1.9985 10.002 10.002 10.000 9.992 9.984 10.006 10.018 10.001 76.06 Tempera- ture, P. 18.00 99.94 156.0 218.1 156.1 100.07 18.00 18.00 156.4 217.9 18.00 18.00 100.40 157.3 156.9 100.36 18.00 18.00 100.20 156.8 156.7 100.04 18.00 18.00 100.20 156.1 156.2 100.09 18.00 18.00 156.1 217.9 18.00 18.00 155.5 217.6 18.00 18.00 155.9 217.7 18.00 18.00 156.0 217.8 18.00 18.00 155.8 217.4 18.00 18.00 99.98 156.4 218.0 Concentra- tion at P. 1.9953 1.9154 1.8209 1.6840 1.8207 1.9153 1.9953 1.9958 1.8207 1.6850 1.9958 9.998 9.585 9.104 9.107 9.587 9.998 9.988 9.587 9.108 9.109 9.588 9.988 9.986 9.585 9.113 9.112 9.585 9.986 9.978 9.105 8.424 9.978 9.971 9.103 8.421 9.971 9.992 9.120 8.438 9.992 10.004 9.130 8.447 10.004 9.988 9.116 8.438 9.988 75.95 72.91 69.29 64.11 Conduct- ance X 10«. 151.57 523.3 792.5 1,036.3 791.8 523.6 151.63 1,008.0 5,280 6,883 1,010.3 723.7 2,494.0 3,751 3,740 2,496.0 724.3 723.5 2,485 3,733 3,727 2,487 725.5 722.1 2,483.9 3,729 3,724 2,478.9 723.4 4,717 24,289 31,390 4,812 4,791 24,661 31,730 4,796 4,808 24,534 31,445 4,815 4,807 24,600 31,480 4,824 4,811 24,552 31,490 4,823 4,904 16,504 24,408 30,350 Conductance capacity. Equivalent conductance. 0.14842 0.14815 0.14803 0.9808 0.9794 0.9783 0.9850 0.9836 0.9825 0.14842 0.14815 0.14803 0.9850 0.9836 0.9825 0.9811 74.55 267.8 425.9 601.2 425.4 267.6 74.30 74.52 426.8 601.1 74.24 70.98 254.6 402.6 401.1 254.4 70.95 70.96 253.6 400.4 399.7 253.7 71.06 71.14 254.6 401.5 400.9 254.0 71.18 70.07 395.1 551.4 71.40 71.23 400.8 5.56.9 71.21 71.33 398.0 550.8 71.34 71.23 398.6 550.8 71.39 71.40 398.4 551.5 71.49 63.59 222.66 346.0 464.4 13^ Conductivity of Aqueous Solutions. — Part V. Table 33. — The conductivity data — Continued. SODIUM ACETATE. Date. Cell No. Concentra- tion at 4°. Tempera- ture, 19 . Concentra- tion at ^. Conduct- ance X 105. Conductance capacity. Equivalent conductance. 1 2 3 4 5 6 7 8 1904 June 23 June 14 II II 76.22 95.55 18.00 100.15 218.3 156.3 100.15 18.00 18.00 100.12 156.2 218.2 156.1 100.05 18.00 76.11 73.06 64.22 69.44 73.06 76.11 95.42 91.59 87.06 80.52 87.07 91.59 95.42 4,927 16,578 30,390 24,426 16,556 4,923 6,034 20,303 29,900 37,020 30,050 20,318 6,0.50 63.75 223.21 464.1 345.5 222.90 63.68 62.28 218.17 337.4 451.0 339.0 218.19 62.43 ACETIC ACID. May 20., May 24., June 2. May 25. May 26. May 12. II 11 II II II II 10.302 10.034 10.003 30.040 30.00 101.67 18.00 99.40 155.4 217.4 155.6 99.64 18.00 18.00 99.90 156.1 217.9 18.00 18.00 100.08 156.1 218.1 18.00 18.00 99.95 156.2 217.9 156.2 99.95 18.00 18.00 99.83 156.2 217.6 156.4 99.75 18.00 18.00 99.95 318.0 10.288 9.880 9.394 8.692 9.393 9.878 10.288 10.020 9.620 9.143 8.460 10.020 9.990 9.589 9.115 8.431 9.990 30.00 28.80 27.37 25.33 27.37 28.80 30.00 29.96 28.76 37.33 25.30 27.33 38.76 29.96 101.53 97.47 85.70 150.07 256.4 223.41 146.85 223.22 256.5 149.87 148.11 353.3 330.84 146.53 148.02 147.90 352.9 219.48 143.95 148.10 259.0 442.4 382.7 249.96 382.5 442.6 259.3 259.5 443.2 382.7 250.7 381.1 443.6 359.6 477.9 814.2 458.2 0.9850 0.9836 0.9835 0.9811 14.369 25.53 23.37 16.577 33.35 35.55 14.349 14.560 25.91 23.73 16.995 14.550 14.583 25.94 23.66 16.753 14.603 8.503 15.109 13.738 9.684 13.730 15.116 8.515 8.533 15.133 13.755 9.719 13.700 15.136 8.536 4.636 8.217 5.246 Section jj. — Summary of Equivalent Conductances. 1^3 Table 33. — The conductivity data — Continued. ACETIC ACID. Date. Cell No. Concentra- tion at 4°. Tempera- ture, P. Concentra- tion at P. Conduct- ance X 105. Conductance capacity. Equivalent conductance. 1 2 3 4 5 6 7 8 May 13 May 16 II 101.67 101.67 18.00 99.98 156.0 217.9 156.1 100.03 18.00 18.00 30.00 99.56 101.02 98.02 155.8 217.7 99.67 18.00 101.53 97.46 92.65 85.71 92.65 97.46 101.53 101.53 101.24 97.50 97.39 97.61 92.67 85.74 97.49 101.53 478.5 815.6 704.2 457.3 703.7 813.2 478.0 478.3 572.0 815.5 815.0 815.7 705.0 459.4 814.8 478.3 4.642 8.231 7.468 5.236 7.463 8.307 4.638 4.641 5.565 8.228 8.231 8.221 7.475 5.257 8.331 4.641 53. SUMMARY OF THE EQUIVALENT-CONDUCTANCE VALUES. The separate conductance values given in table 33 were all corrected so as to correspond to the uniform temperatures of 18°, 100°, 156°, and 318° by means of temperature-coefficients obtained by plotting those values. In the case of acetic acid, since the equivalent conductance varies rapidly with the concentration, the preceding values w^ere also corrected so as to eliminate the small variations in concentration in the different experiments. This was done with the help of the equation A^C = const., the substantial validity of which will be shown subsequently. The so-corrected equiva- lent conductances are summarized in table 34. The concentration is ex- pressed in milli-equivalents (referred to oxygen as 16.00) per liter at 4°. In the columns headed "Initial" are given the equivalent conductances obtained from the measurement at the temperature in question before go- ing to the higher temperatures ; while in the columns headed "Final" are given the equivalent conductances obtained after returning to the temper- ature in question from a higher one. The means are based upon both the initial and final values in cases where there was no systematic difference between them ; otherwise upon the initial values alone : in which of these ways the mean value was obtained in each separate case, is indicated in the table by its position. From a comparison of the separate initial values at any temperature and concentration the degree of agreement of the deter- minations made at different times, and often with different solutions, may be seen. A comparison of the initial and final values in the separate ex- periments shows the contamination that resulted from the heating. 134 Conductivity of Aqueous Solutions. — Part V. Table 34. — Equivalent conductance at round temperatures. SODIUM CHLORIDE. Date. Concen- tration at 4°. 18° 100° 156° 218°. Initial. Final. Initial. Final. Initial. Final. 1904 Jan. 4 Jan. 5 Jan. 8 Jan. 9 Mean .. 1903 Nov. 28... Dec. 17... Dec. 18... Mean . . Nov. 17... Nov. 19... Nov. 20... Nov. 23... Jan. 20... Mean .. 0.5003 0.5003 0.5002 0.5002 107.34 107.65 107.61 *tl07.46 107.30 113.10 108.17 355.7 356.2 355.4 356.1 369.8 357.1 546.6 *t550.4 545.8 546.7 565.0 546.4 742.6 *t752.0 739.4 737.3 0.5002 107.53 355.8 546.2 739.8 2.0009 2.0009 2.0009 105.31 105.66 105.41 106.05 106.43 349! 5 349.7 351.1 352.0 536.0 536.4 537.0 538.9 731.3 725.4 727.9 2.0009 105.46 349.6 536.2 728.2 10.013 10.013 10.013 10.013 10.009 101.88 101.77 101.81 101.89 102.09 »102.47 102.11 102.03 335.9 335.4 336.1 335.6 336.4 512.7 512.1 513.1 512.7 511.9 688.7 688.8 688.2 10.012 101.94 336.0 512.5 688.6 HYDROCHLORIC ACID. 1904 Feb. 10.. Feb. 12.. Feb. 13.. Feb. 15.. Mar. 15.. Mar. 16.. Apr. 8.. Apr. 9.. Apr. 15.. Apr. 16.. Mean . Feb. 16.. Feb. 17.. Feb. 18.. Mean . Feb. 20.. Feb. 23.. Feb. 24.. Mean . Mar. 18.. Mar. 21. . Mean. . 0.4991 0.4996 0.4442 110.4992 0.4977 0.4995 0.4995 375.4 375.7 375.0 375.0 373.8 374.1 375.8 375.9 375.9 375.6 374!6' 373.0 374.1 276.1 376.1 836.0 834.6 834.1 1,064.3 *§1,056.7 1,059.7 1,068.4 1,067.2 1,068 14 1,063! 2 1,070.1 1,069.1 *§1,234!6 1,241! 2 1,237.8 1,246.4 1,247.0 1,244.3 832.5 837.7 837.6 836.2 837.0 836.0 839.1 838.2 0.499 375.2 835.9 1,064.9 1,343.3 1.9997 373.8 373.5 373.5 374.0 373.0 373.8 827.4 826.4 827.8 826.1 1,048.5 1,048.4 1,051.7 1,048.8 1,284.2 1,215.4 1,220.3 2.000 373.6 826.9 1,049.3 1,219.6 9.994 368.2 368.7 368.3 367.8 367.2 368.2 808.3 808.9 808.7 808.1 1,018.5 1,019.2 1,019.5 1,016.6 1,172.0 1,176.5 1,173.2 9.994 368.1 808.5 1,018.5 1,173.9 100.66 350.4 350.3 350.8 350.8 755.6 755.2 756.7 755.8 933.6 933.5 934.3 932.8 1,041.3 1,038.8 1,040.1 100.66 350.6 755.8 933 .6 •Data indicated by stars are not included in the mean, on account of their wide deviation from the other values or for some known cause pi error stated in the foot notes. tit is evident from the disagreement of the initial and final values that in tiiis experiment contamination occurred at the higher temperatures. tThe reading in this case was not of the usual accuracy. SAs the readings were not constant, this value was omitted in computing the mean. II The water used in preparing this solution was unusually good, having a specific conductance of only 0.5 X lO-e. Section 5J. — Summary of Equivalent Conductances. 755 Table 34. — Equivalent conductance at round temperatures — Continued. SODIUM ACETATE. Date. Concen- tration at 4°. 18 100° 156 218°. Initial. Final. Initial. Final. Initial. Final. 1904 Apr. 23... Apr. 26... Apr. 27... Mean . . Apr. 12... Apr. 20... Apr. 21... July 14... Mean .. Mar. 24.. . Mar. 25... June 10... June 27... July 5... July 6... July 7. . . July 11... Mean . . June 16... June 23.. . Mean .. June 14. . . 0.5008 0.4988 0.5015 75.82 76.28 75.80 74.83 75.17 75.09 374.3 375.9 374.1 273.0 373.9 271.8 440.7 441.4 438.8 434.5 436.6 434.1 623.8 629.3 637.4 0.500 75.97 75.03 374.8 272.2 440.3 435.0 636.8 1.9903 1.9980 1.9980 1.9985 *73.77 74.57 74.55 74.52 74.16 74.30 74.30 74.34 267.2 268.2 268.0 266.7 267.3 267.4 423.7 426.6 425.9 427.3 422.8 435.6 435.1 602.3 600.9 601.4 1.996 74.55 74.28 267.8 267.1 425.9 434.5 601.5 10.003 10.002 10.000 9.992 9.984 10.006 10.018 10.001 70.98 70.96 71.14 *70.07 71.33 71.33 71.23 71.40 70.95 71.06 71.18 71.40 71.31 71.34 71.39 71.49 253.6 253.1 354.1 253.5 253.6 353.8 399.3 398.4 401.3 394.8 403.1 398.3 398.6 398.9 398.8 397.9 400.4 551.6 *557.9 551.5 551.3 552.9 10.00 71. 33 253.6 399 .1 551.8 76.06 76.22 63.59 63.75 'esies 222.68 223.89 332.58 345.2 344.9 464.3 463.6 76.14 63. 67 222.72 345 .1 464.0 95.55 62.28 *63.43 317.83* 218.09 337.0 *338.8 450.7 ACETIC ACID. 1904 May 20... May 24... June 2... Mean .. May 25... May 26... Mean . . May 12... May 13... May 16... Mean .. 10 14.585 14.589 14.583 14.564 14.579 14.603 35.93 35.96 35.94 35.94 23.68 »t23.79 23.67 23.68 16.730 *tl7.013 16.768 16.749 10 14.586 14.581 35.94 23.68 30 8.513 8.533 8.534 8.536 15.134 15.123 15.131 15.138 13.761 13.764 13.753 13.718 9.685 9.683 9.684 30 8.533 8.530 15.134 13.763 100 4.673 4.679 4.678 "4!678 8.383 8.397 8.394 8.373 8.387 7.528 7.530 7.524 5.288 5.271 5.386 100 4.677 8.291 7.529 5.282 *Omitted in computing the mean. tOmitted in computing the mean since the readings were uncertain, owing to the fact that a relatively high vacuum was produced in this case, which permitted the formation of bubbles on the electrode. In connection with these results, attention may be called to the degree of agreement of the "initial" and "final" values, which gives a measure of the change in concentration resulting from the heatings. In the cases of the 0.1 and 0.01 normal solutions of sodium chloride, hydrochloric acid, acetic acid, and sodium acetate the differences between these two sets of 136 Conductivity of Aqueous Solutions. — Part V. values at all temperatures are scarcely greater than the possible experi- mental errors of the separate determinations. Remarkably enough, the same is true, in the case of the hydrochloric acid, of the still more dilute solutions, 0.002 and 0.0005 normal. In the case of sodium chloride at these two concentrations the final values at 18° are as a rule somewhat larger than the initial values, but on an average only by 0.5 per cent. In the case of sodium acetate, on the contrary, the final values are smaller by 0.3 to 0.4 per cent for the 0.002 normal solution and by 1.0 to 1.5 per cent for the 0.0005 normal solution. Table 35 contains a summary of the mean values of the equivalent conductances given in table 34, after correcting them upon the basis described in section 16, Part II, for the change in conductance caused by the heating (only, however, in cases where the initial and final values at 18° differed by more than 0.25 per cent). The acetic acid values given under the heading "corrected" were obtained by decreasing the "uncorrected" values by a fractional amount equal to the ratio of the actual conductance in the bomb of the water (section 51) to that of the solution in question. The values of the concentrations here given are those at the temperatures of the measurements. They were obtained by dividing the concentration at 4° by the appropriate specific-volume-ratio. Table 35. — Mean values of the equivalent conductance. Temper- Concen- Sodium Hydro- Sodium Acetic acid. ature. tration. chloride. acid. acetate. Uncor- Cor- rected. rected. 18° 0.500 107.53 375.2 75.97 1.998 105.46 373.6 74.55 9.99 101.94 368.1 71.22 14.59 14.50 30.0 8.52 8.49 75.9 63.67 99.9 350.6 4.68 4.67 100° 0.479 355.8 836 274.8 1.917 349.4 827 267.8 9.59 336.0 808 253.6 25.94 25.64 28.8 15.12 15.01 72.9 222.7 95.9 756 8.29 8.26 156° 0.456 546 1,065 440.3 1.82 535 1,049 425.9 9.11 513 1,018 399.1 23.68 23.14 27.3 13.76 13.57 69.2 345.1 91.1 934 7.53 7.47 218° 0.422 740 1,243 631 1.69 725 1,220 603 8.43 689 1,174 552 16.75 15.93 25.3 9.68 9.40 64.1 464 84.3 1,040 5.28 5.20 Section 54. — Equivalent Conductance at Round Concentrations, i^j 54. EQUIVALENT-CONDUCTANCE VALUES AT ROUND CONCENTRATIONS. In order to show more clearly the change of conductance with the tem- perature the values in table 35 have been reduced so as to correspond to the same concentration at alt- temperatures. This has been done by graphic interpolation with the help of the approximately linear function — • = 1- A A„ KiCS.y' in the cases of sodium chloride, hydrochloric acid and sodium acetate; and with the help of the function A ^ if (i)*, also approximately linear, in the case of acetic acid. Values extrapolated for any considerable interval are indicated by inclosure in parentheses. The limiting values for zero concentration (A^) were derived for hydrochloric acid and sodium acetate by determining graphically what function of the exponential form — = — +iC(CA)»-^ would best express the results at 0.5, 2, 10 and 100 A Ao (or 75 or 85) milli-normal and extrapolating for zero concentration (see section 42, Part IV). For sodium acetate the conductance values at 156° and 218° were first corrected for the hydrolysis of the salt in the way to be described in section 58, before making this extrapolation. The cor- rected values are given in the table below the uncorrected ones. At 18° and 100° the hydrolysis is inappreciable. For acetic acid the A^ values were calculated from those for the other three substances by the law of the independent migration of the ions. Table 36 contains the results of these computations. The concentra- tions, as usual in this article, are expressed in milli-equivalents per liter (referred to oxygen as 16.00) and the temperatures are on the hydrogen gas scale. Table 36. — Equivalent conductance at round concentrations. Substance. Concen- tration. 18°. 100°. 156°. 218°. Sodium Ohlorids 0.5 2.0 107.53 105.46 355.5 349.0 545 534 738 733 F<_/ V^Vt-L 1 1, ■ ■ .^ \_>.L'..1.\,^J. A.\^k.\^ #■»*••■■»■ 10.0 101.94 335.5 511 684 Hydrochloric Acid 379 850 1,085 1,265 0.5 375.2 835 1,064 1,241 3.0 373.6 826 1,048 1,217 10.0 368.1 807 1,016 1,168 80.0 353.0 762 946 1,044 100.0 350.6 754 939 1,006 Sodium Acetate (uncor- 78.1 285 rected for hydrolysis ) 0.5 73.97 274.6 439.5 628 2.0 74.55 367.6 434.5 598 10.0 71.22 253.3 397.0 546 80.0 63.4 231.0 340.0 453 ^38 Conductivity of Aqueous Solutions. — Part V. Table 36. — Equivalent conductance at round concentrations — Continued. Substance. Concen- tration. 18°. 100°. 156°. 218°. Sodium Acetate (cor- rected for hydrolysis) 2.0 10.0 80.0 450 421 396 340 660 578 542 452 Acetic Acid (uncorrect- ed for conductance of water) . 10 30 80 100 14.59 8.52 5.23 4.68 25.40 14.80 9.10 8.13 22.65 13.13 8.07 15.43 8.90 5.42 Acetic Acid (corrected for conductance of water). 10 30 80 347 14.50 8.50 5.22 773 25.10 14.70 9.05 980 22.15 12.95 8.00 1,165 14.70 8.65 5.34 100 4.67 8.10 The results with sodium chloride were in an earlier part of this publica- tion combined with the other results obtained with this substance in this laboratory and were discussed in connection with them (see section 16, Part II). The results with the other substances will alone be considered in the following pages. In the case of the acetic acid we shall employ the values corrected for the conductance of the water. It is of interest to compare these results with those of previous investi- gators in the few cases in which duplicate data already exist. In table 37 such data are placed side by side. Table 37. — Comparison of the values of the equivalent conductance at 18° obtained by different investigators. Concen- tration. Hydrochloric Acid. Sodium Acetate. Acetic Acid. j Noycs and Cooper. Kohl- rausch* Goodwin and Haskell.t Noyes and Cooper. Kohl- rausch.* Noyes and Cooper. Kohl- rausch.* 0.5 2.0 10.0 100.0 375.2 373.6 368.1 350.7 370 351 375.4 375.0 369.3 351.4 76.0 74.5 71.2 75.8 74.3 70.2 14.50 4.67 14.3' 4.60 *Kohlrausch and Holborn, Leitvermogen der Elektrolyte, 159-160, (1898) tProc. Am. Acad., 40, 409, 416 (1904); Phys. Rev., 19, 383, 386 (1904). The values here given, like our own, are uncorrected for the influence of the water. Our results with hydrochloric acid at 18° agree on an average within 0.35 per cent with those determined with great care by Goodwin and Has- kell. This is also true of the values for this acid extrapolated for zero concentration, which are 379 and 380 respectively. Our values for sodium acetate in 0.01 normal and for acetic acid in 0.1 normal solution differ, however, from the early ones of Kohlrausch by 1.4 and 1.5 per cent respectively. Section 55. — Change of Conductance with Concentration. 759 55. CHANGE OF THE EQUIVALENT CONDUCTANCE WITH THE CONCENTRATION AND TEMPERATURE. The change of the conductance with the concentration may be first discussed. In the case of the sodium acetate values uncorrected for hydrol- ysis there is, owing to this phenomenon, an abnormally large increase between the highest and lowest concentrations, especially at the higher temperatures. Moreover, it is not probable that the values corrected for hydrolysis are as accurate as those for unhydrolyzed salts. This makes it scarcely worth while to investigate fully the form of function applicable to the change of conductivity with the concentration in the case of this salt. Of much interest, however, is such a study in the case of hydro- chloric acid, especially with reference to the conformity of its behavior to that of the neutral salts. We have therefore tested the applicability to the data of the three functions A„ — A = i<^C' (Kohlrausch), Ao — A = KC*A> (Barmwater), and A„ — A=i^tCi (van't Hoff), by plotting the values of A along one co-ordinate axis and those of C*, A'C*, or A^C* along the other axis, drawing the best representative straight line through the points in such a way as to make the percentage deviations of the two con- ductivity values for the more concentrated solutions (10 and 100 or 10 and 85 milli-normal) and also of those for the more dilute solutions oppo- site and equal, and reading off the deviations of the separate points from the line. These deviations, expressed as percentages of the conductance values, are given in table 38. Table 38. — Deviation of the observed conductance values for hydrochloric acid from those calculated by various empirical formulas. Temper- ature. Concen- tration. Equivalent conduct- ance. Percentage deviation of observed from calculated conductance values. c"= A^'V" ^3/2 ^1/2 18° 100° 156° 218° 0.5 2.0 9.99 99.9 375.2 373.6 368.1 350.6 —0.19 +0.17 +0.32 —0.34 —0.20 +0.19 +0.37 —0.27 —0.08 +0.06 —0.02 +0.01 Mean. 0.31 0.34 0.04 0.479 1.917 9.59 95.9 836 827 808 756 —0.05 +0.05 +0.07 —0.07 —0.08 +0.06 +0.13 —0.13 +0.11 —0.13 —0.22 +0.31 Mean. 0.06 0.10 0.17 0.456 1.82 9.11 91.1 1,065 1,049 1,018 934 +0.01 —0.01 0.00 0.00 —0.05 +0.02 +0.08 —0.09 +0.18 —0.18 —0.40 +0.43 Mean. 0.01 0.06 0.30 0.431 1.69 8.43 84.3 1,243 1,220 1,174 1,040 —0.09 0.00 +0.10 —0.12 —0.09 +0.10 +0.22 —0.33 +0.31 —0.38 —0.74 +0.68 Mean. 0.08 0.18 0.47 140 Conductivity of Aqueous Solutions. — Part V. It will be seen from the table that as in the case of the salts previously investigated, the cube-root function of Kohlrausch expresses the results almost perfectly at the three higher temperatures, but that at 18° the de- viations reach 0.25 per cent. That of Barmwater is nearly, but not quite, as satisfactory. On the other hand, the function of van't HofI well rep- resents the data at 18°, but does so less and less perfectly the higher the temperature, so that at 318° the deviations reach 0.7 per cent. We have also determined graphically, by plotting 1/A against (AC)""^ (see section 17, Part II), what value of the exponent n in the function C(A(, — A) ^X'(CA)" best expresses the results at the different tem- peratures both for hydrochloric acid and sodium acetate (unhydrolyzed values). The results are given in table 39. Table 39. — Values of the exponent n in the function C{A, — A)=K(CA)n Substance. 18°. 100°. 156°. 218°. HCl 1.45 1.45 1.38 1.45 1.40 1.42 1.47 1.36 NaCsHjO..... The effect of temperature is mainly of interest when considered with reference to the conductivity values extrapolated for zero concentration; for this effect then consists solely in a change in the migration velocity of the ions, while at higher concentrations upon this the change in ionization is superposed. To show the character of this effect, we have calculated the mean absolute temperature-coefficient of the conductivity at zero con- centration AAo/At between 18° and 100°, 100° and 156°, and 156° and 218°. These coefficients are given in the following table, together with the value of the equivalent conductance at 18°. The coefficients for sodium acetate are based on the conductance values corrected for hydrolysis. Table 40. — Mean temperature-coetHcients of the equivalent conductance at zero concentration. Substance. Condnct- ance at 18°. Temperature-coefficient. 18°-100°. 100°-156°. 156°-218° NaCl 109 78.1 379 3.09 2.53 5.76 3.44 2.95 4.20 3.31 3.40 2.90 NaCiiHsOj... HOI It is evident from the preceding table that the temperature-coefficient of sodium acetate, like that of the other uni-univalent salts discussed in Parts II and IV first increases rapidly,* attains a maximum, and then ♦According to Arrhenius (Ztschr. phys. Chem., 4, 99, 1889) its absolute tempera- ture-coefficient for the interval 18-52° is 2.08, thus much smaller than that from 18° to 100°. Section 56. — lonization-values. 141 somewhat decreases. Hydrochloric acid, on the contrary, exhibits a con- stantly decreasing temperature-coefficient.* It is also worthy of note that the migration velocities of the ions of these three substances differ by a less percentage amount the higher the temperature. Thus the ratio of the equivalent conductance of sodium ace- tate and of hydrochloric acid at zero concentration to that of potassium chloride has the following values at the various temperatures : 18° 100° 156° 218° NaC2Hs02 : KCl 0.60 0.69 0.73 0.80 HCl : KCl 2.91 2.05 1.73 1.53 The effect of temperature on the conductivity at the higher concentra- tions does not require special discussion, since the phenomenon is better analyzed through the consideration, presented in the following section, of the relation of ionization to temperature. It is, however, of some interest to note that acetic acid, owing to the decrease in its ionization overcom- pensating the increase in the migration velocity of its ions, has a maxi- mum value of the equivalent conductance at some temperature between 18° and 156°. 56. lONIZATION-VALUES AND THEIR CHANGE WITH THE CONCENTRATION AND TEMPERATURE. Table 41 shows the percentage degree of ionization of the various sub- stances. These values were obtained merely by dividing the conductances at the different concentrations by the conductance at zero concentration, all of which are given in table 36. The values corrected for hydrolysis were used in the case of sodium acetate, and those corrected for the con- ductance of the water in the case of acetic acid. Table 41.— Percentage ionization. Substance. Concen- tration. 18°. 100°. 156°. 218°. Hydrochloric 100.0 100.0 100.0 100.0 Acid. 0.5 99.0 98.2 98.0 98.3 3 98.5 97.3 96.5 96.0 10 97.1 95.0 93.6 93.3 80 93.3 89.7 87.2 83.5 100 92.6 88.7 85.6 79.5 Sodium Ace- 0.5 97.2 96.4 tate. 3 95.3 93.8 93.7 87.3 10 91.2 88.8 88.0 83.3 80 81.1 77.6 75.6 68.5 Acetic Acid. 10 4.17 3.34 2.36 1.26 30 3.45 1.90 1.33 0.743 80 1.50 1.17 0.815 0.458 100 1.34 1.05 ♦Its value for the interval 10-30° is 6.30 (computed from the data of Noyes and Sammet [Ztschr. phys. Chem., 43, 70, 1903] and our value of A„ at 18°). 142 Conductivity of Aqueous Solutions. — Part V. The discussion, given in section 55, of the change of conductivity of hydrochloric acid with the concentration is substantially also a discussion of the change of ionization ; for the three functions there considered, pro- vided each be assumed to hold down to zero concentration and therefore to give the true value of Aq, may be written in the forms : l — y = KO; l — y = K{CyY and C(l — y) =K{Cyy The conductivity functions corresponding to the first two of these have been shown to express the results fairly satisfactorily in all cases; but this is not true, especially at the higher temperatures, of the function cor- responding to the last of these expressions. It was in fact shown that the exponent in the expression corresponding to the general exponential function C(i — y) =^ K {Cy)^ has both for hydrochloric acid and sodium acetate values differing from 1.5 and varying somewhat with the tempera- ture (see table 39). The question of the applicability of the mass-action law to the results with acetic acid at the higher temperatures is of considerable interest. The values of its ionization-constant (multiplied by 10") calculated from the data of table 41 by the equation K := Cy^/{1 — y) are given in table 42, the concentration used in the calculation and given in the table being expressed in equivalents (not milli-equivalents) per liter. Table 42. — lonization-constants {W^K) for acetic acid. Concen- tration. 18°. 100°. 156°. 218°. 0.01 0.03 0.08 0.10 18.15 18.46 18.20 10.85 11.04 11.14 5.23 5.30 5.36 1.61 1.67 1.69 .... It is evident from these results that the mass-action law holds true, at least approximately, for this acid at 318°, just as it does at 18°. The values given in the last rows — those for the more concentrated solutions — are doubtless the best values of the constant. It will be seen from table 41 that the ionization of all these substances decreases steadily with rising temperature. In 0.1 normal solution the decrease between 18° and 318° is nearly the same (9 to 11 per cent) for the first three substances, and consequently their relative degrees of ioniza- tion are not much different at the higher and lower temperatures. The decrease in the case of acetic acid is very great, the ionization at 318° being only about one-third of that at 18° ; moreover, the decrease is especially rapid above 100°. Correspondingly, its ionization-constant (given in table 43) has decreased at 100° to about 0.6 and at 218° to about 0.1 of its value at 18°. Section 5/. — Conductivity Data for Mixtures. 14J 57. CONDUCTIVITY DATA FOR MIXTURES OF SODIUM ACETATE AND ACETIC ACID. Table 43 gives the results that were obtained with the mixtures of sodium acetate and acetic acid. The values of the conductance are the measured values in reciprocal ohms, multiplied by 10" and corrected for the instrumental errors and the lead resistance. The values of the specific conductance were calculated from these by applying the water-correction and multiplying by the conductance-capacity. It will be seen that with the 2 and 76 milli-normal salt solutions the ini- tial and final values of the specific conductance agree in every case with- in about 0.1 per cent, and that with the 10 milli-normal solution the two values differ on an average by only 0.2 per cent. This makes it improbable that the results are affected by an error arising from contamination or adsorption. 58. HYDROLYSIS OF SODIUM ACETATE AND IONIZATION OF WATER. The increase in conductance due to hydrolysis of the salt can be derived from the data of table 43 and those obtained with sodium acetate alone (table 35). It is first necessary to subtract from the former values the conductance which the acetic acid itself possesses in the mixture. This can be determined by the application of the mass-action law, which has already been shown to apply to acetic acid at all the temperatures. Accord- ing to this law — y:^ ^= A'. Now Cac is substantially equal to the con- ChAc centration of the ionized sodium acetate in the solution, which is readily calculated b\- multiplying its concentration (Cs) by the corresponding ionization value (ys) taken from table 41. The ionization of the acetic acid -^ is then found by dividing its ionization-constant bv this pro- duct, and its specific conductance (la) is equal to the product of this ion- ization value by the concentration of the acid (Ca) and by its equivalent conductance when completely ionized (Aoa), i. e., La ^ — ^^ — . CaA(,a- L-sys The specific conductance of the acid is then subtracted from the specific conductance of the mixed solution, whereby the specific conductance of the unhydrolyzed salt is obtained. It is assumed hereby that the acetic acid has been added in suflficient amount to reduce the hydrolysis to a value not differing appreciably from zero ; that this was the case was proved experimentally by the addition of varying amounts of acetic acid, and it will also be shown theoretically that even the smallest addition made in our experiments must have sufficed. 144 Conductivity of Aqueous Solutions. — Part V. The data and results of these calculations are given in table 44, which is more fully explained on page 146. Table 43. — The conductivity data for mixtures of sodium acetate and acetic acid. Cell No. Concentration at A°. Temper- ature. Conduct- ance X 106. Specific Date. Sodium Acetic conductance X 10«. acetate. acid. 1904 July 15... Ill 1.9925 1.594 18.00 156.5 217.7 18.00 1,039.4 5,252 6,660 1,039.9 153.34 772.9 978.7 152.56 July 18... III 2.0043 0.874 18.00 156.3 18.00 1,027.1 5,267 1,026.4 151.55 775.2 150.56 July 19... III 2.0071 0.456 18.00 156.3 217.4 18.00 1,019.6 5,268 6,712 1,020.7 150.41 775.3 986.5 149.71 July 20... III 2.0021 0.464 18.00 155.8 217.2 18.00 1.017.3 5,245 6,691 1,017.9 150.07 771.9 983.3 149.30 June 7.. . II 9.967 5.53 18.00 217.7 723.4 4,706 711.7 4,610 June 8... II 10.052 1.951 18.00 217.9 726.9 4,755 715.1 4,658 June 9... II 10.003 3.61 18.00 218.4 724.7 4,738 713.0 4,642 June 28... III 10.002 3.50 18.00 157.2 217.9 18.00 4,823 24,673 31,290 4,839 714.9 3,650 4,624 716.4 June 29.. . III 10.023 2.739 18.00 155.8 217.6 18.00 4,819 24,588 30,890 4,839 714.4 3,637 4,565 716.4 July 7... III 10.016 2.225 18.00 155.9 217.8 18.00 4,827 24,594 31,180 4,828 715.5 3,638 4,608 714.8 July 8... in 10.036 2.162 18.00 217.9 18.00 4,833 31,350 4,843 716.4 4,633 717.0 July 9.. . III 10.015 2.228 18.00 217.9 18.00 4,819 31,240 4,827 714.4 4,617 714.7 June 17.. II 76.18 20.54 18.00 156.3 218.3 18.00 4,912 24,402 30,320 4,914 4,837 23,998 29,736 4,838 June 20... 11 76.06 20.67 18.00 156.0 217.7 18.00 4,888 24,079 30,100 4,876 4,814 23,654 29,526 4,801 June 24... II 76.08 20.67 18.00 100.08 156.3 218.0 4,911 16,532 24,361 30,270 4,836 16,258 23,936 29,686 18.00 4,912 4,836 Section §8. — Hydrolysis of Sodium Acetate. 145 Table 44. — Specific conductance of the constituents of the sodium acetate solutions. Date. Tem- pera- ture, t°. Concentration at^°. Specific conductance X lO''. Dii?er- cncc. Percent- age dif- ference. Salt. Acid. Mixture. Acid in mixture. Salt in mixture. Salt in water alone. 1 2 3 4 5 6 7 8 9 10 July 15. July 18. July 19. July 20. Mean . June 7. June 8. June 9. June 28. June 29. July 7. July 8. July 9. Mean . June 17. June 20. June 24. Mean . July 15. July 18. July 19. July 20. Mean . June 28. June 29. July 7. Mean . June 17. June 20. June 24. Mean . July 15. July 19. July 20. Mean . 18 18 18 18 1.990 2.002 2.004 1.999 1.592 0.873 0.455 0.464 153.34 151.55 150.41 150.07 5.31 3.90 1.51 1.54 148.03 148.65 148.90 148.53 148.35 149.22 149.43 149.05 0.32 0.57 0.53 0.53 .... 0.49 0.33 18 18 18 18 18 18 18 18 9.953 10.038 9.989 9.989 10.010 10.002 10.023 10.001 5.52 1.949 3.60 3.49 2.735 2.222 2.159 2.225 711.7 715.1 713.0 714.9 714.4 715.5 716.4 714.4 3.9 1.4 2.5 2.4 1.9 1.5 1.5 1.5 707.8 713.7 710.5 713.5 712.5 714.0 714.9 712.9 708.9 714.9 711.5 711.5 713.9 712.3 713.8 712.2 1.1 1.2 1.0 —1.0 0.4 —1.7 —1.1 —0.7 —0.1 0.0 18 18 18 76.08 *75.95 75.98 20.51 20.64 20.64 4837 4814 4836 3 3 2 4835 *4812 4834 4844 4836 4838 9 *24 4 6 0.1 156 156 156 1.56 1.815 1.826 1.829 1.824 1.453 0.796 0.415 0.423 770.8 773.9 774.0 772.7 4.6 2.5 1.3 1.3 766.2 771.4 772.7 771.4 773.0 777.7 779.0 776.8 6.8 6.3 6.3 5.4 1.824 770.4 6.2 0.80 156 156 156 9.113 9.132 9.125 3.19 2.495 2.027 3626 3641 3640 2 2 1 3624 3639 3639 3637 3645 3642 15 6 3 8 0.23 156 156 156 69.41 *69.30 69.32 18.72 18.83 18.83 23962 23654 23900 2 2 2 23960 *23652 23898 23953 23915 23922 — T *263 24 8 0.05 218 218 218 1.680 1.692 1.688 1.344 0.384 0.391 979.8 988.5 986.3 1.8 0.5 0.5 978.0 988.0 986.0 1013.1 1020.3 1017.9 35.1 32.3 31.9 1.687 984.0 33.1 3.25 June 7, June 8. June 9. June 28. June 29. July 7. July 8. July 9. Mean . June 17. June 20. June 24. Mean . 218 218 218 218 218 218 218 218 8.402 8.473 8.432 8.431 8.454 8.443 8.460 8.442 4.66 1.645 3.04 2.95 2.309 1.875 1.823 1.878 4615 4660 4635 4636 4571 4611 4635 4619 1 1 1 1 1 1 1 4614 4660 4634 4625 4570 4610 4634 4618 4638 4677 4654 4654 4667 4661 4670 4660 24 17 20 29 97 51 36 43 8.442 4621 40 0.85 218 318 218 64.22 *64.11 64.13 17.32 17.43 17.42 29716 29546 39686 1 1 1 29715 *29545 29685 29798 29747 29757 83 *202 68 64.18 29700 75 0.25 ♦Values to which an asterisk is attached were, on account of tlieir large deviation, omitted in computing the mean. I4 2 2 2 2 2 Bomb... CeU I... Bomb... CeU 11... Bomb... Bomb . . . CeU II... 76.5 1 76.5 50.22 1 50.22 1 21.06 \ 21.50 1 21.50 1 101,490 101,430 1,783.4 1,785.0 67,850 67,800 1,187.0 1.186.8 29,250 29,230 29,240 29,880 29,840 520.3 520.8 196.24 196.12 197.08 197.26 199.9 199.8 200.7 200.6 205.6 205.4 205.5 205.7 205.4 205.5 205.6 196.18 197.17 j 199.85 200.65 • 205.50 j 205.55 205.55 It is evident from these results that when the conductance in the bomb does not exceed 30,000 X 10'° the difference between the equivalent con- ductance derived from it and that derived from the measurement in the U-shaped cell is inconsiderable; but that the difference is 0.5 per cent when the conductance is 100,000 X 10"'. Although it is uncertain whether this ♦Those on October 19-20, 1904, were made with a solution prepared by diluting stock solution No. 1, which was then three months old. The absolute values are therefore not accurate. Section 65. — The Conductivity Data. 163 difference between the true value and that derived from the measurement in the bomb would be substantially the same at different temperatures, and whether it would be proportional to the conductance of the solution^ it has nevertheless seemed to us that values nearer the truth would be obtained by applying a correction to our results with sodium hydroxide in accordance with these assumptions than by leaving them uncorrected ; for there is certainly some error in this direction. We recognize, however, that there may still be an error in the corrected results as great as the correction apphed ; and it is expected that more accurate data will be later obtained with a bomb containing the electrode within a cup to increase the resistance. The percentage correction actually applied was equal to 5 times the conductance measured in the bomb ; that is, it was 0.5 per cent when the conductance was 100,000 X 10"°, 1 per cent when it was 200,000 X 10-', etc. This correction has been introduced in table 51 in the process of calculating the equivalent conductance from the observed conductance. The results obtained in the bomb with the solutions of sodium hydroxide, ammonium hydroxide, and ammonium chloride are given in tables 51-53. The first column gives the date of the experiment ; the second, the con- centration at 4° in milli-equivalents per liter (the number of milli-equiva- lents being based upon the atomic weights referred to oxygen as 16.000 and weights being reduced to vacuo) ; the third, the temperature corrected for thermometric error at which the conductance was measured; the fourth, the concentration at the temperature of the measurements, calcu- lated by dividing the concentration at 4° by the corresponding specific- volume ratio* and in the case of the sodium hydroxide measurements at 156° applying the correction for the solvent in the vapor space;! *The specific-volume ratio (that is, the ratio of the specific volume of the solu- tion at the temperature of the measurements to that at 4°) was assumed to be iden- tical with that of pure water, the values determined by Noyes and Coolidge being used at 318°. This assumption is justified since they showed that up to 218° the expansion of a 0.1 normal sodium chloride solution is identical with that of a 0.002 normal solution. The values of the ratio are 1.0013 at 18°, 1.0125 at 51°, 1.0257 at 75°, 1.0433 at 100°, 1.0660 at 125°, 1.0978 at 156°, and 1.1862 at 218°. tSince tlie bomb was usually filled so as to have a vapor-space of only 1 or 3 c.cm. at either 156° or at 318°, the correction for the amount of the liquid vaporized was insignificant and was not as a rule applied, the only exception being in the case of the sodium hydroxide solutions at 156° where the vapor space was about 11 c.cm. and where the concentration was correspondingly increased by 0.04 per cent. In the case of the ammonia solutions tlie possibility existed that the solute also passed into the vapor space in appreciable quantity; but this was disproved by comparative conductivity measurements made with varying quantities (76 and 113 c.cm. at 18°) of solution in the bomb. Thus, a 97.07 millimolal NH4OH solution_ showed in the bomb the following conductances, the usual procedure in heating being followed in each case : 4969 and 4973, mean 4970 at 100° ; 4735 and 4735, mean 4735 at 156°, when 113 ccm. at 18° were introduced: and 4964 and 4977, mean 4970, at 100°; and 4675 and 4703, mean 4689 at 156°, when 76 c.cm. at 18° were introduced. There is seen to be no difference at 100° and one of only 1 per cent at 156°. Since the lat- ter arises from a difference in vapor-space of 40 c.cm., it is evident that the error would be inappreciable when the vapor-space was, as was usual, about 1 c.cm. 164 Conductivity of Aqueous Solutions. — Part VI. the fifth, the measured conductance in reciprocal ohms, multiplied by 10' and corrected for the instrumental errors — those in the slide wire and the resistance coils and for the lead resistance (0.03 ohm) ; the sixth, the equivalent conductance calculated from the value of the conductance in the fifth column by applying the water correction (in the cases specified in the last section), multiplying by the conductance-capacity,* and divid- ing by the concentration given in the fourth column (also in the case of the 0.019 and 0.049 normal sodium hydroxide solutions applying the cor- rection for polarization described in the text following the experiments with this substance). In the experiments with ammonium chloride, a small quantity (about one-tenth as many equivalents) of ammonium hydroxide were added in order to eliminate entirely the hydrolysis possi- ble in such dilute solutions at the higher temperatures; the tables there- fore contain additional columns giving the concentration of this substance and the conductance of the solution corrected for that of the ammonium hydroxide, which correction was calculated by the mass-action expression ■■pr- KsA-a in which Cb and Cs represent the concentration of the base and salt respectively, Kb the ionization-constant of the base (section 69, table 64), and A^ its equivalent conductance when completely ionized (section 67, table 59). ♦Unless otherwise stated, all measurements were made in the bomb, whose con- ductance-capacity (constant throughout the whole series of experiments) was given for each temperature in section 63. Section 63. — The Conductivity Data. Table 51. — Conductivity data for sodium hydroxide. 165 FROM STOCK SOLUTION No. ] (PREPARED JULY 20, '04.) Concentration Temperature Concentration Conductance EqaivalcDt .14°. V") at/°. X 10». coDductance. 1904 Aug. 17.... 19.151 17.93 19.127 26,780 207.4 217.2 16.158 102,340 940.0 17.93 19.127 26,630 206.2 Aug. 18.... 19.151 17.93 19.127 26,900 208.3 217.4 16.154 102,430 941.0 17.93 19.127 26,650 206.4 Aug. 18.... 19.151 17.93 19.127 26,820 207.7 217.4 16.154 102,490 941.6 17.93 19.127 26,550 205.6 Aug. 19 19.151 17.93 19.127 26,800 207.6 100.12 18.357 69,760 563.4 156.1 17.449 91,060 774.5 100.08 18.157 69,600 562.7 17.93 19.127 26,790 207.5 Aug. 20 19.151 17.93 19.127 26,790 207.5 100.20 18.356 69,410 561.19 155.6 17.864 90,880 772.7 100.20 18.356 69,360 560.80 17.93 19.127 26,743 207.1 Aug. 22 19.151 100.20 18.356 69,290 560.23 155.6 17.457 90,880 772.7 217.5 16.151 103,200 939.1 155.6 17.457 90,160 766.6 100.20 18.356 98,260 551.91 Aug. 24 49.08 17.93 49.02 66,670 201.9 100.18 47.89 171,640 543.84 155.7 44.74 223,500 746.0 Aug. 25.... 49.08 17.93 49.02 66,630 201.7 100.16 47.89 171,240 542.5 155.6 44.74 220,100 734.6 217.4 41.38 245,600 886.5 155.6 44.74 221,200 738.7 100.16 47.89 169,720 537.8 17.93 49.02 65,890 199.5 Aug. 26.... 49.08 17.93 49.02 66,770 202.1 100.16 47.89 171,500 543.3 155.6 44.74 223,600 746.1 100.16 47.89 171,520 543.5 17.93 49.03 66,710 202.00 Aug. 30 49.08 17.93 49.02 66,530 201.4 217.7 41.38 247,200 892.8 17.93 49.02 66,140 200.2 Aug. 30 49.08 17.93 49.02 66,510 201.4 217.7 41.38 247,200 892.8 17.93 49.02 66,290 200.7 Aug. 31 49.08 17.93 49.02 66,604 201.6 155.6 44.74 221,800 740.3 17.93 49.03 66,530 201.4 i66 Conductivity of Aqueous Solutions. — Part VI. Table 51. — Conductivity data for sodium hydroxide — Continued. FROM STOCK SOLUTION No. 2 (PREPARED OCT. 22, ANALYZED NOV. 3). Date. Concentration Temperature Concentration Conductance Equivalent at 4°. (i°) at<°- X10«. conductance. 1904 Nov. 17... 3.974 17.93 3.970 5,669 211.4 218.3 3.344 2,266 999.1 Nov. 18... ' 3.974 17.93 3.970 566.3 211.1 1 218.2 3.344 2,263 997.4 17.93 3.970 534.6 199.28 Nov. 19... 3.974 17.93 3.970 566.7 211.3 100.05 3.810 1,490.8 578.4 155.6 3.622 1,967.4 802.3 17.93 3.970 563.6 210.1 Nov. 22 4.401 17.93 4.395 639.8 212.1 217.5 3.707 2,501. 994.4 17.93 4.395 613.2 206.5 Nov. 23.... 4.026 17.93 4.031 573.5 311.1 217.3 3.392 3,291. 995.6 17.93 4.021 562.4 307.0 Nov. 23.... 4.026 17.93 4.021 573.8 311.2 99.57 3.861 1,501.1 574.7 155.5 3.669 1,989.7 801.0 99.61 3.861 1,498.3 573.6 17.93 4.031 573.3 310.6 Nov. 26.... 4.026 17.93 4.031 574.3 311.4 99.90 3.860 1,507.2 577.2 155.8 3.668 1,995.2 803.4 99.90 3.860 1,504.2 576.1 17.93 4.031 573.5 211.1 Nov. 29.... 3.972 [ 17.93 3.967 566.8 211.5 217.7 3.346 3,259. 995.3 1 17.93 3.967 550.6 305.4 Nov. 30 3.972 17.93 3.967 564.2 210.5 1 99.71 3.809 1,478.6 573.9 ' 156.1 3.617 1,966.5 803.0 99.68 3.809 1,475.9 572.8 17.93 3.967 563.4 209.8 Dec. 1 3.069 17.93 2.066 396.3 213.2 99.79 1.9839 779.8 581.1 155.6 1.8853 1,035.5 811.3 ! 99.81 1.9839 778.5 580.1 1 17.93 2.066 294.6 311.0 Dee. 2 2.069 17.93 2.066 395.5 311.6 100.15 1.9832 780.5 581.8 155.9 1.8848 1,035.3 811.3 100.13 1.9832 778.1 580.0 [ 17.93 2.066 293.5 310.3 Dec. 3 1.9925 1 17.93 1.9900 285.1 212.0 100.25 1.9098 753.4 583.1 1 156.2 1.8147 1,000.0 814.0 100.23 1.9098 750.6 581.0 1 17.93 1.9900 283.6 210.9 Dec. 4 1.9925 j 17.93 1.9900 ! 384.3 211.4 100.04 155.9 1.9102 1.8153 752.3 999.5 583.2 813.3 100.03 1.9102 ' 749.6 580.1 17.93 1.9900 282.5 210.1 Section 65. — The Conductivity Data. Table 52.— Conductivity data for ammonium hydroxide. 167 FROM STOCK SOLUTION No. 1 (PREPARED JANUARY 9, 1905.) Date. Concentra. Tempera- Concentra- Conduct- Equivalent tion at 4°. ture, t°. tion at t°. ance X 10«. conductance. 1905 Jan. 13t.. 33.44 17.93 33.40 1,190.9 5.432 99.88 31.10 3,811 13.297 156.2 29.54 2,635 13.005 Jan. 14... 33.44* 17.93 33.40 1,189.5 5.415 Jan. 16... 32.44 17.93 32.40 1,193.5 5.433 155.6 39.56 3,651 13.130 Jan. 17.... 33.08 17.93 33.04 1,304.4 5.377 99.77 31.71 2,841 13.175 156.0 30.13 2,670 12.978 17.93 33.04 1,175.4 5.341 Jan. 18 33.08 17.93 33.04 1,205.2 5.381 100.03 31.71 2,851 13.334 156.6 30.11 2,673 12.990 17.93 33.04 1,196.7 5.337 Jan. 20 33.07 17.93 33.03 1,203.8 5.375 99.74 31.71 2,847 13.203 155.6 30.14 3,670 12.966 Jan. 21 33.07 17.93 33.03 1,211.6 5.410 99.98 31.70 3,863 13.282 155.9 30.13 2,699 13.104 Jan. 27.... 33.05 17.93 33.01 1,307.3 5.394 99.91 31.69 3,860 13.377 Jan. 28 33.05 17.93 33.01 1,307.1 5.394 99.80 31.69 3,870 13.320 157.1 30.06 3,705 13 . 160 99.76 31.69 2,864 13.284 17.93 33.01 1,205.3 5.380 Jan. 30 33.05 17.93 33.01 1,207.3 5.394 100.20 31.68 2,869 13.320 156.2 30.09 2,710 13.173 100.28 31.68 3,871 13.326 17.93 33.01 1,204.8 5.378 Jan. 31 — 97.07 17.93 96.95 2,078 3.166 100.23 93.04 4,954 7.850 156.3 88.37 4,657 7.742 100.18 93.05 4,950 7.841 17.93 96.95 2,075 3.161 Feb. 1.... 97.07 17.93 96.95 2,078 3.166 99.95 93.07 4,968 7.870 155.8 88.41 4,733 7.865 99.91 93.07 4,981 7.889 17.93 96.95 2,082 3.172 Feb. 3.... 97.07 17.93 96.95 2,082 3.172 99.93 93.07 4,971 7.874 155.9 88.40 4,733 7.867 99.95 93.07 4,981 7.889 17.93 96.95 3,083 3.173 Feb. 9 9.9085 17.93 9.896 655.5 9.740 99.91 9.500 1,558.1 24.02 156.4 9.019 1,480.8 33.84 99.85 9.500 1,539.3 23.71 17.93 9.896 647.2 9.603 *Where the concentration was the same in successive measurements they were made with different portions of the same diluted solution. tin the experiments of January 13-21, only 103 c.cm. solution were put into bomb, while in all later experiments 113 c.cm. were introduced. The air was not in any case exhausted. i68 Conductivity of Aqueous Solutions. — Part VI. Table 53. — Conductivity data for ammonium hydroxide — Continued. FROM STOCK SOLUTION No. 1 (PREPARED JANUARY 9, 1905.) Date. CoDcentra- Tempera- Concentra- Conduct- Equivalent tioo at 4°, ture, t°. tion at t°. ance X 106. conductance. Feb. 10... 9.9085 17.93 9.896 655.2 9.735 99.52 9.504 1,560.3 34.03 156.5 9.019 1,480.2 23.83 99.54 9.504 1,544.7 23.78 17.93 9.896 647.3 9.605 STOCK SOLUTION No. 1 (WHEN 35 DAYS OLD). *Feb. 11.. 97.07 17.93 96.95 2,096 3.193 100.10 93.06 5,032 7.975 *Feb. 13.. 97.07 17.93 96.95 2,097 3.194 99.07 93.14 5,044 7.985 155.4 88.44 4,840 8.043 99.13 93.15 5,041 7.981 17.93 96.95 2,101 3.200 Feb, 14... 97.07 17.93 96.95 2,095 3.193 99.86 93.07 5,042 7.988 156.4 88.36 4,832 8.021 99.81 93.08 5,046 7.994 17.93 96.95 2,097 3.193 FROM STOCK SOLU TION No. 2 (PREPARED FEBRUARY 20, 1905.) Feb. 21... 99.90 17.93 99.77 2,095 3.101 100.07 95.77 4,956 7.629 156.6 90.92 4,629 7.479 17.93 99.77 2,096 3.100 Feb. 23... 99.90 17.93 99.77 3,094 3.100 99.92 95.79 4,965 7.641 156.4 90.93 4,663 7.533 99.85 95.79 4,981 7.663 17.93 99.77 3,094 3.098 Feb. 24... 99.90 17.93 99.77 3,094 3.099 155.6 91.00 4,657 7.516 (7.549) 17.93 99.77 2,089 3.093 Feb. 25... 33.29 17.93 33.24 1,211.7 5.375 99.52 31.93 2,863 13.300 155.4 30.33 2,706 13.058 17.93 33.24 1,210.0 5.366 E"eb. 27... 9.853 17.93 9.841 651.5 9.735 99.64 9.451 1,548.4 33.83 155.7 8.975 1,454.6 33.53 17.93 9.841 646.8 9.650 Feb. 28... 9.853 17.93 9.841 651.9 9.741 99.59 9.450 1,543.2 33.93 155.8 8.974 1,457.0 23.56 99.64 9.449 1,534.7 23.76 17.93 9.841 646.5 9.645 •Although every precaution was taken to preserve this stock solution, the results of these experiments of February 13 and 14 when compared with those of January 31 to February 3 show that contamination had suddenly taken place. They are included here merely to illustrate the great eflfect especially at the higher temperatures of what must have been a minute contami- nation; this effect consisted in this case of an increase of about 0.8 per cent at 18" and of 2.5 per cent at 156°. That it was not due to contamination in transferring the solution to the bomb is shown by the excellent agreement of the three earlier and of the two later values among themselves. Section 65. — The Conductivity Data. 169 Table 52.- -Conductivity data for ammonium hydroxide- — Continued. STOCK SOLUTION No. 3 (PREPARED MARCH 16, 1905.) Date. Concentra- Tempera- Concentra- Conduct- Equivalent tion at 4°- ture,/°. tion at t°. ance X 10«. conductance. Mar. 17. 102.59 17.93 102.46 2,121 3.057 75.20 100.01 4,540 6.700 100.02 98.35 5,018 7.521 124.8 96.24 5,072 7.760 17.93 102.46 2,120 3.055 Mar. 18. 102.59 17.93 102.46 2,120 3.056 51.00 101.30 3,709 5.404 75.20 100.01 4,543 6.704 99.60 98.39 5,010 7.506 124.8 96.24 5,069 7.755 17.93 102.46 2,117 3.050 Table 53. — Conductivity data for ammonium chloride. Concentration at 4^. Tempera- Concentration at t^. Conductance X 10**. Equiva- NH,C1. NHjOH, ture, l°- NHjCl. NH,OH. Obscrred. Corrected for NHjOH. conduct- ance. 1905 May 17.... 12.492 0.00 17.93 12.474 10,233 121.31 May 17.... 12.492 0.00 17.93 12.474 10,233 121.31 May 18.... 12.513 1.486 17.93 12.497 1.485 10,264 10,261 121.47 99.52 12.000 1.425 30,690 30,690 377.9 155.5 11.403 1.354 43,820 43,820 567.4 17.93 12.497 1.485 10,270 10,267 121.54 May 19 12.523 1.389 17.93 12.506 1.387 10,273 10,270 121.49 99.53 12.011 1.332 30,720 30,720 378.0 155.3 11.415 1.265 43,880 43,880 567.6 99.55 12.011 1.332 30,700 30,700 377.7 17.93 12.506 1.387 10,271 10,267 121.46 May 20 1.9791 0.2228 17.93 1.9766 0.223 1,691.5 1,688.5 126.43 99.73 1.8978 0.214 5,108 5,102 397.5 155.6 1.8036 0.203 7,369 7,365 603.5 17.93 1.9766 0.223 1,709.0 1,706.0 127.74 May 24.... 2.076 0.2383 17.93 2.0730 0.238 1,772.9 1,769.9 126.34 100.06 1.9900 0.228 5,385 5,379 399.6 155.9 1.8910 0.217 7,743 7,739 604.8 100.06 1.9900 0.228 5,417 5,411 402.0 17.93 2.0730 0.238 1,788.6 1,785.6 127.47 66. SUMMARY AND DISCUSSION OF THE EQUIVALENT-CONDUCTANCE VALUES AND THEIR CORRECTION TO ROUND TEMPERATURES. The following tables present the equivalent conductance values corres- ponding to round temperatures calculated from the values given in the previous tables with the help of temperature-coefficients obtained by plot- ting graphically the conductance values at each concentration at the differ- ent temperatures (including those at 51°, 75.3°, and 124.8° in the case of ammonium hydroxide). The values obtained from the measurements at each temperature before going to a higher one are headed "Initial"; and those on coming back, "Final." lyo Conductivity of Aqueous Solutions. — Part VI. Table 54. — Equivalent conductance of sodium hydroxide at round temperatures. Date. Concentra- tion at 4°. 18° 100° 156° 218°. Initial. Final. Initial. Final. Initial. Final. 1904 Aug. 24 Aug. 25 Aug. 26.... Aug. 30 Aug. 30 Aug. 31 Mean . . . Nov. 11 Aug. 17 Aug. 18 Aug. 18.... Aug. 19 Aug. 20 Aug. 22.... Mean ... Nov. 8 Nov. 17 Nov. 18 Nov. 19 Nov. 22 Nov. 23.... Nov. 25 Nov. 26.... Nov. 29 Nov. 30. . . . Mean . . . Dec. 1 Dea 2 Dec. 3 Dec. 4 Mean ... 49.08 49.08 49.08 49.08 49.08 49.08 202.2 202.0 202.4 201.7 201.7 201.9 '199! 8 202.2 200.5 201.0 201.7 543.2 542.0 542.8 '537!2 542.9 747.0 *736.0 747.4 741.6 740.1 887.9 893.5 893.5 49.08 202.09 t200.4 542.7 t542.8 745.3 740.1 891.6 50.31 19.151 19.151 19.151 19.151 19.151 19.151 +200.65 207.7 208.6 208.0 207.9 207.8 §202.0 206.5 206.7 205.9 207.8 207.4 561.9 560.4 559.4 §537.2 562.4 560.0 551.1 774.2 774.1 774.0 '768!o 941.6 942.2 942.8 '94o!3 19.151 208.0 t206.4 560.6 t561.3 774.1 768.0 941.7 21.55 3.974 3.974 3.974 4.401 4.026 4.026 4.026 3.972 3.972 t205.55 210.7 211.4 211.6 212.4 211.4 211.5 211.7 211.8 210.8 §207.6 *199.6 210.4 206.8 207.3 210.9 211.4 205.7 210.1 '578!2 576.6 577.6 '575.2 §551.1 575.3 576.5 '574 '.2 803.7 802.8 804.1 802.7 998.3 996.9 995.7 997.5 "996!6 4.038 211.5 (§210.9 jt206.7 576.9 575.3 803.3 996.9 2.069 2.069 1.992 1.992 212.5 211.9 212.3 211.7 211.3 210.5 211.2 210.4 582.0 582.4 582.0 582.0 580.9 580.5 580.1 580.0 812.5 811.7 813.2 812.9 1 2.031 212.1 210.9 582.1 580.4 812.6 *In taking the means, the values marked with an asterisk have been omitted on account of their large deviation. tMean of experiments carried to 218*. tMean of the two concordant determinations made in the U-shaped cell. |Mean of experiments carried to ISG''. It will be seen from table 54 that the results of the separate experiments with sodium hydroxide agree closely with one another, very few of the ini- tial values deviating from their mean by as much as 0.3 per cent. A comparison of the initial and final values at 18° shows that heating to 156° produced a decrease of conductance of less than 0.3 per cent in the three stronger solutions and one of 0.6 per cent in the 2 milli-normal solu- tion, but that heating to 218° decreased it by 0.8 per cent in the 49 and J9 milli-normal and by 2.4 per cent in the 0.4 milli-normal. The latter decrease is so large that in deriving the best value at 218° we shall increase the mean value by half this amount or 1.2 per cent, it being prob- able that the observed decrease in conductance at 18° had taken place in some measure at 218°. At 18° with the 49 and 19 milli-normal solutions the mean results obtained in the U-shaped cell will be adopted as the best Section 66. — Summary of Equivalent Conductances. 171 values, since these were not affected by polarization. In all other cases the mean of the initial values will be adopted. Table 55 contains the results for ammonium chloride, which are derived from measurements with solutions of the salt containing about one- tenth as many equivalents of ammonium hydroxide (see table 53) by correcting the observed conductance for the conductance of the ionized portion of the base. In the case of the first two measurements (made on May 17), however, no free ammonia was added. Table 55. — Equivalent conductance of ammonium chloride at round temperatures. Date. Concentra- tion at 4'-'. Equivalent conductance. 18° 100° 156°. Initial. Final. Initial. Final. 1905 May 17... May 17... May 18... May 19... Mean . . Mas' 80... May 24... Mean . . 12.492 12.492 121.49 121.49 12.513 12.523 121.65 121.62 121.72 121.64 379.5 379.5 '379!2 569.1 570.0 12.518 121.63 121.68 379.5 379.2 569.5 1.9791 2.076 126.62 126.53 127.93 127.65 398.4 399.4 401.8 605.0 605.1 2.027 126.57 127.79 398.9 401.8 605.0 The results of the separate experiments with ammonium chloride given in table 55 are in almost complete agreement. The two measurements of May 17 at 18°, made with the salt alone without the addition of ammonia, show that no considerable contamination resulted in the other cases from the presence of the base. A comparison of the initial and final values shows that no change in conductance was produced by the heating in the 12.5 milli-normal solution, but that there resulted from it an increase of 0.7 per cent at 100° and of 1.0 per cent at 18°. It has therefore seemed best to decrease the value at 156° at 2 milli-normal by 0.5 per cent in order to eliminate this effect as far as possible. This will be done in table 58 where the best values are brought together. The initial and final values at 18° obtained with ammonium hydroxide (table 56) show that the heating had scarcely any effect on the 100 milli- normal solution, but that it caused a decrease of 0.7 per cent in the 33, and of 1 per cent in the 10-milli-normal solution. That this decrease, occurring in spite of the fact that almost any contaminating substance either by its own conductance or through salt- formation would produce an opposite effect, is due to destruction of the ammonia by oxidation, has been shown in connection with experiments made at 218° by Mr. R. B. Sosman in this laboratory, which will be later described. The effect in our experiments was fortunately not so great as to produce an important error, and it has seemed best not to attempt to correct for it, since contami- nation tends to compensate it. 172 Conductivity of Aqueous Solutions. — Part VI. Table 56. — Equivalent conductance of ammonium hydroxide at round temperatures. Date. No. o( stock sol. Concentra- tion at 4°. 18° 100° 156°. Initial. Final. Initial. Final. 1905 Feb. 9 Feb. 10 Feb. 27 Feb. 28 Jan. 13 Jan. 14 Jan. 16 Jan. 17 Jan. 18 Jan. 20 Jan. 21 Jan. 27 Jan. 28 Jan. 30 Feb. 25 Jan. 31 Feb. 1 Feb. 3 Feb. 21 Feb. 23 Feb. 24 2 2 2 9.91 9.85 32.44 33.08 33.07 33.05 33.29 ■ 97.07 99.90 9.758 9.753 9.753t 9.759t 5.432t 5.425t 5.443 5.387t 5.391 5.385t 5.420 5.404t 5.404 5.404 5.385t 3.171 3.171 3.177 3.106t 3.104t 3.104t 9.620 9.623 9.668 9.663 5.251 5.347 5.390 5.388 5.370 3.166 3.177 3.178 3.105 3.103 3.097 24.03 24.04 23.86t 23.95t 13.302t liiisst 13.223 13.214t 13.283 13.284t 13.329 13.311 13.196t 7.845 7.871 7.876 7.627t 7.643t 23.72 23.81 23.79 13.294' 13.318 7.837 7.891 7.890 7!667' 23.86 23.86 23.50t 23.55t 12.998t 13.110 12.978t 13.010 12.952t 13.101 13.197 13.180 13.037t 7.748 7.861 7.865 7.490t 7.540t 7.508t Mar. 17 Mar. 18 3 3 102.59 102.59 18° 3.062t 3.061t 51° 5!404 75.2° 6.700t 6.704t 100° 7.521t 7.520t 124.8° 7.760t 7.755t The results show that in general lower values were obtained the fresher the solution, the differences being especially large at the highest tempera- ture (156°). In deriving the most probable values, we shall therefore Table 57. — Equivalent conductance of ammonium hydroxide at uniform concentrations. Date. No. of stock sol. Concentra- tion at 4°. 18°. 100°. 156°. 1905 Feb. 21 Feb. 23 Feb, 34 May 17 May 18 Mean- Jan. 13 Jan. 17 Jan. 20 Jan. 27 Feb. 25 Meani. Feb. 27 Feb. 28 Mean 2 2 2 3 3 99.90 3.106 3.104 3.104 3.101 3.100 7.627 7.643 7.622 7.621 7.490 7.540 7.508 99.90 3.103 7.628 7.513 1 1 1 1 2 • 33.07 5.382 5.387 5.385 5.404 5.400 13.169 13.185 13.214 13.284 13.236 12.868 12.978 12.952 13.076 33.07 5.392 13.218 12.968 2 2 9.853 1 9.753 9.759 23.86 23.95 23.50 23.55 •• 9.853 9.756 23.90 23.52 Section 6^. — Equivalent Conductance at Round Concentrations, i^j select the results obtained in the earlier measurements with each solution (those to which a dagger is attached in the table). In order to combine them, those at nearly the same concentrations have been reduced to a uni- form concentration at 4° by means of the fomiula A^C = const. As the agreement of the separate results can best be judged in this way, we give the so-obtained values in table 57. As the final values the mean of these will be adopted. Table 58 contains what we regard as the best values which can be derived in the way stated in the preceding paragraphs from the summaries of the separate values given in tables 54, 55, and 57. Table 58. — Best values of the equivalent conductance at round temperatures. SODIUM HYDROXIDE. Concentra- tion at 4°. 18°. 100°. 156°. 218°. 2.031 4.038 21.55 19.151 50.31 49.08 212.1 211.8 205.5 200.6 582.1 576.9 560.6 542.7 812.6 803.3 774.1 745.3 1008 8 7 6 941 891 AMMONIUM CHLORIDE. 2.027 12.49 126.6 121.5 398.9 379.5 602.0 569.5 AMMONIUM HYDROXIDE. 9.853 33.07 99.90 9.756 5.392 3.103 23.90 13.218 7.635 23.52 12.968 7.513 67. EQUIVALENT CONDUCTANCE AT ROUND CONCENTRATIONS. The values given in table 58 refer to a different concentration at each temperature owing to the expansion of the solution. In order to show the effect of temperature alone they must be corrected to a uniform concentra- tion at each temperature. This has been done with the values for sodium hydroxide and ammonium chloride by means of the empirical equation Aj — A2 = i2'(C2* — Ci*), which states that the change of the equivalent conductance (A) at any one temperature is proportional to the change in the cube-root of the concentration (C*) ; and with the values for ammo- mum hydroxide by means of the mass-action expression Ao — A The results are given in table 59. A^alues extrapolated for a considerable interval are inclosed in parentheses. 174 Conductivity of Aqueous Solutions. — Part VI. Table 59. — Equivalent conductance at round concentrations. SubstaDce. Concentra- tion. 18°. 100°. 156°. 218. SodiTiTti hydroxide AinTnonium 2 4 20 40 50 9, (216. 212. 211. 205. 5) 1 3 i 5 (594) 582.0 576.6 559.4 (835) 813.5 804.8 770.6 746.0 (738.2) (628) 600.9 (1060) 1003 ' 930 889 200. (130 540.2 (873) 1 126.6 121.5 (99.8) 91.7 88.2 398.7 380.7 379.3 (338) 299.8 286.5 1 11 ^9. a 570.4 (567.1) (523) 1 . 456 426 1 ATnTnonimn acetate 10 Substance. Concentra- tion. 18°. 51°. 75.2° 100°. 124.8° 156°. A-mTnoTiinTn hydroxide 1(238) 10 9.678 (404) (526) 6.702 (647) 1(764) 23.25 (908) 22.31 12.99 7.170 30 .^.G.ifi 13.58 i 100 3.100 5.404 7.465 j 7.757 The values (A,,) for zero concentration or complete ionization have been calculated for ammonium chloride and for sodium hydroxide except at 318° by the graphical method which has been used throughout this series of investigations and is described in section 17, Part II. Since in the case of ammonium chloride the data did not suffice to determine the value of the exponent n, this was assumed to be the same as for potassium chloride, namely, 1.42. The results with sodium hydroxide at 318° are not accurate nor extensive enough to make this method reliable. The value of Ao at 318° given in the table is an estimated one derived from the value of A^ at the lower temperatures and from the corresponding A, values for sodium chloride and hydrochloric acid in the way described in section 84, Part VII. The values of Ao for ammonium hydroxide have been calculated by add- ing to the difference between the values for ammonium chloride and sodium chloride that for sodium hydroxide. The values for sodium chloride used were those given by Noyes and Coolidge, section 16, Part II, namely, 109.0 at 18°, 363 at 100° and 555 at 156°. The A„ values for ammonium hydroxide at 51.0, 75.3 and 134.8° were interpolated graphically between those at the other three temperatures, and are less accurate than the values at the other temperatures. The concentrations are expressed in milli- equivalents per liter of solution. The values given for ammonium acetate at 18° and 100° are based on the specific conductance values for the unhydrolyzed salt given below Section 68. — Change of Conductance tenth Concentration. 775 in table 67 under Lba. They have been corrected to round concentrations by means of the cube-root function. The values at 156° are similarly derived except that a correction was first applied by subtracting from the concentration of the salt (Cba) that of the hydrolyzed portion still exist- ing even in the presence of the largest quantity of added acid or base. The Ao values are calculated from those for sodium acetate and chloride given in table 36, section 54, and those for ammonium chloride here given. It is of some interest to compare the results at 18° with those obtained previously by Kohlrausch.* As far as the data are comparable the}' are placed side by side in the following table. Table 60.- -Conductivity results of different investigators. Temper- ' Concen- aturc. tratioD. 1 Sodium hydroxide. Ammonium ctiloride. Ammonium hydroxide. Noyes and Kato. Kohl- I Noycs rausch. 1 and Kato. Kohl- rausch. Noyes and Kato. Kohl- rausch. 18 2 4 10 12.5 20 30 50 212.1 211.8 205.8 200.6 206 204 197 190 126.6 121.5 126.2 'i2i!3 9.68 5.66 9.6 5.8 100 3.10 3.3 The agreement of the ammonium chloride values is within about 0.3 per cent. Kohlrausch's values for sodium hydroxide, however, are 4 to 5 per cent lower than ours, and his value for ammonium hydroxide at 100 milli-normal is 6 per cent higher. As Kohlrausch's data are derived from his earlier measurements made in 1885, it is probable that the discrepancy arises from impurities in the substances or water used by him, especially since his values for potassium hydroxide (231 at 4 milli-normal, 219 at 50 milli-normal) after allowing for the difference in equivalent conductance of the potassium and sodium ions (21 or 19 units) accord within 1 per cent with ours for sodium hydroxide. 68. CHANGE OF THE EQUIVALENT CONDUCTANCE WITH THE CONCENTRATION AND TEMPERATURE. With reference to the change of the conductivity with the concentration, we will limit ourselves to a consideration of the data for sodium hydrox- ide; for those with ammonium chloride and acetate do not cover a sufH- cient range of concentration. ♦See Kohlrausch and Holborn's Leitvermogen der Elektrolyte, pp. 159-160. //d Conductivity of Aqueous Solutions. — Part VI. It may first be shown that this base, like the neutral salts, conforms fairly closely at all temperatures to the simple cube-root formula of Kohl- rausch ( A„ — A = KO) . Applying it in the form Aci — Acj =^K{C^ — C^) we have first calculated the value of the constant K for C^ =50 (at 18° and 100°) or 40 (at 156° and 218°) and Cj = 4, and have then calcu- lated the value of Aoi for the intermediate concentration C^ = 30. The percentage deviations of the so-calculated values from the observed values given in table 59 are as follows: At 18°, 4" 0-0; at 100°, — 0.4; at 156°, — 0.3 ; and at 318°, + 0.3. These deviations are not greater than the possible experimental errors.* We have also determined graphically, by plotting -—against (CA)"-^ as described in section 17, Part II, what value of the exponent n in the func- tion C(Ao — A)=:i - r 3.109 17.18 lb 99.7 3.108 17.17 3 89.4 3.287 17.24 6 Mean 5b 85.75 3.352 17.30 loeTe ^" 17.16 3.003 17.13 5a 106.6 105.55 89.0 3.005 2.997 5.110 17.15 1.797 5p 106.6 105.1 89.55 3.000 2.998 5.096 17.09 1.794 5(J 106.6 105.35 89.8 3.005 2.989 5.073 17.15 1.783 i 93.85 92.7 78.2 3.306 3.209 5.458 17.20 1.798 'a 89.75 3.281 17.23 7b Mean 9.4 89.75 88.75 75.8 3.278 3.258 5.557 17.20 1.807 17.16 1.796 13.615 12.34 10.42 8.34 8.64 15.08 17.26 1.84 9.2 12.685 12.16 10.26 8.60 8.72 15.31 17.13 1.87 9.3 12.63 10.955 9.255 8.64 9.38 16.36 17.21 1.93 9.1a 10.495 9.41 17.02 9.1b 10.495 9.70 8.185 9.43 9.63 16.76 17.09 1.79 6.2 10.155 9.77 8.255 9.58 9.66 17.19 17.08 1.90 6.1 Mean 9.335 8.!)-. 7.. 56 9.98 10.22 18.44 17.08 2.00 17.12 1.89 306° 306° 306° 11 520.0 1 . 295 15.44 12 510.1 459.9 319.4 1.315 1.363 0.760 15.60 0.0935 13b 418.9 414.9 285.7 1.462 1.444 0.807 15.84 0.0940 13a 418.9 414.3 285.1 1.461 1.445 0.797 15.82 0.0915 13c Mean 10b 418.9 411.9 284.4 1.465 1.453 0.814 15.91 0.0955 147.2 i 0.0935 2.546 16.97 8 146.1 2.558 17.00 9 134.25 3.671 17.04 13.1a 144.85 138.5 96.2 2.556 3.571 1.357 16.83 0.0895 13.1b 144.85 137.65 95.75 2.549 2.590 1.356 16.74 0.0890 10a 147.3 133.8 93.8 2.547 2.698 1.374 16.98 0.0895 lOc 147.2 126.1 80.85 3.544 2.723 1.483 16.94 0.0900 lOe 147.2 97.75 68.55 2.544 *3.636 1.598 16.94 0.0S85 lOd Mean 147.2 97.0 61.7 2.. 5-16 3.195 1.681 16.97 0.0885 i 16.93 0.0895 :5° 25° 25° lOe 147.0 3.963 17.82 9 Mean 134.0 3.115 17.96 1 17.89 *This was the conductance at 25" 22i^ Conductivity of Aqueous Solutions. — Part VII. A comparison of the separate values of the ionization- constants for nearly the same concentrations in tables 82 and 83 shows at each tem- perature an entirely satisfactory agreement. Moreover, the mean of the first series of values for ammonium hydroxide, which were obtained with solutions prepared from a pure commercial aqua ammonia, will be seen to be identical with the mean of the second series of values, which with solutions prepared from a pure commercial aqua ammonia, will be 84. FINAL VALUES OF THE EQUIVALENT CONDUCTANCE AND THEIR VARIATION WITH THE CONCENTRATION AND TEMPERATURE. Final values of the equivalent conductance at round concentrations for ammonium chloride and sodium acetate and for ammonium hydroxide and acetic acid have been derived from those given in tables 80 to 83. This has been done in the case of the two salts at 306° with the help of the function C(Ao — A) = if (CA)" by first determining the values of the three constants A^, K, and n, by substituting the values of A at the three widely different concentrations, and then calculating in the reverse way the value of A for various round concentrations. In the case of ammonium chloride at 18° and 218°, however, since only two widely different concentrations were investigated, the value of n was assumed to be identical with that found for the very analogous salt potassium chloride, namely 1.42 at 18° and 1.50 at 218°. (At 18° and 25° the measurements with the pure salt, without excess of ammonium hydroxide, were alone utilized.) The values of A and of Aq so obtained are sum- marized in Table 84. The values of n at 306° derived as just described are 1.44 for ammonium chloride and 1.49 for sodium acetate. In the cases of ammonium hydroxide and acetic acid values for A„ were first obtained indirectly by the relations : Ao(NH40H) = Ao(NH40n -f-ApCNaOH) Ao(NaCl) Ao(HAc) = Ao(NaAc) +Ao(HOn AoCNaCU Most of the Ao-values for the substances on the right were taken from the various parts of this publication. In the case of sodium hydroxide, how- ever, no measurements exist at 306°, and those at 218° are not suf- ficiently accurate nor extensive. Ao-values for it were therefore derived under the assumption that it lies at such a proportional distance between the A(,-values for sodium chloride and hydrochloric acid at these tem- peratures as is indicated by its position between them at the lower temperatures of 18°, 100°, and 156°. All these Ap-values are given in the following table. Those for ammonium acetate which are needed in the subsequent calculation of the hydrolysis of this salt are also included. They were derived by combination of those for ammonium chloride. Section 84 — Final Values of the Equivalent Conductance. 22^ sodium acetate, and sodium chloride. The Roman numerals within parentheses show the Part of this publication, and the immediately fol- lowing number, the table, from which the Ao values were taken. Substance. NH^Ol NaCjHjO, NaOH HOI NaOl NH^OH ... HOsH.Oo . is° 25° NH.OsH^O,. 130.9* 78.1 (V, 36) 216.5 (VI, 59) 379 (V, 36) 109. Of 238.4 348.1 100.0 152.0 (VII, 84) 270. 6t 841 (VII, 84) 660 (V, 36) 1,060 1,265 (V, 36) 760 (II, 9) 1,141 1,165 741 306° 1,176 (VII, 84) 924 (VII, 84) 1,310 1,424 (VIII, 109) 1,080 (II, 9) 1,406 1,268 1.020 *Mean of the results presented in this Part, Table 84, and in Part VI, Table 59. tVahie of Kohlrausch. jCalculated from the NH4OH value at 18° by means of Kohlrausch's temperature-coei^cients for the ions (Sitzungsber. preuss. Akad., 1901, 1031). With the help of these A^-values for the ammonium hydroxide and {CkY acetic acid the ionization-constants ";77~ , already given in tables C ( Aq a ) Aq 82 and 83 were calculated; and from the means of these for each near- lying series of concentrations, the values of A at round concentrations were obtained by reverse calculation. The latter are summarized in table 84. Table 84. — Final values of the equivalent conductance at round temperatures. Milli- Substance. equivalents per liter. 18°. 25°. 218°. 306°. Ammonium 30 118.1 828 chloride 10 122.5 141.7 758 925 2 126.5 146.5 801 1031 131.1 152.0 841 1176 1 Sodium ace- 30 613 tate 10 2 702 801 924 Ammonium 500 1.325 hydroxide 300 1.752 0.785 100 3.103 3.62 4.821 1.329 80 3.466 5.389 10 9.66 15.56 238.4 270.6 1141 1406 Acetic acid 300 2.682 0.841 100 4.685 4.824 1.567 80 5.234 5.393 348.1 1165 1268 226 Conductivity of Aqueous Solutions. — Part VII. For the sake of comparison the values obtained by other workers in this laboratory are here tabulated. 0.002 Normal NH4CIatl8°. 0.1 normal NH40H. 0.08 normal HC2H3OS. | at 18°. at 25°. at 18°. at 218°. Noyes and Cooper. Noyes and Kato... Kanolt 126.6 *i26!5 siio' 3.11 3.10 3.62 5.22 5.23 5.34 *KohIrausch found 126.2. It is of interest to consider the change with the temperature of the A„-values for ammonium chloride and sodium acetate, taken in combi- nation with the results of Noyes and Kato (table 59, Part VI) and of Noyes and Cooper, table 40, Part V). The values of AA/At for the successive temperature-intervals are given in table 85; and the ratio of their Ao-values to those of potassium chloride and sodium chloride at the same temperature are given in table 86. Table 85. — Temperature-coefUcients of the equivalent conduct- ance at zero concentration (AAo/Af). Substance. -^o »'18°. 18-100°. 100-156°. 156-218°. 218-306°. NH4CI 130.9 NaOjHjOa 78.1 3.47 2.53 3.80 3.43 2.95 3.40 3.81 3.00 Table 86. — Ratio of -^a-values to those for other substances. Substance. 18°. 100°. 156°. 218°. 306°. NH,01 : KCl 1.01 0.60 0.72 1.00 0.69 0.79 1.00 0.72 0.81 1.02 0.80 0.87 1.05 0.82 0.86 NaOjHsO^ :KC1 NaOjHaOj : NaCl It will be seen from these tables that the A^-values for ammonium chloride increase with the temperature in nearly the same way as do those for potassium chloride, there being two points of inflexion in the con- ductance-temperature curve, namely, between 100° and 218°, and 218° and 306°. For sodium acetate, on the contrary, the rate of increase with the temperature becomes steadily greater up to 218°. The equivalent conduct- ance of the acetate ion, however, steadily approaches that of the chloride ion (except through the interval 218°- 306° where the slight decrease in the ratio for sodium acetate to sodium chloride may be due to error). Section 85. — Ionization Values. 22y With respect to the change of equivalent conductance with the con- centration, mention need only be made of the fact that the values of the exponent n in the function C(Ac — A) ^i^(CA)" are about the same for these two salts at 306° as for the other salts previously investigated, namely, 1.44: for ammonium chloride and 1.49 for sodium acetate. In the cases of the base and acid the value of n is approximately 2, as the mass- action law requires (see section 85). The equivalent-conductance values for the base and acid ( for example, at 100 milli-normal) decrease greatly between 218° and 306° and are less at the latter temperature than at 18°. This arises, of course, from a greatly decreased ionization, which overcompensates the increased equivalent conductance of the ions. 65. IONIZATION VALUES AND THEIR VARIATION WITH THE CONCENTRATION AND TEMPERATURE. Table 8T contains the percentage ionization-values for the four sub- stances whose equivalent conductances were given in table 84. These values are simply those of the ratios lOOA/A,,. Table S7. — Percentage ioiiizatioii. Milli- Substance. equivalcnts per liter. 1S°. 25°. :is°- 306°, Ammonium 30 00.1 70.4 chloride 10 93.5 93.2 90.1 78.7 96.5 96.4 95.3 87.7 Sodium 30 66.4 acetate 10 76.0 86.7 Ammonium 500 0.556 hydroxide 300 0.735 0.0558 100 1.302 1.338 0.422 0.095 80 1.454 0.472 10 4.05 1.36 Acetic acid 300 0.771 0.0663 100 1.346 0.414 0.124 80 1.504 0.463' The ionization values for ammonium chloride and sodium acetate even at 306° are only sHghtly less than those for sodium and potassium chlo- rides, for which in 10 milli-normal solution the values 79.6 and 81. '3 per cent were found by Noyes and Coolidge (see table 1?, Part II). The ionization of both ammonium hydroxide and acetic acid is seen to have become very much less at the higher temperatures. The separate values of their ionization-constants have already been given in tables S2 and 83. 328 Conductivity of Aqueous Solutions. — Part VII. In table 88^ are given the means of these for each group of nearly equal concentrations, which means correspond to the ionization values given in table 87. In computing these constants the concentration has been expressed in equivalents per Uter. In the last line under each substance are given in black type, what are probably the best values for dilute solu- tions, taking into consideration the experimental errors in the more dilute solutions and the deviation from the mass-action law in the more con- centrated ones. Table 88. — Ionization- constants X 10° for ammonium hydroxide and acetic acid. Substance. Equivalents per liter. 18°. 25°. 218°. 306°. Ammonium hydroxide Acetic acid 0.52 0.42 0.30 0.15 0.10 0.01 Best Value 0.43 0.30 0.14 0.10 Best Value 15.5 15.9 0.094 16.9 17.2 17.1 17.2 17.4 17.9 1.80 1.89 1.80 0.090 6!693 0.132 18.4 18.3 18.3 1.72 1.72 0.153 0.189 It will be noted that at 18° the ionization constants of both substances are considerably less at 0.4 normal than at 0.1 normal, doubtless because of inaccuracy in the assumptions involved — the validity of the mass- action law or the proportionality between ionization and equivalent con- ductance. That at the higher temperatures of 318° and 306° the mass- action law holds, at any rate approximately, at moderate concentrations is shown for ammonium hydroxide by these results. This has previously been shown to be true for acetic acid at 218° by Noyes and Cooper. Their values of the constant (18.2 and 1.69 X 10"") also agree well with mine (18.4 and 1.72 X 10~°). This is especially true when the somewhat different manner of correcting for the conductance of the water is con- sidered; thus their value at 218° when corrected as described in section 79 of this part becomes 1.72. Section 86. — Hydrolysis of Ammonium Acetate. 22g> 86. HYDROLYSIS OF AMMONIUM ACETATE AND IONIZATION OF WATER AT 218° AND 306°. In order to derive the degree of hydrolysis of ammonium acetate, the specific-conductance values given in table 78 have been first corrected to round temperatures by means of the temperature-coefficients given in table 79, and the content by weight has been reduced in the usual way to volume-concentration at the temperature of the measurement. These conductance values were previously corrected for the conductance of the impurities in the water; and a correction has now been applied for that of the ionized water, or of the base or acid added, in those cases where the correction exceeds 0.1 per cent. This correction was calculated from the ionization-constants for these substances and the equivalent conductance of the ions, as described in section 79. In no case did the correction exceed 0.25 per cent. Table 89 contains the so-corrected data for the pure salt, and table 90 those for the salt with an excess of base or acid. In the latter table are given for 218° and 306° in two additional columns (1) the specific conductance (Lj,) which the pure salt has at the same concentration as that (C) of the salt in the mixture, and (2) the ratio of the specific con- ductance (l) of the salt in the mixture to this conductance l„. The specific conductance l^ is calculated from that given in table 89 for nearly the same concentration under the assumption of proportionality between conductance and concentration through the small interval involved. Table 89. — Specific conductance at round temperatures of pure ammonium acetate solutions. Experi- ment No. Milli-equivalents per liter. Specific conductance X 10^. 18°. 218°. 306°. 18°. 218°. 306°. 1.3 1.4 2.1 2.15 Mean . 2.3 2.10 2.11 Mean . 2.34b 2.24a 2.34c Mean . 2.19a 2.19b Mean . 14.57 14.44 14.01 14.18 11.81 12.01 1,311.5 1,302 1,366 1,281.5 3,770 3,830 14.30 11.91 1,290 3,800 7.10 7.11 7.045 5.93 6.025 5.96 656.0 657.0 651.0 1,918.5 1,944.5 1,921.5 7.085 5.97 654.7 1,928 43.10 43.10 43.10 29.38 29.33 3,691 3,694 2,413 2,394 43.10 39.35 3,693 2,403 14.335 14.335 9.97 10.015 1,294.5 1.294.5 813 818 14.335 9.995 1,294.5 815 ^30 Conductivity of Aqueous Solutions. — Pari VII. Table 90. — SpeciHc conductance at round temperatures of ammonium acetate solutions containing ammonium hydroxide or acetic acid. Milli-equivalents per liter. Specific conductance X 106, Tem- Experi- pera- tare. ment No. Salt in mixtare. Acid (A) base (B or Salt in mixture. Salt in water alone. Ratio. 1° c : < io» C^orCgXlOS L X 106 io X 10° i/io 218 2.16 11.94 11.88 A 5,057 3,809 1.328 2.7 12.015 12.075 B 5,010 3,833 1.307 ' 2.17 11.90 23.61 A 5,651 3,797 1.488 2.8 11.92 23.41 B 5,482 3,803 1.442 2.18 11.825 47.38 A 6,173 3,773 1.636 2.9 11.875 46.75 B 6,093 3,789 1.608 t 2.12 6.08 5.985 A 2,606 1,963 1.328 2.4a 2.4b 6.00 6.04 6.25 6.25 B B 2,563 \ 2,562 / 1,944 1.318 2.13 6.10 12.055 A 2,944 1,969 1.495 1 1 2.5a 6.025 11.78 B 2,875 1 2,863 / 1 2.5b 6.015 11.78 B 1,944 1.476 2.14 5.975 24.12 A 3,207 1,930 1.663 2.6 6.015 23.62 A 3,150 1,942 1.622 306 2.26 28.76 31.91 A 3,430 3,355 1.457 3.1 27.53 88.6 A 4,482 2,254 1.988 2.25 28.34 68.4 B 4,210 2,320 1.813 2.20a 9.96 10.025 A 1,146 \ 1,150 / 2.20b 9.965 10.01 A 813 1.412 2.22 10.01 8.19 B 1,093 816 1.338 2.21 9.855 30.06 A 1,589 803 1.979 2.23 9.735 25.22 B 1,480 794 1.864 From the data given in table 90 the hydrolysis of the salt at 218° and at 306° has been calculated in two different ways. The first of these is that used by Noyes and Kate (section 73, Part VI) in connection with their hydrolysis experiments at 156°. In this method, the following expressions for hydrolysis equilibrium and for the empirical relation of van't Hoff between the ionization and concentration of salts are combined: (t)* = l~h- lO^L C\„ 1 — /r„ — 10^ C'A,-, and thereby the values of /;„ and h, the hydrolysis of the salt at concen- tration C in pure water and in the mixture respectively, are calculated. A(, is the equivalent conductance of completely ionized ammonium acetate ; its values are 741 at 218° and 1020 at 306° (see section 84). Section 86. — Hydrolysis of Aininonium Acetate. 2^1 In the second method the ion-concentration is, as before, calculated by dividing the specific conductance of the solution (multiplied by 10=) by the equivalent conductance of the completely ionized salt; and then the concentration of the un-ionized salt is estimated under the assumption that it has the same value as in a solution of an ordinary unhydrolyzed salt of the same ionic type at the same ionic concentration. Then merely by subtracting the un-ionized fraction (m) and the ionized fraction (y) from unity, the hydrolyzed fraction {h) is obtained ; that is, /i = 1 — y — u. In this calculation the mean ionization of potassium and sodium chlorides as determined by Noyes and Coolidge (table 12, Part II) wras used as a basis. This calculation can give accurate hydrolysis values only when the hydrolyzed fraction is large and the un-ionized fraction very small; but under such conditions, which are in fact realized in the foregoing experiments fairly well at 218° and in much higher degree at 306°, it is the most direct method and a fairly reliable one. For example, suppose the hydrolyzed, ionized, and un-ionized parts were 80 per cent, 18 per cent, and 2 per cent respectively; then an error of even 3 per cent in the ionized, and of 25 per cent in the estimated un-ionized fraction, would make, if they lay in the same direction, an error of only one per cent in the hydrolyzed fraction.* Table 91 contains the results of the calculations. In the fifth and sixth columns are given the values of the percentage hydrolysis (100/t) calculated by the first and second methods, respectively. In the seventh column is given a mean derived from these. Since the results by the second method are more accurate the greater the hydrolysis, in deriving this mean a weight has been assigned to them equal to the percentage hydrolysis, the results by the first method being always given a weight of 100. It is desirable to combine the results by the two methods in some such way as this, since any error in the conductance ratio l/l^ influences them in opposite directions. In the last three columns of the table are given the values of the percentage hydrolysis (100 h^ of the salt in pure water at the same concentration C. The values in the first of these columns are derived by the first method simultaneously with those of 100 h. Those in the second of these columns are calculated from the mean value of lOO/i given in the seventh column by the equation h 2 — — . , — ^ — '-: Those in the last column are obtained directly by the second method from the conductance in pure water. *The calculations were also made by still a third method, namely, that described by C. W. Kanolt in Section 103, Part IX, but in this case where the hydrolysis is very large the results were found to be much more influenced by the experimental error than those calculated by the first method. They are therefore not recorded here. 232 Conductivity of Aqueous Solutions. — Part VII. Table 91. — Hydrolysis an i ionization o f ammonium acetate at 218° and 306°. Temper- ature. 1° CoDcentra- of salt CXIOS Concentra- tion ratio _or _^ C C Salt in mixture. Salt in pure water. Ioniza- tion 100 y Perceotaee hydrolysis tlOOftJ. Ioniza- tion lOOVo Percentage hydrolysis ( 100 fto ) By first method. Bt second metbod. Weieht- edmean. By first metbod. From mean yalue of 4. By second metbod. 218 11.91 11.94 11.90 11.825 0.995 A 1.984 A 4.007 A 43.1 43.1 43.1 43.1 53.3 57.2 64.1 70.5 35.5 26.2 16.5 37.4 29.5 22.3 36.0 27.0 17.6 52.1 51.6 50.7 52.6 52.4 51.7 Mean .. 1 51.5 52.2 12.015 11.92 11.875 1.005 B 1.964 B 3.937 B 56.3 62.1 69.2 29.6 21.5 15.5 38.4 31.8 23.7 32.0 24.0 17.1 43.1 43.1 43.1 47.5 47.4 49.5 49.8 50.5 52.1 Mean . . i 48.1 50.8 5.97 6.08 6.10 5.975 0.984 A 1.976 A 4.037 A 43.6 43.6 43.6 43.6 53.7 57.8 65.1 72.4 36.0 27.1 17.6 38.0 30.0 22.0 36.5 27.8 18.4 52.4 52.2 51.8 52.9 52.9 53.0 Mean .. 52.1 52.9 6.02 6.02 6.015 1.038 B 1.957 B 3.927 B 57.5 64.3 70.7 30.6 25.2 16.1 38.4 30.9 23.8 32.7 26.5 17.6 43.6 43.6 43.6 48.6 50.6 50.0 50.7 52.0 52.4 Mean . . 49.7 51.7 306 29.35 28.76 27.53 1.110 A 3.218 A 8.03 8.03 8.03 94.8 91.0 92.4 90.9 90.9 11.69 15.96 93.4 81.2 86.3 81.0 90.1 81.1 Mean . . 92.9 91.6 28.34 10.00 9.965 9.855 2.414 B 1.006 A 3.050 A 14.56 85.0 82.8 84.0 8.03 7.99 7.99 7.99 91.8 91.1 91.2 11.29 15.81 90.2 86.0 87.5 82.3 88.9 84.3 92.9 92.7 91.9 91.6 Mean . . 92.8 91.7 10.01 9.735 0.818 B 2.591 B 10.70 14.91 86.7 85.8 88.2 83.4 87.4 84.7 7.99, 90.3 7.991 92.3 90.9 91.5 Mead .. 91.3 91.2 A comparison of the values of the percentage-hydrolysis (100 It) of the salt in the mixture calculated by the two methods shows at 218° a considerable divergence, especially in the experiments where an excess of base was added. This was doubtless due largely to the destruction of some of the base during the heating. At 306° where this was determined and allowed for, and where the calculation by the second method is more accurate, the agreement is far more satisfactory (except in the first experiment which appears to be affected b\- some accidental error). From an examination of the values of the percentage hydrolysis (100 h^) of the salt in pure water it is seen that the experiments in which different quantities of acid were added gave ver}- concordant results, whether Section 86. — lonisation of Water. 233 calculated directly by the first method or from the weighted mean value of the percentage hydrolysis (100 /i) for the salt in the mixture. The mean value calculated from the latter is, however, to be considered the most accurate. It will be seen that this agrees well in all cases with the value given in the last column, which was calculated directly by the second method from the conductance of the salt in pure water. To get the best final value from each group of experiments we have combined these two b>' assigning to the former a weight of 100 and to the latter a weight equal to the percentage hydrolysis. Table 92 contains the final hydrolysis values so obtained, the ionization values for the salt, the ionization-constant of water calculated from them by the equation /v'w ^ KAKsho'/yo^- ^iid the square root of the constant, which represents the concentration Ch of the hydrogen (or hydroxide) ion in pure water. Table 92. — lonisation of zi.'ater at 218° and 306° Temper- Bture Final results with ammonium acetate. Ionization constant of water X 10". Equivalents of hydroeen- ion per 10' liters Equiva- lents per liter. PcrcentaEe ioniza- tion. Percentage hydrol- ysis. i° C lOOVo 100*0 K^ X 101* C„ X 10' 218 306 0.012 0.006 0.030 0.010 43.1 43.6 8.03 7.99 53.6 53.2 461 461 21.5 21.5 Mean 91.3 91.5 461 : 21 . 5 167 ' 12.9 170 13.0 Mean 168 , 13.0 A comparison of these values of the ionization-constant with those presented in Part ^T by Noyes and Kato (48 at 100° and 223 at 156°) shows that the constant is considerably greater at 218° than at the lower temperatures, but that it has become much less at 306°. From a plot of the values it appears probable that the maximum lies between 250° and 275° 5j^ Conductivity of Aqueous Solutions. — Part VII. 87. SUMMARY. In this article have been presented the results of conductivity measure- ments with ammonium hydroxide, acetic acid, and ammonium chloride at 18°, 218°, and 306°, and with sodium acetate at 306°. The final values of the equivalent conductance will be found in table 84, and of the corres- ponding ionization in table 87. The equivalent conductance of completely ionized ammonium chloride, which at 18° is nearly equal to that of potassium chloride, becomes 2 per cent greater at 218° and 5 per cent greater at 306° ; and that of sodium acetate, which at 18° is only 71 per cent of that of sodium chloride, becomes 86 per cent of it at 218° and 306°. The ionization of the two salts is at all temperatures only a little less than that of sodium and potas- sium chlorides; thus at 306° the differences are about 2 per cent and 4 per cent, respectively. The hydrolysis of these salts was not measured, but was reduced substantially to zero by the addition of an excess of the weak base or acid. Its value can, however, be calculated from the ionization-constants of water, ammonium hydroxide, and acetic acid deter- mined in this research*; and it is of interest to note that in 0.01 normal solution both salts at 218° are 1.56 per cent hydrolyzed, and that at 306° ammonium chloride is 4.1 and sodium acetate 3.4 per cent hydrolyzed, while at 18° the hydrolysis is only 0.02 per cent. The ionization of the slightly ionized substances, acetic acid and ammo- nium hydroxide, decreases with great rapidity as the higher temperatures are reached; thus the ionization-constants (X 10°), as determined from the measurements at 218° and 306° presented in this article and from the earlier ones at 18°, 100°, 156°, and 218° by Noyes and Cooper, and Noyes and Kato, are as follows : Acetic Acid. Ammonium Hydroxide. 18° 18.3 17.2 100° 11.1 13.5 156° 5.42 6.28 218° 1.72 1.80 300° 0.139 0.093 *These calculations were made, for sodium acetate for example, by the substan- . „ ... Ch'yj, A'w , . _ tially exact mass-action relation 7- — yf-^ -r^ . wnerem C represents the concentra- (1 — n)y Aa lion of the salt, h the hydrolyzed fraction of it, 7 the ionized fraction of the quantity of it unhydrolyzed (C — Ch), 7b the ionized fraction of the total quantity of free base (Ch), Kj^ the ionization-constant for the acid, and K-^ that for water. For the ionized fractions 7 and 7^ in the mixture may be taken the value for the pure salt and that for the pure base, respectively, when present alone at the concentration C, the principle being here applied that in a mixture of largely ionized substances the ionization of each is the same as if it were present alone at a concentration equal to the sum of the concentrations. Section 8/. — Summary. 2j5 In this article have also been presented determinations of the degree of hydrolysis of ammonium acetate at 218° and 306°. This has been derived from measurements of the change in conductance produced when to the solution of the neutral salt acetic acid or ammonium hydroxide is added. In 0.01 normal solution the pure salt was found to be 53 per cent hydrolyzed at 218° and 91 per cent at 306°, while it can be shown by calculation to be only 0.35 per cent hydrolyzed at 18° ; thus showing the enormous eflrect of temperature in increasing the hydrolysis of salts. From the hydrolysis and ionization of the ammonium acetate and from the ionization-constants of the acid and base the ionization of water itself at 218° and 306° has been calculated. The final results together with those obtained at lower temperatures by the previous workers in this laboratory, are as follows. The values show the equivalents of hydrogen- ion or hydroxide-ion present in ten million liters of pure water. 100° 156° 218° 306° 6.9 14.9 21.5 13.0 The considerable increase between 100° and 218° and the decrease between 218° and 306°, indicating a maximum between these temperatures, will be noted. Part VIII. The Conductivity and Ionization of Hydrochloric, Nitric, and Sulphuric Acids up to 306°, and OF Phosphoric Acid and Barium Hydroxide up to 156°. By Arthur A. Noyes and Guy W. Eastman. Part VIII. THE CONDUCTIVITY AND IONIZATION OF HYDROCHLORIC, NITRIC, AND SULPHURIC ACIDS UP TO 306°, AND OF PHOSPHORIC ACID AND BARIUM HYDROXIDE UP TO 156°. 88. OUTLINE OF THE INVESTIGATION. In this article, after a brief description of experimental details, are given the results of conductivity measurements with aqueous solutions of sul- phuric, phosphoric, and nitric acids, and barium hydroxide at various concentrations at temperatures up to 156°. The measurements were for the most part made at 18°, 55°, 50°, 75°, 100°, 128°, and 156°, and at the concentrations 100, 50, 12.5, 2, and 0.5 milli-nonnal. Conductivity meas- urements with nitric and sulphuric acids at the still higher temperatures of 218° and 306°, and with hydrochloric acid at 260° and 306° were also made, and these are included with the others. Some results with sul- phuric acid extending up to 218° which were obtained somewhat earlier in this laborator}- by Mr. Yogoro Kato are also here presented in con- junction with our own. Finally, the results are all discussed with reference to the ionization of the various substances and the equivalent conductance of their ions at different temperatures. 89. DESCRIPTION OF THE APPARATUS AND METHOD. CONDUCTIVITY-VESSEL. The conductivity bomb (No. 1) employed in most of this work, was the first one made in this laboratory as described in Part II of this series. It had been used just previously by j\Ir. Yogoro Kato for the investigation described in Part VI and for his measurements with sulphuric acid pre- sented below. It then contained an open cylindrical platinum-iridium electrode arranged as shown in figure 13, Part III ; and in that form will be designated Cell i below. For our experiments this electrode was replaced by a flat platinum-iridium electrode placed at the bottom of a quartz cup, 1.45 cm. in height and 1.40 cm. in diameter. The vessel in this form will be called Cell ii. For some of our later measurements another 339 240 Conductivity of Aqueous Solutions. — Part VIII. bomb (No. 3) with a similar electrode was used, the quartz cup in which was 1.40 cm. in height and 1.37 cm. in diameter. This will be called Cell III. CONDUCTIVITY MEASURING APPARATUS AND INDUCTOR. A slide-wire bridge of the roller type, described by Kohlrausch and Holborn, and made by Hartmann and Braun, was used to measure the conductance. The coils were of manganine and of 1, 10, 100, 1,000, and 10,000 ohms resistance. Each coil was compared directly in the Insti- tute's testing laboratory with manganine standards having the Reichs- anstalt seal and certificate. The slide-wire was calibrated twice by the method of Strouhal and Barus. The corrections both to the coils and sUde wire agreed within the experimental error with the results of Kate obtained a few months earlier. An ordinary interrupter was used. The minimum sound in the tele- phone was very good except for the most dilute and most concentrated solutions, and fairly good for them. HEATERS. For the work up to and including 156°, a liquid bath of pseudocumene, heated electrically by an inside and outside coil, and well stirred, was used. Cooling was effected by running tap water through a copper coil immersed in the bath. The temperature was regulated by the observer, by varying the current through the coils. It could be held at a desired tem- perature within the negligible variations of 0.02° at 18° and 0.1° at 156°. For the temperatures of 318°, 260°, and 306° vapor baths of boiling naphthalene, isoamyl benzoate. and benzophenone, respectively, were used. THERMOMETERS. Up to and including 100°, mercury thermometers graduated in tenths of a degree were used. Since stem exposure could not always be avoided, they were calibrated in position as used by comparison with a standard Baudin thermometer, having a Bureau of Standards' certificate. The ice and steam readings remained substantially constant throughout the work. The error in the bath temperature could hardly have exceeded 0.02'° at the 18°, 25°, 50°, and 100° points, but at 75°, owing to the necessity for applying a large stem-exposure correction to the standard Baudin, the error may have been as much as 0.05°. The temperatures above 100° were probably determined with an accuracy of 0.2° -0.3°. At these tem- peratures a 360° Alvergniat thermometer, graduated in degrees, was used. The ice, steam, naphthalene, and benzophenone points were directly deter- mined. Intermediate corrections were computed for 138° and 156° from the bore calibration, allowing for deviations of the mercury from the Section 8p. — Apparatus and j\Iethod. 241 gas scale, as given by Crafts.* The correction at 260° was determined by comparison with a platinum resistance thermometer which had been standardized in this laboratory by Mr. R. D. Mailey. The values used for the boiling points of naphthalene and benzophenone were those of Jacquerod and Wassmer;t namely, at a pressure of 76 cm. mercury, 317.7° for the former substance and 305.44° for the latter. METHOD OF PROCEDURE. No important change in the method of procedure as described in Part IV was made. The contents of the bomb were always well shaken within the bath by rotating the bomb several times before and between the readings. Constant uniform temperature was tlius quickly obtained, and any contamination in the quartz cup distributed through the whole solu- tion. In the measurements up to 156° the bomb was filled from a pipette with such a quantity of solution that the vapor space at 156° was about 7 c.cm. In those extended to still higher temperatures such a quantity of solution was always placed in the bomb as sufficed to fill it within 2 or 3 c.cm. at the highest temperature of the experiment in question. The solutions were always placed in the bomb the day they were made up from the stock solution. Only after the temperature of the bath had remained constant for at least 15 minutes were final bridge-readings taken; then at five minute intervals, double settings (reversing the commutator) were made with each of three diflferent resistances in the box. Before introducing the most dilute solution of any substance, the bomb was first soaked out by heating with conductivity water or the solution itself to 218° or 306°. The solutions successively introduced into the bomb were then always of increasing conductance, ^^'ashing with alcohol and ether was avoided as far as possible, as their use seemed to be always followed by greater differences than usual between the initial and final 18° conductances. 90. PREPARATION OF THE SUBSTANCES AND SOLUTIONS. The potassium chloride used for detemiining the conductance-capacity of the bomb was made from J. T. Baker's "Analyzed C. P." salt, said to contain only "traces"' of magnesium and of sodium chlorides. This was precipitated from solution with hydrochloric acid and then showed no flame test for sodium. This precipitated salt was w-ashed with hydro- *Ara. Cheni. J., 5, 307-338 (1883-84). A check on these corrections \vas obtained by comparing the correction at 218° computed from the bore calibration and the steam and benzophenone determinations, with the actually observed correction m the naphthalene bath. The results agreed within 0.1°. A further check was obtained some months later hv comparison with a certified German thermometer divided in tenths, between 100° and 200°, the greatest discrepancy berag 0.3 . tj. chim. phys., 2, 73 (1904). 2/^2 Conductivity of Aqueous Solutions. — Part VIII. chloric acid, dried, dissolved in boiling water, and crystallized at 5°. The crystals were washed and dried. A second sample was obtained by adding hydrochloric acid to the mother liquor from these crystals. No difference was noticed in the conductances of these two lots. In making standard solutions this substance was freshly ignited almost to the fusing point, weighed out, and dissolved in a graduated flask. Sodium chloride was also used for determining the conductance-capac- ity. This was purified by twice precipitating Kahlbaum's "chemically pure" product with hydrochloric acid. The final precipitate was dried and gently ignited. The stock sulphuric acid solution used for all the measurements was a fifth-normal one prepared by Mr. Y. Kato on August 10, 1905, by dilut- ing with conductivity water a sample of the "strictly chemically pure sulphuric acid" furnished by Baker and Adamson. The concentrated acid (usually 10 c.cm. portions) was tested by him for arsenic with hydro- gen sulphide, for nitric acid with diphenylamine, for nitrous acid with starch and potassium iodide, for hydrochloric acid with silver nitrate, for selenium with ferrous sulphate, and for ammonia with Nessler solution. Xone of these impurities was present in appreciable quantity, if at all. The concentration of the solution was determined on August 11—15, 1905, both by precipitating and weighing the acid as BaSO^ and by titration with phenolphthalein against a hydrochloric acid solution previously standardized by weighing the AgQ yielded by it. The sulphuric acid was restandardized on December 9, 1905, against an ignited sample of sodium carbonate furnished with an analysis showing substantial purity by J. T. Baker.* To the solution of a known weight of the carbonate, a slight excess of the stock sulphuric acid was added, the solution boiled for ten minutes and then titrated with 0.01 normal potassium hydroxide with the help of phenolphthalein as an indicator. We are indebted to Mr. G. A. Abbott for the preparation and analysis of the stock solution of phosphoric acid which was used in this part of the investigation. This sample of acid was prepared by Mr. Abbott by direct oxidation of yellow phosphorus. The method is summarized as follows: Carefully selected clean pieces were heated in a retort with nitric acid (sp. gr. 1.20). After the phosphorus had disappeared the contents of the retort were evaporated in small portions with addition of enough nitric acid to insure complete oxidation of any phosphorous acid until the white *The BaSOi determinations gave for the concentration, expressed in millimols H2S0i in a kilogram of solution, 110.54, 110.51, and 110.52, from which by correcting the weighings to vacuo, the value 110.43 results. The atomic weights used were O = 16.00, Ba = 137.4, S = 32.06, and H = 1.01. By the titration against the hydro- chloric acid the value 110.70 was obtained ; and from that against sodium carbonate 110,71 resulted. The mean 110.61 was adopted. Section go. — Preparation of Solutions. i-^j fumes of metaphosphoric acid appeared. The cooled residue was taken up in conductivity water and saturated with hydrogen sulphide, in order to precipitate possible traces of arsenic or platinum. The metaphosphoric acid solution thus obtained was converted to the ortho acid by boiling in a platinum dish for three hours. That the conversion in this solution was complete was shown by the fact that the conductance of the diluter solu- tions prepared from it was not changed by heating to 156°. The solution received January 17, 1906, from Mr. Abbott was part of a stock solution which he had analyzed gravimetrically by precipita- ting the phosphoric acid with magnesium ammonium chloride and weigh- ing as magnesium pyrophosphate. The five analyses made by him gave as a mean value 20.0866 grams of HjPO^j per kilogram of solution. Assuming 1 mol H3PO4 ^ 98.02 grams, the concentration of this solu- tion becomes 0.2049 mols per kilogram of solution. The nitric acid solution was made by diluting a portion of "C. P. nitric acid," of specific gravity 1.43, taken from a newly opened carboy, with half as much water, bubbling through it for one day a current of carefully purified air, so as to remove nitrous acid, and finally diluting with enough conductivity water to give a ^■er^• nearly 0.1 normal solution. The stronger solution was tested for nitrous, ''= sulphuric and hydrochloric acids, for ammonium salts (with Nessler reagent), and for non-volatile residue. None of these impurities were present in quantity as large as 0.01 per cent of the nitric acid present. The acid was standardized by compari- son with the sulphuric acid solution just described through a 0.1 nomial sodium hydroxide solution, and also directh' against sodium carbonate. Its concentration was thus found to be 99.70 and 99.87 (mean 99.78) milli-equivalents per kilogram of solution. The barium hydroxide used for preparing the stock solution of this substance was purified by twice crystallizing from hot water in procelain vessels a "chemically pure" preparation of ]\Ierck's. The crystals so obtained were dissolved in hot conductivity water, the solution filtered immediately out of contact with ordinary air, the filtrate allowed to run into about three liters of water of specific conductance 0.6 X 10"° con- tained in a "Kon-Sol" bottle (furnished by \^■hitall, Tatum & Co.). After standing for 34 hours, this solution, from which crystals separated on cooling, was forced over into a second "Xon-Sol" bottle containing enough more conductivity water to dilute it to about 0.2 normal. The final solution was perfectly clear and remained so. *The test for nitrous acid was made by adding to 1 c.cm. of the stronger solution 100 can. water, 10 c.cm. of an acetic acid solution of sulphanilic acid, and 10 c.cm. of a solution of naphthylamine acetate, and allowing the mixture to stand. For com- parison a minute quantity of nitrite was added in a duplicate test. The result showed that, while one part of nitrous acid in a million could be detected, less than this was present in the strong nitric acid. ^^^ Conductivity of Aqueous Solutions. — Part VIII. This solution was tested for chloride, and the original substance was tested for nitrate,* with negative results. That it contained no import- ant quantity of non-volatile impurities was shown by precipitating the barium by running the solution into an excess of the stock sulphuric solution, allowing it to stand, filtering, and evaporating the filtrate first in a porcelain beaker and finally in a weighed platinum dish. The residue so obtained from 100 c.cm. of the cold-saturated barium hydroxide solu- tion weighed 5.6 milligrams, of which only one milligram was shown to be silica by treatment with hydrofluoric acid. Some of the remainder was doubtless unprecipitated barium sulphate; but even if the whole of it had been an impurity in the barium hydroxide, it would not amount to more than 0.1 per cent. A more conclusive test of purity of both the barium hydroxide and sulphuric acid was obtained as follows : 118.77 grams of the stock barium hydroxide solution were run into 113.38 grams of the stock sulphuric acid solution, previously heated to boiling. This should have left, according to computation, a slight excess of acid in the clear filtrate. The specific conductance of this filtrate was measured, and it was com- puted therefrom that assuming only sulphuric acid to be present an excess of 0.39 grams of its solution must have been added. Titration with 0.01 normal sodium hydroxide showed almost exactly the same quantity (0.42 grams), indicating that not enough impurity was present to aflfect appreciably the measured conductance. This last experiment evidently gives also a means of comparing the stock solution of barium hydroxide with that of sulphuric acid, and thus tying together the whole series of values. The concentration of the barium hydroxide, so computed, is 0.17 per cent less than the adopted value, a difference not greater than the discrepancies in the analyses by independent methods of the same solution. The concentration of the stock solution of barium hydroxide was found on March 20, 1906, by means of three titrations against the stock nitric acid, using phenolphthalein as indicator, to be 210.83 milli-equivalents per kilogram of solution. The stock solution of hydrochloric acid was made by bubbling the gas produced by the action of pure sulphuric acid on pure sodium chlo- ride through a little water and then absorbing it in conductivity water. It was standardized against the barium hydroxide solution and found to contain 114.42 millimols HCl per kilogram of solution. Its conductance at 18° agreed closely with the values obtained by Goodwin and Haskellf *In making this test, about 1 gram was dissolved in acetic acid, and a drop of indigo solution and several cubic centimeters of sulphuric acid (1.84 sp. gr.) were added. The blue color remained, whereas when one drop of a 0.1 normal nitric acid was added, the solution was decolorized at once. fProc. Am. Acad., 40, 413 (1904). Phys. Rev., 19, 386 (1904). Section pi. — Errors and Corrections. 2j.§ 91. DISCUSSION OF ERRORS AND CORRECTIONS. The errors inherent in the use of the conductivity bomb and the correc- tions for them are fully discussed in section 10, Part II. A few additional words in regard to the relation of them to the present work will suffice. In the earlier experiments with sulphuric acid made by Mr. Yogoro Kato the bomb was always charged so as to have only from 1 to 2 c.cm. vapor-space at 218° and no correction for this was applied at any temperature. The air pressure in the bomb was in all cases reduced to 3 or 4: cm. before the first measurement at 18°. The bomb was usually removed and shaken by hand at each temperature before the measurement was made, as the rotating carriage had not at that time been introduced. At 218° with the 0.0005 normal solution a considerable increase of con- ductance always took place within one or two minutes after the current was passed, but after this time no further change took place even in 15 minutes. The constant values resulting after the passage of the current for 2 minutes or so are those given below in the table. This increase is perhaps due to the throwing out of adsorbed substance from the elec- trodes. With the 0.002 normal solution the effect was less regular and far less pronounced. In our own experiments, the air was removed from the bomb only in those extending to 218° or above, since its pressure at the lower tempera- tures could not have a considerable effect. The correction for solvent in the vapor space was neglected below 218°, as computation showed that under the prevailing conditions the cor- rection was less than 0.02 per cent even at 156°, where the vapor space measured about 7 c.cm.; nor was this correction applied at 306°, since the vapor space amounted to only 2 to 3 c.cm. and since the specific volume data used are affected by a corresponding error, which at any rate par- tially eliminates the effect of the vaporization of the solvent on the values of the equivalent conductance, as mentioned in section 10, Part II. At 218° whenever the vapor-space exceeded 2 to 3 c.cm. this correction was made as there described. In the case of hydrochloric acid at 260° the correction for vaporization of the solvent was combined with that for the solute and was computed upon the basis of a direct experiment, which will be now described. An estimate of the extent to which the solute volatilized was obtained in the cases of nitric acid at 218° and of hydrochloric acid at 260° by comparative experiments in which the bomb was charged with very dif- ferent quantities of solution so that the vapor-space varied considerably ; the difference in conductance was thus found in the case of nitric acid at 218° to correspond to that which would have resulted from the vola- 246 Conductivity of Aqueous Solutions. — Part VIII. tilization of the solvent alone. In the case of hydrochloric acid at 260°, the observed change in conductance was only about three-fourths of that which would have resulted from the volatilization of the solvent alone, a fact which indicated some volatilization of the solute.* This was allowed for in all the experiments with hydrochloric acid at 260° by diminishing the calculated correction for solvent-vaporization by one- fourth. No correction for conductance of the water was applied, except in the case of the neutral salts used in determining the conductance-capacity. Unusually good water was used for the very dilute solutions, the measured specific conductance just before mixing being almost always below 0.5 X 10-", and in some cases as low as 0.3 X lO""- The final values of the conductance were corrected for contamination wherever the difference between the initial and final 18° values exceeded 0.25 per cent, by the arbitrary rule that the conductance at the highest temperature of the experiment be increased by two-thirds of the percen- tage change observed at 18°, and at the next lower temperature by one- fourth of that percentage change. No such correction was applied to the results with hydrochloric acid, since there seemed to be no variation at the higher temperatures corresponding to that at 18°. The expansion of all the solutions on heating was assumed to be the same as that of pure water and the change in concentration was calcu- lated by dividing the concentration at 4° by the specific volume of pure water at the temperature in question.f *The data upon which this conckision is based are as follows : Solute. Concentra- tion at 18°. Grams of solution in bomb. Tempera- ture of meas- urement (t). Volume of vapor-space at<5. Cooduciance at/°. HCL 100 100 95.9 56.5 84.7 102.5 259.3 259.8 217.8 218.2 2 53 24 2 6,a57 6,158 58,070 57,870 The concentrations were only approximately those given in the table. The specific volume of the saturated vapor was taken as 85 at 218° and 39 at 260° upon the basis of the estimates referred to in section 34, Part IV. fFor the specific volume the following values were used: 100° 1.0431 260° 1.277 128° 1.0685 306° 1.433 156° 1.0980 218° 1.1862 are derived by graphic interpolation from Him's 32 (1867)] after correcting them to the pressures 18° 1.0014 25° 1.0029 50° 1.0119 75° 1.0257 The values at 128° and 156 values [Ann. chim. phys. (4), 10, of saturated vapor by means of the compression-coefficient of water, obtained by extrapolating from the data of Pagliani & Vincentini given in the Landolt-Bomstein- Meyerhoffer Tabellen. The values at 218° and 306° are those experimentally deter- mind by Noyes & Coolidge; that at 260° was obtained by gfraphic interpolation. Section g2. — Conductance-Capacity of the Bomb. 92. CONDUCTANCE-CAPACITY OF THE BOMB. -'-// The conductance-capacity of the bomb at 18° (i. c. the factor by which the observed conductance must be multiplied to give the specific conduct- ance) was determined with known solutions of sodium and potassium chlorides. The values adopted for the equivalent conductances of these salts are those given by Kohlrausch.* Table 93 gives the actual conductances in the bomb of the various solu- tions, diminished by the conductance of the water, as determined from a measurement made just before mixing. Separate fresh solutions were used in each case. The conductances are given in reciprocal ohms, the concentrations in milli-equivalents per liter of solution. Table 93 — Conductan :e-capacity. — Data and final values. Date. Cell No. Salt. Concentra- tion at 18°. Conduct- anceXlO'. Conductance-capacity. Separate values. Final values. 1905 Aug. 17 Aug. 17 ■ i KCl.. NaCl. 10.00 10.00 *8.195 *6,829 0.14939 0.14929 j 0.14934 Aug. 29 Aug. 29... -1 KCl.. NaCl. 10.00 10.00 *8,201 6,834 0.14928 0.14918 j 0.14923 Nov. 20 Nov. 21 Nov. 25.... Nov. 2S ' II \ KCl.. KCl.. KCl.. NaCl. 19.963 9.982 99.87 99.88 1,968.4 1,003.1 9,184 7,539 1.2164 1.2183 1.2183 1.2192 ■ 1.2181 1906 Feb. 3 Mar. 7.... Mar. 8 fKCl.. ■ II -i NaCl. [NaCl. 99.98 10.006 19.986 9,192 838.1 1,634.6 1.2186 1.2172 1.2180 ■ 1.2179 Mar. 24 Mar. 26 Apr. 3 Apr. 9 f NaCl. I liNaCl. 1 II liNaCl. J l;KCi.. 49.91 100.00 100.03 10.002 3,916.9 7,545 7,552 1,004.6 1.2197 1.2197 1.2189 1.2190 ■ 1.2193 i July 10.... July 24.... July 31 NaCl. III^' KOI.. [KCl.. 100.00 50.01 20.015 6,836 4,294.5 1,777.8 1.3461 1.3485 1.3506 ■ 1.34S4 Sept. 17.... Sept. 28.... 1 jjiKCl.. ("Mkci.. 19.958 10.002 1,774.2 908.6 1.3495 1.3477 1.3486 *Mean of two almost completely concordant experiments. The results dated August, 1905, are those of ]\Ir. Kato. The first of his final values was used in connection with his conductance data obtained up to August 26 inclusive. The second mean value was used with all his later data — those obtained from August 31 to September 16. In computing the conductance from our measurements made prior to March 20, 1906, the value (1.2181) for the conductance-capacity obtained *K6nigl. preuss. Akad., 1900, 2, 1002-1008. 248 Conductivity of Aqueous Solutions. — Part VIII. from the first four determinations made in November, 1905, was used. This will be seen to be substantially identical with that obtained in Feb- ruary and March, 1906. In connection with the data on barium hydroxide (obtained between March 28 and April 4, 1906) the slightly higher value (1.2193) was used, which was derived from the four determinations made during the work on this substance. In connection with the data obtained after July 10, 1906, for which another bomb was used, the last value of the conductance-capacity given in the table was used. The variation of the conductance-capacity with the temperature was computed, as described in section 36, Part IV, from the dimensions of the quartz cup used.* 93. THE CONDUCTIVITY DATA. Tables 94 to 100 contain the conductivity data for all the solutions. The measurements dated August and September, 1905, were made by Mr. Y. Kato, while all the later ones are our own. The first column gives the date; the second, the concentration at 4° in milli-equivalents per literf referred to the equivalent weight of oxygen taken as 8.00 and the weights being reduced to vacuo ; the third, the tem- perature of the measurement expressed on the hydrogen-gas scale; the fourth, the concentration at that temperature calculated as described in section 91; the fifth, the measured conductance in reciprocal ohms, cor- rections having been applied for the errors in the slide-wire, resistance- coils, and leads, but not for the impurities in the water; the sixth, the equivalent (or molal) conductance calculated from the conductance g^ven in the fifth column, the concentration given in the fourth column, and the value of the conductance-capacity appropriate at that date, as given in section 92, the last being corrected to the temperature of the measurement. *This had an effective inside height of 1.45 cm. in Cell 11 and of 1.40 cm. in Cell m and an inside diameter of 1.40 cm. in Cell 11 and of 1.37 cm. in Cell in. The percentage corrections applied to the 18° value of the conductance-capacity were the same for the two cells and at the different temperatures were as follows : 50° 75° 100° 128° 156° 218° 260° 306° — 0.06 — O.U —0.16 —0.31 —0.27 —0.41 —0.52 —0.63 tExcept in the cases of phosphoric acid and potassium hydrogen sulphate, where the concentration is expressed in milli-formula-weights per liter at 4°. Section pj. — The Conductivity Data. 349 Table 94. — Conductivity data for sulphuric acid up to 2iS°. [Results of Y. Kato.] Date. Concentra- Temperature Concentra- Conductance Equivalent tion at 4°. 1°. tion at i°. X 10». conductance. 1905 Aug. 23 11.748 18.00 11.733 23,660 301.2 155.9 10.707 34,460 479.9 217.4 il.913 35,790 537.9 18.00 11.733 23,920 304.5 Aug. 24 11.762 18.00 11.747 23,810 302.8 99.83 11.279 33,040 437.1 155.9 10.720 34,300 477.2 217.5 9.924 35,560 533.9 18.00 11.747 24,020 305.4 Sept. 14 11.643 18.00 11.627 23,720 304.5 100.20 11.161 32,970 440.3 157.6 10.592 34,150 480.3 217.9 9.818 35,220 533.9 18.00 11.627 23,720 304.5 Sept. 15 11.94:-. 18.00 11.927 24,140 301.9 100.30 11.447 33,730 439.2 157.9 10.865 35,060 480.7 218.0 10.070 36,140 534.1 158.4 10.860 35,220 483.1 100.30 11.447 33,750 439.5 18.00 11.927 24,230 303.1 Sept. 16 11.945 18.00 11.927 24,240 303.8 100.20 11.447 33,760 440.6 18.00 11.927 24,240 303.8 Sept. 16 11.901 18.00 11.886 24,180 303.6 100.11 11.408 33,650 439.6 158. 10.830 34,940 480.6 217.6 10.039 36,140 535.7 18.00 11.886 24,180 303.5 Sept. 9 2.050 18.00 2.047 4,864 354.5 217.8 1.7287 6,569 565.6 18.00 1 2.047 4,866 354.6 Sept. 10 2.050 18.00 i 2.047 4,864 354.5 217.8 1.7287 6,542 563.3 18.00 2.047 4,866 354.6 Sept. 11 0.5052 18.00 0.5046 1,265.4 374.1 100.06 0.4844 2,317 713.0 156.4 0.4600 2,023 654.6 217.5 0.4262 1,683.3 587.8 18.00 0.5046 1,265.4 374.1 Sept. 12 0.5670 18.00 0.5663 1,409.4 371.5 99.80 0.5436 2,553 699.9 156.3 0.5165 o 222 640.7 217.4 0.4785 1.S77.6 584.0 156.5 0.5165 2.32 S 643.4 99.81 0.5436 3,560 i 702.0 18.00 0.5663 1,409.9 1 371.6 Sept. 13 0.5238 18.00 1 0.5232 1,307.5 372.9 99.82 0.5022 2,392 ' 709.9 156.5 0.4772 2,086 651.1 217.1 0.4419 1,749.2 589.0 18.00 0.5232 ' 1,309.9 373.6 Auff 25 1.9924 156.3 1.8149 6,590 541.4 A^i.1^. i~-^ 217.3 1.6809 6,337 561.7 250 Conductivity of Aqueous Solutions. — Part VIII. Table 94. — Conductivity data for sulphuric acid up to 3i8° [Results of Y. Kato.] -Continued. Concentra* Temperature Concentra- Conductance Equivalent lion at 4°. at/°- tion at t°. X10«. conductance. 1905 Aug. 26 2.032 156.5 1.8200 6,758 543.6 217.3 1.7148 6,535 567.7 Aug. 31 2.047 18.00 2.044 4,838 352.9 99.82 1.9630 7,545 573.0 Sept 1 2.107 18.00 2.104 4,993 353.9 100.14 3.020 7,751 572.1 156.0 1.9195 6,954 539.6 217.5 1.7778 6,710 561.9 18.00 3.104 5,009 355.1 Sept. 6 2.091 18.00 2.089 4,965 354.6 217.2 1.7642 6,667 562.5 156.0 1.9051 6,932 541.9 18.00 2.089 4,960 354.3 Sept. 7 2.075 18.00 2.072 4,868 350.5 99.95 1.9894 7,651 573.3 156.2 1.8903 6,904 544.0 217.7 1.7499 6,766 575.5 156.4 1.8902 6,920 545.3 100.05 1.9891 7,675 575.3 18.00 2.073 4,936 354.7 Table 95. — Additional conductivity data for sulphuric acid. [Results of Noyes & Eastman.] Concentration Temperature Concentration Conductance Equivalent at 4°. t°. at/°. X108. conductance. 1905 Dee. 14 99.98 18.00 99.84 19,150 333.6 35.00 99.69 20,590 251.5 50.00 98.81 34,400 300.6 75.00 97.48 37,000 337.0 100.00 95.85 29,130 369.6 138.0 93.57 31,220 405.6 156.0 91.06 32,780 437.2 18.00 99.84 19,140 333.6 1906 1 Jan. 5 ! 100.08 18.00 99.94 19,130 233.3 25.00 99.79 20,580 351.3 1905 Dec. 13 50.06 18.00 49.99 10,405 253.5 25.00 49.93 11,196 273.1 50.00 49.48 13,165 333.9 75.00 48.81 14,316 356.9 100.00 48.00 15,214 385.5 128.0 46.86 16,129 418.4 155.9 45.60 16,886 449.8 1 18.00 49.99 10,399 253.4 1906 Jan. 3 12.503 18.00 12.485 3,093 301.7 25.00 12.467 3,355 327.7 50.00 12.356 3,996 393.7 75.00 12.189 4,341 423.4 100.00 11.986 4,307 437.0 128.0 11.701 4,371 454.0 156.0 11.387 4,475 477.4 18.00 12.485 3,093 301.7 Section pj. — The Conductivity Data. 251 Table 95 — Additional conductivity data for sulplturic acid — Continued. [Results of Noyes & Eastman.; Date. Concentration Temperature Concentration Conductance Equivalent at4° t°. at^''. X10». conductance. 1906 Jan. 3 3.0013 18.00 1.9984 580.3 353.7 25.00 1.9954 640.5 390.9 50.00 1.9777 815.3 501.9 75.00 1.9511 903.7 563.0 100.00 1.9186 906.7 574.8 128.0 1.8730 859.3 557.7 156.0 1.8226 813.7 543.3 18.00 1.9984 580.5 353.8 1905 Dec. 19 0.4992 18.00 0.4985 153.0 371.4 35.00 0.4977 168.8 413.1 50.00 0.4933 334.1 552.9 75.00 0.4867 363.0 657.5 100.00 0.4785 278.9 708.9 138.0 0.4673 370.3 703.0 156.0 0.4546 245.3 655.1 18.00 0.4985 153.7 373.1 Dec. 31 0.5005 18.00 0.4998 152.7 372.1 35.00 0.4991 169.8 414.4 50.00 0.4946 225.2 554.4 75.00 0.4880 364.3 659.1 100.00 0.4798 380.5 711.0 128.0 0.4684 371.7 704.9 156.0 0.4558 346.7 657.4 18.00 0.4998 153.9 372.7 1906 Jan. 10 0.1983 18.00 0.1980 61.04 375.5 35.00 0.1977 68.05 419.2 50.00 0.1959 91.40 567.8 75.00 0.1933 110.33 694.5 100.00 0.1901 122.64 784.6 128.1 0.1856 124.78 817.4 156.0 0.1806 115.22 775.1 18.00 0.1980 61.53 378.5 .Tan. 1?. 0.3013 18.00 0.2010 61.73 374.0 35.00 0.3007 68.87 417.8 50.00 0.1990 93.56 566.3 75.00 0.1963 111.91 693.8 100.00 0.1930 134.35 783.6 128.1 0.1884 136.87 818.5 156.0 0.1834 117.29 777.1 18.00 0.2010 62.80 380.5 Jan. IS 0.1989 18.00 0.1986 61.15 375.0 100.00 0.1907 122.40 780.7 138.4 0.1861 124.23 811.4 155.9 0.1812 114.67 768.9 18.00 0.1986 61.00 374.1 Oct. 30 3.647 18.00 3.643 683.5 348.7 304.3 1.853 882.3 638.1 18.00 3.643 682.5 348.3 Aug. 36 114.67 18.00 114.51 19,501 229.6 318.0 97.01 34,904 483.3 303.2 80.63 28,490 473.6 1 18.00 114.51 19,387 338.9 3^2 Conductivity of Aqueous Solutions. — Part VIII. Table 96. — Conductivity data for phosphoric acid. Date. Concentration Temperature Concentration Conductance Molal at 4°. t°. at/°. X108. conductance. 1906 Feb. 7 0.22663 18.00 0.2263 61.30 329.9 25.00 0.2360 67.94 366.1 50.14 0.2240 90.47 491.8 75.00 0.3210 108.53 597.7 100.00 0.2173 122.40 685.1 128.0 0.2121 132.36 758.5 156.0 0.2064 136.23 801.8 18.00 0.3363 61.38 330.4 Jan. 22 1.9989 18.00 1.9961 463.9 383.1 25.00 1.9931 510.6 313.0 50.14 1.9753 651.9 401.8 75.00 1.9488 745.8 465.7 100.00 1.9163 793.6 503.0 128.1 1.8706 795.2 516.7 156.1 1.8203 753.6 503.9 18.00 1.9961 463.5 282.9 Jan. 24 2.0003 18.00 1.9974 464.5 283.3 25.00 1.9945 511.1 312.1 50.14 1.9767 653.8 403.0 75.00 1.9502 747.0 466.1 100.00 1.9176 793.7 503.3 128.0 1.8721 796.5 517.3 156.1 1.8316 754.9 503.4 18.00 1.9974 464.3 283.1 Jan. 26 12.507 18.00 12.489 1,962 191.3 25.00 12.471 2,133 208.3 50.14 12.360 2,592 355.3 75.00 12.194 2,814 280.8 Jan. 29 12.501 18.00 12.483 1,960.4 191.3 100.00 11.984 2,839.6 388.3 128.0 11.699 2,699.7 280.5 156.0 11.385 3,436.5 360.0 75.00 12.187 2,814.3 281.0 18.00 12.483 1,960.3 191.3 25.00 12.464 3,131.7 308.3 50.14 12.353 3,590.0 355.3 Jan. 30 50.016 18.00 49.94 5,034 122.8 25.00 49.87 5,435 133.7 50.14 49.43 6,441 158.6 75.00 48.76 6,833 170.3 100.00 47.95 6,737 170.6 128.0 46.81 6,251 163.3 156.0 45.55 5,533 147.6 18.00 49.94 5,032 122.7 Feb. 1 100.00 18.00 99.86 7,918 96.6 25.00 99.71 8,524 104.1 50.14 98.83 10,004 123.3 75.00 97.49 10,509 131.2 100.00 95.87 10,392 130.6 138.0 93.60 9,501 123.4 156.0 91.07 8,377 111.7 18.00 99.86 7,Q11 96.5 Section pj. — The Conductivity Data. ^53 Table 97. — Conductivity data for nitric acid. Date. Concentration Temperature Concentration Conductance Equivalent at 4°. /°. at t°. X 109. conductance. 1906 Feb. 20 0.5010 18.00 0.5003 153.66 374.1 25.00 0.5000 171.06 417.0 50.14 0.4951 229.65 564.7 75.00 0.4884 279.88 697.3 1 100.00 0.4803 321.85 815.0 1 127.8 0.4690 358.88 930.1 155.8 0.4564 386.33 1,028.3 18.00 0.5003 153.49 373.7 Feb. 24 0.4975 18.00 0.4968 152.51 373.9 100.00 0.4769 319.68 815.3 156.00 0.4531 383.73 1,028.8 18.00 0.4968 153.60 374.1 Feb. 26 1.968S 18.00 1.9661 599.3 371.2 35.00 1.9631 666.8 413.7 50.00 1.9457 893.3 558.9 75.00 1.9196 1,090.0 691.0 100.00 1.8874 1,352.3 806.8 138.0 1.8426 1,394.9 920.1 156.0 1.7931 1,496.6 1,013.9 18.00 1.9661 598.4 370.8 Feb. 28 12.498 18.00 12.481 3,728 363.9 35.00 12.463 4,144 405.0 50.00 12.351 5s543 546.3 75.00 12.185 6,747 673.7 100.00 11.981 7,719 783.5 128.0 11.697 8,555 889.0 156.1 11.382 9,133 974.7 18.00 12.481 3,730 363.1 Mar. 3 50.02 18.00 49.95 14,505 353.7 25.00 49.88 16,108 393.3 50.00 49.43 31,464 528.6 75.00 48.77 26,028 649.4 100.00 47.95 29,621 751.2 128.0 46.81 32,637 847.4 156.0 45.56 34,554 921.4 18.00 49.95 14,491 353.4 Mar. 5 100.12 18.00 99.98 38,430 346.4 25.00 99.83 31,560 385.0 50.00 98.94 41,930 515.9 75.00 97.61 50,740 633.5 100.00 95.98 57,600 729.9 ! 128.00 93.70 63,210 820.0 156.1 91.18 66,530 885.9 18.00 99.98 28,420 346.3 Oct. 18 2.277 18.00 2.274 625.0 370.7 218.3 1.918 1,661.6 1,163 18.00 3.274 620.6 368.1 Oct. 11 2.879 18.00 2.875 790.8 370.9 303.9 2.021 1,733.7 1,150 18.00 2.875 781.3 366.4 Aug. 25 100.12 18.00 99.98 25,654 346.0 317.8 84.72 • 58,072 920.5 303.6 70.39 26,233 .500.1 18.00 99.98 25,361 343.0 Nov. 13 100.13 18.00 99.98 35,629 345.7 218.3 84.38 57,870 931.0 18.00 99.98 1 25,629 345.7 254 Conductivity of Aqueous Solutions. — Part VIII. Table 98. — Conductivity data for barium hydroxide. Date. Concentration Temperature Concentration Conductance Equivalent al 4°. t°. 3t<°. X10». conductance. 1906 Mar. 28 0.5011 18.00 0.5004 90.1 319.5 25.00 0.4996 103.9 351.0 50.00 0.4952 150.1 369.3 75.00 0.4886 197.5 493.4 100.00 0.4804 340.6 609.7 128.0 0.4689 280.0 737 156. 0.4563 301.9 804 18.00 0.5004 56.2 136.9 Apr. 4 3.000 18.00 1.997 352.4 215.3 50.00 1.976 580.1 357.7 100.00 1.917 931.6 585.3 156.0 1.821 1,187.9 793.1 18.00 1.997 323.0 197.3 Apr. 5 2.003 18.00 3.000 353.9 215.8 50.00 1.979 583.1 359.0 100.00 1.930 927.0 587.8 18.00 2.000 351.0 314.0 Apr. 6 12.516 18.00 13.499 2,106 205.4 35.00 13.480 3,393 333.8 50.00 12.369 3,433 338.1 75.00 13.203 4,438 443.1 100.00 11.999 5,333 541.1 156.0 11.400 6,609 705.1 100.00 11.999 5,260 533.7 18.00 12.499 3,069 301.8 Apr. 2 49.99 18.00 49.92 7,822 191.1 35.00 49.85 8,794 315.1 50.00 49.40 13,508 308.5 75.00 48.74 15,983 399.4 100.00 47.92 18,893 480.1 128.0 46.79 31,314 551.7 156.0 45.53 23,316 596.0 18.00 49.93 7,730 188.8 Mar. 21 99.98 18.00 99.84 14,750 180.1 35.00 99.69 16,700 , 204.3 50.00 98.80 23,630 391.5 75.00 97.48 39,950 374.3 100.00 95.85 35,080 445.5 128.0 93.57 38,910 506.0 156.0 91.06 40,390 538.1 18.00 99.84 14,680 179.3 Section pj. — The Conductivity Data. Table 99. — Conductivity data for potassium hydrogen sulphate. ^55 Concentration Temperature ConcentTation Conductance Molal at 4°. 1°. Mi°. X 106. conductance. 1906 Jan. 8 100.19 18.00 100.05 21,660 263.7 25.00 99.90 23,230 283.2 50.00 99.01 26,820 329.7 75.00 97.68 28,570 355.9 100.00 96.05 29,810 377.4 128.0 93.77 31,350 406.4 156.1 91.24 33,100 440.7 18.00 100.05 31,660 263.7 Jan. 16 1.994 18.00 1.991 744.5 455.5 25.00 1.988 827.0 506.6 50.00 1.970 1,072.0 662.3 1 \ 75.00 1.944 1,210.4 757. G 100.00 1.911 1,240.8 789.5 128.0 1.866 1,198.9 780.9 156.0 1.816 1,137.8 761.2 18.00 1.991 743.0 454.5 *JuIy 10 50.04 18.00 49.97 10,971 295.5 25.00 49.90 11,804 318.4 50.00 49.45 13,795 375.3 75.00 48.79 14,689 404.9 100.00 47.97 15,181 425.3 128.0 46.83 15,728 451.1 156.0 45.57 16,426 483.8 18.00 49.97 10,969 295.5 *The conductance-capacity here used was that of Cell III as determined July 10, namely, 1.3461 at 18°. Table 100. — Conductivity data for hydrochloric acid. Concentration Temperature Concentration Conductance Equivalent at 4°. <°_ at<°. X 10». conductance. 1906 July 18 2.870 18.00 2.866 796.1 374.5 259.6 2.259 2,233 1,326 305.9 2.003 2,001 1,338 18.00 2.866 793.5 373.3 July 19 14.327 18.00 14.307 3,899 367.4 259.6 11.374 10,227 1,216.8 306.5 9.985 8,650 1,160.8 18.00 14.307 3,797 357.8 July 21 14.323 18.00 14.303 3,893 367.0 259.1 11.284 10,323 1,315.3 303.6 10.059 8,778 1,169.4 18.00 14.303 3,853 363.1 July 22 114.60 18.00 114.44 39,586 348.6 July 25 114.60 18.00 114.44 29,551 348.1 360.3 90.04 69,396 1,034.0 303.3 80.56 52,604 875.1 18.00 114.44 29,300 345.2 Sept. 19 3.873 18.00 2.869 797.2 .374.8 SOi.O 2.01:. 2,015 1,340 18.00 2 . 8G9 795.9 374.3 Sept. 2.-, H.3S1 18.00 14.361 3,882 367.1 304.1 10.010 8,728 1,168 18.00 14.261 3,873 366.2 Sept. 26 114.43 304.0 80.27 52,240 872.3 18.00 114.26 348.8 2.^6 Conductivity of Aqueous Solutions. — Part VIII. 94. SUMMARY OF THE VALUES OF THE EQUIVALENT CONDUCTANCE. Tables 101 to 107 contain a summary of the values of the equivalent conductance given in the preceding tables. Kato's values ( and a few other values) have been corrected to round temperatures by means of tem- perature-coefficients obtained from a plot of them. In no case, except at 218° and above, did the correction exceed 0.2 per cent of the whole. In the few experiments where the difference between the initial and final values at 18° exceeds 0.25 per cent, the values at the highest temperatures have been corrected for contamination as described in section 91. When such a correction has been applied it has been indicated in the tables by affixing the letter c to the value in question. Table 101. — Equivalent conductance of sulphuric acid. [Results of Y. Kato.] Concentra- 18° 100° i 156° 218°. tion at 4°. Initial. Final. Initial. Final. Initial. Final. 1905 Sept 11.. Sept 12.. Sept 13.. 0.5052 0.5670 0.5238 374.1 371.5 372.9 374.1 371.6 373.6 713.0 655.4 641.3 652.1 643 14 588 700.0 710.0 ^ 702 .1 584.2 589 3 0.532 372.8 373.1 707.7 : 649.6 587.2 Aug. 23.. Aug. 26.. Aug. 31.. Sept 1.. Sept 6.. Sept 7.. Sept. 9.. Sept 10.. 1.992 2.032 2.047 2.107 2.091 2.075 2.050 2.050 352.9 353.9 354.6 350.5 354.5 354.5 355!i 354.3 354.7 354.6 354.6 573.0 572.1 541.5 543.7 544 !i 541.9 545.3 562.1 568.2 561. OC 573.3 575 .563.1 571. ic 565.7 563.4 Mean . 2.070 2.076 2.052 2.057 353.5 572.8 542.2 564.9 Aug. 23.. Aug. 24.. Sept 14.. Sept 15.. Sept 16.. Sept 16.. Mean . 11.748 11.762 11.643 11.945 11.945 11.901 301.2 302.8 304.5 301.9 303.8 303.6 304.5 305.4 304.5 303.1 303.8 303.5 437.2 440.2 439.0 440.5 439.5 3 480.0 477.3 478.8 478.9 478.7 'isois 534. 6C 530. 8<= 534.0 532.70 536.1 439 ril.824 ■111.839 Ul-820 302.9 304.2 439.3 ... 478.7 'ssals 1 Section 94. — Summary of Equivalent Conductances. ?57 Table 102. — Equivalent conductance of sulphuric acid. [Results of Noyes & Eastman.] Date. Concentra- tion at A^. 18 D 25°. 50°. 75°. 100°. 128°. 156°. Initial. Final. 1903 Jan. 10. . 0.1983 375.5 378.5 419,2 567.8 694.5 784.6 815. 9C 769. 0<= Jan. 12.. 0.2013 374.0 380.5 417.8 566.3 693.8 783.6 814.9'' 771. 0<= Jan. 18.. Means . Dec. 19.. *0.1989 375.0 374.1 780.7 812. ic 769. 7c 1 0.1995 374.9 376.8 782.4 813.7 769.8 ( 0.1998 418.5 567.0 694.1 0.4992 371.4 373.1 413.1 552.9 657.5 703.9 702.2'^' 653. ic Dec. 21... Mean . 1906 0.5005 372.1 372.7 414.4 554.4 659.1 711.0 704.9 657.4 0.4999 371.8 372.9 413.7 553.6 658.3 709.9 703.6 655.2 Jan. 1. . 2.001 353.7 353.8 390.9 501.9 563.0 574.8 557.7 542.3 Jan. 3. . 12.50 301.7 301.7 327.7 393.7 423.4 437.0 454.0 477.4 1905 Dec. 12.. 50.06 253.5 253.4 273.1 323.9 356.9 385.5 418.4 430.0 Dec. 14.. 99.98 233.6 233.6 251.5 300.6 337.0 369.6 405.6 437.2 1906 Jan. 5.. Means . 100.08 233.2 251.2 S 99.98 i 100. 03 300.6 337.0 369.6 405.6 437.2 233.4 251.3 218° 306° Oct. 20.. 2.647 348.7 348.2 639 Aug. 26.. 114.67 229.6 228.9 484C 474c *This experiment was given double weight in computing the mean, on account of the smaller contamination. Table 103. — Molal conductance of phosphoric acid. Date. Concen ra- tion at 4°. IS 25°. 50°. 75°. 100°. 128°. 156°. Initial. Final. 1906 Feb. 7.. Jan. 22.. Jan. 24.. Mean . Jan. 26.. Jan. 29.. Mean . Jan. 30.. Feb. 1.. 0.2266 1.999 2.000 329.9 283.1 283.3 330.4 282.9 283 . 1 366.1 312.0 312.1 491.1 401.3 401.6 597.7 465.7 466.1 685.1 503.0 503.3 758.5 516.7 517.2 801.8 503.0 503 . 5 2.000 283.2 283.0 312.0 401.4 465.9 503.2 517.0 503.2 12.51 12.50 191.3 191.3 191.3 208.3 208.3 255.1 235.1 280.8 281.0 288.2 280.5 260.0 12.50 191.3 208.3 255.1 280.9 288.2 280.5 260.0 50.02 100.00 122.8 96.6 122.7 96.5 132.7 104.1 158.5 123.2 170.3 131.2 170.6 130.6 162.3 123.4 147.6 111.7 25S Conductivity of Aqueous Solutions. — Part VIII. Table 104. — Equivalent conductance of nitric acid. Date. Concentra- tion at 4°. 18° 25°. 50°. 75°. ino° 1(K) . T>00 156°. Initial. Final. 1906 Feb. 20. Feb. 24. Mean .. Feb. 26. Feb. 28. Mar. 2. Mar. 5. 0.5010 0.497.i 374.1 373.9 373.7: 417.0 374.1! 563.9 697.2 815.0 815.2 930.9 1,029.0 1,028.8 j 0.4992 I 0.5010 374.0 373. S i 417.0 ; 563.9 697'.2' 815.1 1,028.9 930.9 1.969 12.50 50.02 100.12 371.2 363.9 353.7 346.4 370. S 363.1 353.4 346. a 413.7 1 405.0 393.3 385.0 558.9 546.3 528.6 515.9 691.0 673.7 649.4 632.5 806.8 783.5 751.2 729.9 920.1 889.0 847.4 820.0 1,013.9 974.4 921.4 885.7 Date. Concentration at 4°. 1S° 306°. Initial. Final. 1906 Oct. 18. Oct 11. Aug. 25. Nov. 12. Mean . 2.277 2.879 100.12 100.12 370.7 370.9 346.0 345.7 368.1 366.4 342.0 345.7 1,168 1,155 482= c 923 921 100.12 345.9 922 1 Table 105^ — Equivalent conductance of barium hydro.ride. Date. Concentra- tion at 4°. 18° 25°. 50°. 75°. 100°. Initial. Final. 1906 Mar. 28. Apr. 4. Apr. 5t Mean . Apr. 6. Apr. 2. Mar. 21. 0.5011 2.000 2.003 219.5 215.2 215.8 136.9 197.2 214.0 251.0 *369.3 357.7 359.0 *492.4 *610 589<= 5910 *800<= * 1,0000 840O 2.002 215.5 358.6 591 840 12.52 49.99 99.98 205.4 191.1 180.1 201.8; 232.8 188.8 215.1 179.3 204.3 338.1 308.5 291.5 443.1 399.4 374.3 t541.1 480.1 445.5 553. 4<" 506. 60 7130 600.80 539.7c *Very rough approximation, owing to great contamination, trouble weight, on account of smaller contamination. JA final value at 100°, after going to 156% was 533.7. §This same correction for contamination was applied to this value as to the one below it, two thirds of the percentage change at 18° in the second experiment. Table 106. — Molal conductance of potassium hydrogen sulphate. Date. Conccntra- ' ^^ 25°. 50°. 75°. 100°. j 128°. 156°. "°"""'"- 1 Initial. Final. 1906 Jan. 16. . July 10.. Jan. 8. . 1 1.994 ' 455.5 50.04 ' 395.5 100.19 263.7 454.5 295.5 263.7 506.6 318.4 283.2 6R2.3 375.3 329.7 757.6 404.9 355.9 789.5 780.9 455.3 451.1 377.4 1 406,4 i 761.2 483.7 440.7 Section Q4. — Summary of Equivalent Conductances. 259 Table 107. — Equivalent conductance of hydrochloric acid. Date. Concentra- tion at 4°. 18° 260°. 306°. Initial. Final. 1906 July 18... Sept. 19... Mean .. . July 19... July 21... Sept. 25... Mean ... July 22... July 25... Sept. 26... Mean ... 2.870 2.873 374.5 374.8 373.3 374.2 1,326 1,338 1,336 2.872 374.6 1,326 1,337 14.33 14.32 14.28 367.4 367.0 367.1 357.8 363.1 366.2 1,217 1,216 1,162 1,162 1,162 14.31 367.2 1,216 1,162 114.60 114.60 114.42 348.6 348.1 345.2 348.8 1,035 862 862 114.5 348.4 1,035 862 The degree of concordance of the results of the experiments carried only to 156° may be first considered. An examination of the preceding tables shows that for sulphuric, phosphoric, and nitric acids and potas- sium hydrogen sulphate in solutions 2 milli-normal and stronger, the agreement between the initial and final values at 18°, and between dupli- cate experiments is in general better than 0.2 per cent, the greatest differ- ence being 0.23 per cent. The same is also true of the 0.2 milli-molal phos- phoric acid and of the 0.5 milli-normal nitric acids. In the 0.2 and 0.5 niilli-normal sulphuric acid solutions, however, the final values at 18° are .somewhat larger than the initial, averaging 0.5 and 0.3 per cent respec- tively. The independent experiments at these two concentrations agreed within about the same limits, the greatest average deviation from the mean being 0.22 per cent. Kato's values (table 101) show about the same differ- ences as our own between the intial and final 18° values, except in three experiments which show an increase of about 1 per cent. A comparison of his individual experiments with one another can hardly be made owing to large differences in concentration, but his final means compared after reducing to round concentrations agree with our own within 0.2 per cent, except at 100° in the 0.5 and 2.0 milli-normal where the differences reach G.4 per cent. The divergence between the initial and final 18° values for barium hydroxide increases rapidly with the dilution, amounting to 0.4 per cent at 100 milli-normal, 1.2 per cent at 50 milli-normal, 8 per cent at 2 milli-normal, and 38 per cent at 0.5 milli-normal, in cases where the solu- tion had been heated to 156°. These large changes in the dilute solutions make, of course, the observed values of the conductance at the higher temperatures very inaccurate : but the error has been doubtless reduced to a relatively small amount (except for the 0.5 milli-nomial solution) by the correction applied for the contamination as described in section 91. 26o Conductivity of Aqueous Solutions. — Part VIII. In the experiments extended to 218°, 260°, and 306° the agreement was not so good, owing to greater contamination. In the first experiments with hydrochloric acid, made in July, 1906, the final values at 18° differed from the initial values by one to three per cent (except in the most dilute solution). This seems to have been due to the presence of gold and platinum dissolved from the lining ; for the strongest solution had a light }-elIow color after the heating, and a small precipitate of gold and a brown coloration was obtained on adding stannous chloride. To diminish this solvent action, the solutions in the later experiments made in September were boiled at about 60° under reduced pressure just after they were intro- duced mto the bomb; and it was then found that the initial and final values at 18° egreed within 0.3 per cent. The fact that the two sets of experiments gave concordant results at 306° shows that the presence of the gold or platinum had no influence at that temperature, probably owing to the hydrolysis of their salts. Differences of about one per cent were observed in some of the experiments with nitric and sulphuric acid, but these solutions did not contain gold or platinum in appreciable quantity. In the course of the experiments with the 2 milli-normal nitric acid, the remarkable phenomenon was observed in four or five cases that the con- ductance rapidly decreased during the heating above 300°, owing evi- dently to decomposition of the acid. Thus, in one case after heating to 306° it was found that the final conductance at 18° was only five per cent of the initial value. This decomposition was apparently started by minute quantities of impurities accidentally introduced into the bomb ; for it was found possible to prevent it by making up the solution with exceptionally pure water and taking special precautions against contamination.* This behavior is entirely analogous to that of silver nitrate as observed by Noyes and Melcher and described in section 39, Part I\^ *The nitric acid seems to decompose into nitrogen (or nitrous oxide), oxygen, and water; for tests for nitrite and for ammonia made by the processes used in water analysis on a 2 milli-normal solution which had been heated to 218° and had greatly decreased in conductance showed that the quantities of these substances present were less than 0.1 per cent of the nitric acid originally in the solution. Section 95. — Final Values of Equivalent Conductance. 261 95. FINAL VALUES OF THE EQUIVALENT CONDUCTANCE AT ROUND CONCENTRATIONS. The mean values of the equivalent or molal conductance given in tables 101 to 107 have been reduced to round concentrations by the help of coeffi- cients derived from curves obtained by plotting A against some function of the concentration (C), or of the product AC The error introduced in reducing in this way to round concentrations probably exceeds 0.1 or 0.3 per cent only for those values, inclosed within parentheses in the table below, which it was necessary to correct for a fairly large difference in concentration. The equivalent conductances at zero concentration (A„) have been obtained in the cases of nitric acid, phosphoric acid, and barium hydroxide at temperatures up to 156° by extrapolation upon plots of 1/A against (AC)""^, as described in section 17, Part II (except that those for barium hydroxide at 75° and 128°were obtained, by interpolation, from a plot of the other Aq values against the temperature). The A^-value for hydrochloric acid at 306° was obtained in the same way ; but to get that at 260° the value of the exponent n was assumed to be 1.50, since the data were not sufficient to determine this with accuracy. The Aj,-values for nitric acid at 218° and 306° were assumed to be 97 per cent of those for hydrochloric acid at these temperatures, just as they are at 100° and 156°. Owing to the con- tamination in the more dilute solution, the A(,-values for barium hydroxide at the higher temperatures are only rough approximations ; and owing to the long extrapolation, those for hydrochloric and nitric acids at 260° and 306° may well be in error by two to three per cent. The A^-values for sulphuric acid at 18°, 100°, 156°, 218° and 306° were obtained by the equation A0H2SO4 = AoHoi + A0K28O4 — AoKci using the values for hydrochloric acid, potassium sulphate, and potassium chloride given in table 36, (§ 54, Part V), table 22, (§ 41, Part IV), and table 9 (§16, Part II), respectively. Those at the intermediate tempera- tures were obtained from the others by graphic interpolation. The final values so obtained are all given in tables 108 and 109. The temperatures are those of the hydrogen-gas scale. The concentration is expressed in milli-equivalents (or milli-formula-weights) of solute per liter of solution at the temperature of the measurement, the atomic weight of oxygen being taken as 16.00 and the weights of substances being cor- rected for air buoyancy; milli-formula-weights per liter are given for phosphoric acid and potassium h_vdrogen sulphate, milli-equivalents per liter for all the other substances. The equivalent or molal conductance is expressed in reciprocal ohms ; the molal conductance is given in the case of phosphoric acid and potassium hydrogen sulphate, the equivalent con- ductance in all other cases. 262 Conductivity of Aqueous Solutions. — Part VIII. Table 108. — Final values of the equivalent or molal conductance up to 218°. insrOs HjSOi H.PO^ Ba(0H)2 KHSO4 Concen- tration. 0.0 0.5 2.0 10.0 12.5 50.0 80.0 100.0 0.0 0.2 0.5 2.0 10.0 12.5 50.0 80.0 100.0 0.0 0.2 2.0 10.0 12.5 .50.0 80.0 100.0 0.0 0.5 2.0 10.0 12.5 50.0 80.0 100.0 2.0 10.0 50.0 80.0 100.0 18°. 377 374.0 371.2 (365) 363.9 353.7 (349) 346.4 383 374.9 371.8 353.9 f309) 301.3 253.5 (240) 233.3 33S 330.8 283.1 (203) 191.2 122.7 (104) 96.5 222 219 215 (207) 205.4 191.1 (184) 180.1 455.3 (379) 295.5 (273) 263.7 421 417.0 413.7 (406) 405.0 393.3 (388) 385.0 (429) 418.5 413.7 390.8 (337) 327.5 273.0 (258) 251.2 376 367.2 311.9 (222) 203.1 132.6 (112.4) 104.0 250 251 !(235) 232.8 ! 215.1 ^(308) ; 204.2 j 508.3 (417) 318.3 ;(294) I 283.1 50°. 75°. 570 563.9 558.8 (548) 546.2 528.4 (521) 515.7 (591) 566.9 553.4 501.3 ("406) 393.1 323.4 (306) 300.3 510 493.0 400.7 (273) 254.1 157.8 1133) 122.7 389 706 697.1 689.7 (676) 673.4 648.9 (637) 631.8 (746) 693.6 657.0 560.8 (435) 421.9 3.56.0 (342) 336.4 631 600.3 463.6 (300) 278.5 168.6 (141) 129.9 (520) 128°. 359 ^342) 338 308 (296) 291 661.0 (508) 374.4 (343) 329.1 (449) 442 399 (382) 373 754.1 (558) 402.8 (369) 354.4 826 814.8 806.2 (786) 782.7 750.1 (735) 728.4 891 779.6 706.3 571.0 (446) 434.9 384.3 (373) 368.8 730 688.5 498.2 (308) 283.9 167.8 (141) 128.4 645 945 930 919 (893) 887 845 (827) 817 (1,041) 807 696 551 (460) 452 417 (408) 404 839 762.1 507.6 (298) 273.6 158.0 (134) 120.2 (760) 591 (548) 539 478 (454) 443 (664) 549 (516) 503 784.0 773 (580) ! (600) 422.1 446 (389) (415) 374.6 (402) 156°. 1,047 1,028 1,012 (978) 972 917 (893) 880 1,176 759 644 536 (481) 475 448 (440) 435 930 804.7 489.0 (274) 250.5 142.0 (118) 107.7 847 (722) 707 593 (551) 531 754 (611) 477 (448) 435 218°. (1,230) 1,166 926' 1,505 586 563 533 529 (502) (488) (483) Table 109. — Final values of the equivalent conductance at 260° and 306°. Concen- tration. 260°. HCl 0.0 2.0 10.0 80.0 HNO3 0.0 2.0 70.0 80.0 HzSO, 0.0 t 2.0 80.0 1,380 1,424 1,332 1,337 1,226 1,162 1,046 862 j (1,380) ' 1,156 482 I (454) (2,030) : 637 ' 474 Section p§. — Final J'ahtes of Equivalent Conductance. 26^ The values given in table 109 for sulphuric acid are the means of those obtained by Mr. Kato and ourselves in the case of the 2 and 13.5 milli- normal solutions. The values derived bv each were as follows: Concentra- tion. 0.5 2.0 12.5 IS" 373 2 354 1 301 100° 156° N. & E. Kato. N. & E. Kato. ] N. & E. 371.8 709.0 353.7 572.3 301.7 I 434.8 706.3 569.8 435.0 645 644 536 1 535 475.4 475.3 We regard our values for the very dilute 0.5 milli-normal solution as more reliable because of the fact that our bomb was rotated, thus remov- ing any contamination from the immediate neighborhood of the electrodes. Table 110 contains a comparative summary of the results at 18° of previous investigations and of our own. From all the earlier values the conductance of the water has been subtracted, while in the case of our values, this has not been done ; but the conductance of the water used (0.3 to 0.5 X 10-" at 18°) amounted to only about 0.2 per cent of that of the 0.5 milli-normal acid solutions. Interpolated values are inclosed within parentheses. Table 110. — Comparison of the conductance values at 18° zcilli those of otlier investigators. Concpntratioii. Sulphuric acid. 1 Phosphoric acid. ! Nitric acid. Kohl- rausch.* Whet- ham. t Noycs & 1 p„.,„ t Noycs & Goodwin& Kohl- Eastman. [ '■"ster.i Eastman. Haskell.? rausch.* Noyes & Eastman. 0.3 ■ 0.5 (368) 2.0 351 12.5 50.0 253 100.0 225 (379) (376) (350) 374.9 1 313 330.8 371.8 (312) i (320) 373.9 353.7 279 283.1 \ 371.4 1 (189) 191.2 [ 253.5 1 (133.9)1 133.7 1 233.3 1 (96.7)j 96.5 374 357 350 373.9 371.2 353.7 346.4 *Kohlrausch & Holborn, Leitveniiogen der Elektrolyte, p. 160. tintcrpolated from a plot of the values given by ^Vl^etIlanl in Z. phys. Chcni.. 55, 205 (1906). These values are dependent on Kohlrausch's at 0.02-0.03 normal. tPhys. Rev. S, 269 (1S99). Interpolated from a plot. §Pi-oc. Am. Acad., 40, 413 (1904); Phys. Rev., 19, 3S6 (1904). Our values for sulphuric acid agree fairly well with those of Kohl- rausch and of Whetham, except for the concentration 100 milli-nomial, where our value is 3.6 per cent greater than that of Kohlrausch. On account of this discrepancy, a check measurement was made (on iMay 14, 1906) at this concentration in a U-shaped glass vessel: and the value 233.6 was obtained for the equivalent conductance, which differs by less than 0.3 per cent from the determination made in the bomb. The values for the stronger solutions of phosphoric acid agree very well with Fos- ter's ; but our values for the dilute solutions are considerably greater than 264 Conductivity of Aqueous Solutions. — Part VIII. his, the difference being 5.5 per cent at 0.2 miUi-molal. This divergence is doubtless largely due to the fact that Foster subtracted the conductance of the water, which in this case amounted to 3.6 per cent of the whole conductance. The values for nitric acid in the dilute solutions are in excellent agreement with those of Goodwin and Haskell, who used a special method to eliminate the effect of impurities in the water. For the stronger solutions, our values exceed Kohlrausch's by about 1 per cent; but here, as for sulphuric acid, our value was checked (on May 11, 1906) by an independent measurement of a 100 milli-normal solution in a U-shaped vessel, whereby the value 346.8 (instead of 346.4) was obtained. 96. CHANGE OF THE EQUIVALENT CONDUCTANCE WITH THE CON- CENTRATION AND THE TEMPERATURE. As in the previous researches in this series we have determined what value of n must be used in the equation C(A„ — A)^i2^(CA)" to make it conform to the results. The values of the exponent so obtained are given in table 111. Table 111. — Values of the exponent n in the function C(A„ — A)=ii:(CA)« Substance. 18°. 25° 50°. 75°. 100°. 128°. 156°. BDSrOj H,PO, Ba(0H)2.. 1.43 1.9 1.55 1.43 1.45 1.43 1.40 1.43 1.45 1.8 1.45 1.45 1.45 1.8 1.45 The values of the exponent at 260° and 306° for hydrochloric acid were found to be 1.35 and 1.60, respectively, while Noyes and Coopers values (see table 39, Part V) at the lower temperatures range from 1.38 to 1.47. For sulphuric acid at 18° (up to 50 milli-normal) the exponent has the value of 1.5; it was not determined at the higher temperatures because the ionization-relations are there complicated by the presence in large quantity of the intermediate HSO4" ion. It will be seen from these results that the conductance of nitric acid and hydrochloric acid changes with the concentration according to the same law as does that of the neutral salts; and that the same is true of the tri-ionic base barium hydroxide and of the tri-ionic acid sulphuric acid at 18°. The insignifi- cant variation of the exponent with the temperature in the case of all these substances is also worthy of notice. It is of interest, too, to note that the exponent for phosphoric acid, which is only moderately ionized, is intermediate between that found for the largely ionized substances and that required by the mass-action law. Section p6. — Change of Conductance zvith Temperature. 265 The change of the Ao-values with the temperature deserves considera- tion only in the cases of nitric acid, phosphoric acid, hydrochloric acid and barium hydroxide; for only for these substances were they directly derived. Table 113 contains the ratios of these Ao-values to those pre- viously given for potassium chloride and for some other substances. Table 112. — Ratio of the Ao-values to those for potassium chloride and other substances. 18°. 100°. 156°. HNO3 :KC1 2.90 0.99 1.70 2.60 0.89 1.71 1.90 1.99 0.97 1.28 1.76 0.86 1.56 1.67 1.67 0.97 1.24 1.49 0.86 1.36 1.53 HNO, -HCl HNO, :Ba(0H)2 H3P64 :K01 H.POi :HC1 Ba(OH), :KC1 Ba(OH)2:Ba(NOs)z... The ratio HC1:KC1 at 306° was found to be 1.27; its value at lower temperatures was found by Noyes and Cooper to be as follows: 2.91 at 18°, 2.05 at 100°, 1.73 at 156°, and 1.53 at 218°. It will be observed that the ratio of the values for hydrochloric and nitric acids is not far from unity at all temperatures, showing that the chloride and nitrate ions always move at nearly the same rate. The values of the other ratios show that the velocities of the hydrogen and hydroxide ions approach those of each other and of the neutral-salt ions as the temperature rises. Table 113 contains the values of the mean temperature-coefificients of the conductance at zero concentration (AAf^/At) for the substances included in this investigation. It will be seen that all these values steadily decrease, showing that the conductance-temperature curve is concave toward the temperature axis and that it has no points of inflexion, as is the case with neutral salts. Table 113. — Mean temperature-coefUcients of the conductance at zero concentration. Substance. Temperature interval. 18°-50°. 50°-100°. 100°-156°. 156°-218°. 218°-306°. HisrOa H2SO4 H3PO4 BaOjHz.... HOI 6.03 6.50 5.22 5.22 5.12 6.00 4.50 5.12 3.95 5.09 3.57 3.58 4.20 2.90 1.81 With reference to the effect of temperature on the conductance values at the higher concentrations, attention may be called to the fact that maximum values are reached in the cases of all the acids investigated, namely, near 75° with 0.1 molal and near 128° with 0.002 molal phos- phoric acid, between 156° and 218° with 0.08 normal nitric acid, and 266 Conductivity of Aqueous Solutions. — Part VIII. between 218° and 260° with 0.08 normal hydrochloric acid. Sulphuric acid shows a very diif erent variation of the conductance with the tempera- ture at different concentrations. This is best seen by reference to figure 18, on which the values for 0.08 normal hydrochloric and nitric acids are also plotted. The most striking feature of this plot is that the conductance values for the most concentrated and the most dilute sul- phuric acid at first diverge rapidly with rising temperature (up to about Temperature Fig. 18. 100°), then approach each other (most closely at 218°), and finally again diverge. This behavior can be satisfactorily accounted for by assuming that the dissociation of this acid takes place in two stages according to the reactions : H2SO4 = H+ + HSO,- and HSO," = H+ -f SOr and that the extent to which these two reactions occur is very different at the different temperatures. This matter will be discussed in the fol- lowing section. Section P/. — Ioni/:atioii of the Substances. 26/ 97. IONIZATION OF THE SUBSTANCES AND ITS CHANGE WITH THE CONCENTRATION AND THE TEMPERATURE. Tables 11-i and 115 contain the values of the ratio 100 A/A^ for the sub- stances for which the equivalent or molal conductances are given in tables 108 and 109. This ratio doubtless represents approximately the percentage ionization in the cases of nitric and phosphoric acids, and almost certainly also in the case of barium hydroxide; for the second hydrogen of phosphoric acid has been shown by the work of Mr. G. A. Abbott* to be less than 0.05 per cent ionized at 18° at even 0.001 molal concentration; and the equivalent conductance of barium hydroxide behaves at all temperatures so entirely like that of neutral uni-univalent and unibivalent salts that it is hardly probable that an)' considerable quantity of an intermediate ion like BaOH+ exists. In the case of sul- phuric acid, two sets of ratios separated by a dash are given in table Hi; the first one is 100 times the ratio of the equivalent conductance (A) of the acid at the concentration in question to the sum of the equivalent conductances of the hydrogen and sulphate ions (Ah -|- Asoi), for which sum the values were given in tables 109 and 110; the second one is 100 times the ratio of the equivalent conductance A to the sum of the equiva- lent conductances of the hydrogen and the hydrosulphate ion (Ah + Ahso^), for which sum values equal to the Ao values for acetic acid were taken, it being assumed that the latter ion has the same equivalent conductance as the C0H3O2" ion, whose molecule consists of nearly the same number of atoms. These two ratios represent the limits between which must lie the percentage of the total hydrogen of the acid which exists in the state of hydrogen-ion in the solution; for if the acid dissociated wholly into 2H+ + SOi", this percentage would have the first value, and, if wholly into H+ and HSOi" the second value.f The value of the percentage ioni- zation would evidently be the same as the first value if the acid dissociated only in the first \va}', and twice the second value if it dissociated only in the second way. ♦Reference is here made to a research executed in this laboratorj', but not yet published. fThis will be evident from the following considerations. The specific conductance L of the solution is given in the two cases by the expressions l^ChAh -|- 2Cs04As04 and l^ChAh + ChsOiAhsoi where the large C's represent molal concentrations ; or since Ch = 2CsOi in the first case and Ch = Chsoi in the second, also by : L=:CH(AH-f AsOi) and l = Ch(Ah -|- Ahso.) ; from which by substituting for l its value cA where c is the equivalent concentration of the acid, we obtain : C AH-f ASO. C Ah-J-AhSO< 268 Conductivity of Aqueous Solutions. — Part VIII. Table 114. — Conductance-ratio lOO A/Ao and approximate percentage ionization up to 2l8°. ! Substance. Concen- tration.* 18°. 25°. 50°. 75°. 100°. 128°. 156°. 218°. i HNO3 0.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100 0.5 99.1 99.0 93. 9 98.7 98.6 98.4 98.2 2.0 98.4 93.2 98.0 97.7 97.6 97.2 96.7 95 10.0 96.8 96.4 96.1 95.8 95.2 94.5 93.4 12.5 96.4 96.2 95.8 95.4 94.8 93.9 92.8 1 50.0 93.7 93.4 92.7 91.9 90.8 89.4 87.6 80.0 92.6 92.2 91.4 90.2 89.0 87.5 85.3 75 100.0 91.8 91.4 90.5 89.5 88.2 86.5 84.0 i H3P0,.... 0.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 0.2 98.0 97.5 96.5 95.0 94.5 91.0 86.5 2.0 84.0 83.0 78.5 73.5 68.5 60.5 52.5 1 10.0 60.0 59.0 53.5 47.5 42.0 35.5 29.4 i 12.5 56.5 55.5 50.0 44.0 39.0 32.5 27.0 1 50.0 36.5 35.0 31.0 26.5 23.0 19.0 15.5 j 80.0 31.0 30.0 26.0 22.5 19.5 16.0 12.5 1 100.0 28.5 27.5 24.0 20.5 17.5 14.5 11.5 1 H2SO4.... 0.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100 0.2 98-108 98-108 96-107 93-105 87-104 78-91 65-77 0.5 97-107 97-106 94-104 8s-ioa 79-91 67-79 55-66 39-50 2.0 92-102 91-101 85-95 75-85 64-74 53-62 46-55 37-48 10.0 81-89 79-87 69-77 58-66 50-58 44-52 41-49 35-46 12.5 79-87 76-84 66-74 57-64 49-56 43-51 40-48 35-45 50.0 66-73 64-70 55-61 48-54 43-50 40-47 38-46 33^3 80.0 63-69 60-66 52-58 46-52 42-48 39-46 37^5 32-42 100.0 1 61-67 59-65 51-57 45-51 41^8 39Ht6 37-44 32-41 Ba(OH)2.. 0.0 ^100.0 100.0 100.0 100.0 100.0 100.0 100.0 0.5 98 98 2.0 97 (96) 92 91 10.0 93 92 88 86 85 87 85 12.5 92 91 87 85 83 83 50.0 86 84 79 77 74 72 70 80.0 83 81 76 73 70 68 65 100.0 81 80 75 72 68 66 63 •Milli-equivalents per liter in the cases milli- formula-weights per liter in the case of nitric and sulphuric acids and of barium hydroxide; of phosphoric acid. Table 115. — Conductance-ratio lOO A/Ao and approximate percentage ionization at 260° and 306°. Substance. Concen- tration. 260°. 306°. HNO3 0.0 100 2.0 • . . . 84 80.0 .... 33 HOI 0.0 100 100 2.0 96 94 10.0 89 82 80.0 76 60 H2SO4.... 0.0 100 2.0 .... 31-50 1 80.0 .... 23-37 It has already been shown that the equivalent conductances of nitric acid and of barium hydroxide up to 156° and that of hydrochloric acid up Section py. — Ionization of the Substances. 269 to 306° change with the concentration according to the same exponential law as does that of neutral salts, the value of the exponent n in the equation C{K — A) = K{CAY, being in all cases approximately 1.5. It follows therefore that the same is true of the ionization (y) of these substances, to which the corresponding equation C(l — y) = K'(Cy)" with « = 1.5, approximately, applies. The change of ionization with the temperature of nitric acid up to 156° and of hydrochloric acid even up to 306° is also about the same magni- tude as that of neutral salts of the same ionic type, as may be seen best by comparing the values at 80 milli-normal in tables 114 and 115 and table 41, Part V, with those in table 28 (Part IV). Thus at 18° the ionization of potassium and sodium chlorides is 86.5 per cent, that of hydrochloric and nitric acids 93 per cent, while at 156° the corresponding values are 80.5 per cent for the two salts and 86 per cent for the two acids. At 306° the ionization of the salts is 63 per cent and that of hydrochloric acid 60 per cent. The ionization of nitric acid, however, at 218° and above decreases much more rapidly than hydrochloric acid, and has fallen to 33 per cent at 306\ This marked difference in the behavior of the two acids at the high temperatures is well shown by the conductance plot in fig. 18. The ionization of barium hydroxide decreases a little more rapidly than the average ionization of the two salts, barium nitrate and potassium sul- phate ; thus at 0.08 normal that of the base is 83 per cent at 18° and 65 per cent at 156°, while that of the salts is 72 per cent at 18° and 60 per cent at 156°. It was shown in the last section that the exponent in the functional relation between equivalent conductance and concentration in the case of phosphoric acid has values (1.8 to 1.9) which approach much more nearly to the value (2.0) required by the mass-action law, but do not entirely conform to it, even at the higher temperatures where the ionization is com- paratively small. To show better what the order of magnitude of this deviation is, and to furnish a better basis of comparison of the ionization- tendency of this acid with that of other weaker acids, we have summarized in table 116 its ionization-constants calculated by the usual formula K =z CyV(l — y), the concentration C being here expressed in formula- weights per liter, and the constants being multiplied by 10". Table 116. — lonisation-coiistants for phosphoric acid. Concentra- tion. Ionization-constants X W>. 18°. 25°. 50°. 75°. 100°. 128°. 156°. 0.0125 0.050 0.100 9,200 10,400 11,400 8,700 9,400 10,400 6,300 7,000 7,600 4,300 4,800 5,300 3,100 3,400 3,700 1,960 2,230 2,460 1,2.50 1,420 1,490 zyo Conductivity of Aqueous Solutions. — Part VIII. The great effect of temperature in reducing the ionization of this acid will be apparent from an inspection of these constants or of the ionization values themselves given in table 114. The values given for sulphuric acid in tables 114 and 115 show the per- centage of the total hydrogen which exists as hydrogen-ion under the two limiting assumptions that the acid dissociates on the one hand only into hydrogen-ion and sulphate-ion and on the other only into hydrogen-ion and hydrosulphate-ion (HSO^"). It will be seen that the two limits do not differ greatly from each other, except at the highest temperatures, and therefore that the uncertainty as to the hydrogen-ion concentration, which is really the most important datum relating to the acid, is not very large. It is evident that this hydrogen-ion concentration decreases rapidly with rising temperature; for example, at 0.08 normal from about 66 per cent at 18° to about 45 per cent at 100° and about 30 per cent at 306°, if the mean values be taken. By this hydrogen-ion concentration, however, not much light is thrown on the extent to which the two stages in the dissociation take place. It might seem that additional information in regard to this could be derived from the transference determinations made at 11°, 23°, and 96° by Bein* and between 8° and 33° by Tower.f But calculation shows that the trans- ference nmnbers of the cathion calculated under the two limiting assump- tions of dissociation only into hydrogen-ion and sulphate-ion and of disso- ciation only into hydrogen-ion and hydrosulphate-ion (HSO^") do not differ from each other by much more than the possible experimental error or than the error arising from the uncertainty in the values to be assumed for the equivalent conductance of the separate ions.J The conclusion pre- viously drawn by one of us§ from Tower's transference data that sulphuric acid at 18° up to 0.3 normal does not contain an important quantity of hydrosulphate-ion is therefore not justified in consideration of the effect of the possible errors. Further light is thrown on the ionization relations of sulphuric acid through a consideration of those of potassium hydrogen sulphate. Con- clusions in regard to the hydrogen-ion concentration in solutions of this salt may be drawn from its molal conductance (A), provided we make certain approximate assumptions. For, designating b}- yi, y^, and y^ the *Z. phys. Chem., 27, 53 (1898). fj. Am. Chem. Soc, 26, 10 (1904). JThus at 18° assuming Ah = 315, As04 = 68, and Ahso* = 35, the two transference numbers for the cathion are 0.823 and 0.800, while, if as concluded by Noyes & Kato (see section 116, Part XI) Ah = 335 (for a 0.05 normal solution) , the two transference numbers become 0,831 and 0.811. Tower found 0.823 and Bein 0.813 at 18°. The value of AhsOj is also very uncertain. §A. A. Noyes, Z. phys. Chem., 53, 251 (1905). Section p/. — Ionization of the Substances. 2ji fraction of the salt which dissociates according to the three reactions KHSO, = K+ + HSOr, KHSO, = K+ + H+ + SOr, and 2KHSO, = 2K^ + SO,- + H,SO, respectively,* it is evident that A =yi(AK + AHS04) + y.(AK + Ah + SAso,) + yA^VL + AsoJ or, putting 7 = 71 + 72 + 73. that A = 7(Ak + AHSO4) +7 2(Ah + 2Aso4 — Ahso,) + 73(A SO4 — Ahso,). Now the two limiting values of 73 are zero and 7 — y. (when 71 = 0), whence it follows that A — 7(Ak + AHSO4) y^< (Ah + ASO4) + ( ASO4 — AHSO4) and 72 ^ A — 7(Ak + AS04) Ah + ASO4 Limiting values of 70, the fraction dissociated into hydrogen-ion, can be calculated in this way from the data presented in this monograph with the help of the assumptions that the un-ionized fraction (1 — 7) of the salt has the same value as in the case of other salts of the uni-univalent type at the same concentration and temperature, and that the equivalent conductance of the hydrosulphate-ion is the same as that of the acetate ion at the same temperature. Table 117 contains the results of these calculations f for four concentrations at 18°, 100°, and 156°. *The dissociation according to the reactions 2KHS04 = KjSOi + H+ + HSOr and 2KHSOj = Kl2SO< + 2H+-)- SOi= is neglected in this prehminary calculation; but the KsSOj formed must be small in most cases owing to the small concentration of sulphate-ion. tThe data used are as follows : 18°. 100°. 156°. Ak + Aso^ 133 99 34 382 318 455 337 118 891 773 715 520 195 1175 980 Ak + Ahso^ AS04 — AhSO^ Ah + Aso^ Ah + Ah so. 2 45.1 0.97 10 379 0.94 2 784 0.96 10 580 0.92 2 754 0,95 10 1 611 0.91 A 50 295 0.88 100 264 0.85 50 422 0.85 100 375 0.81 50 477 0.83 100 0.79 A . . . The values of A are copied from table 108. Those of 7 are the mean ionizations for potassium and sodium chlorides as given in table IS, Part II. 272 Conductivity of Aqueous Solutions. — Part VIII. Table 117. — Preliminary values of the percentage ratio (IOO72) of hydrogen-ion concentration to total hydrogen concentration in solutions of potassium hydrogen sulphate. Concentration. 18°. 100°. 156°. 2 10 50 100 85-86 67-69 47-50 40-^3 39-46 18-27 4-13 1-10 6-19 0-10 0- 3 0- 2 These preliminary values are given here, because they are essential to the fuller discussion of the ionization-relations of sulphuric acid and its acid salt. More accurate values of the hydrogen-ion concentration in Solu- tions of this salt are derived below and will be found in table 119. It is seen from these results that at 18° the potassium hydrogen sulphate is in 0.002 molal solution almost completely dissociated into hydrogen-ion and sulphate-ion ; but that in 0.1 molal solution this dissociation has taken place only to an extent of 42 per cent, the rest of the salt existing to an extent of 15 per cent as un-ionized KHSO4 and to an extent of 43 per cent either as HSO^" or as H2SO4 -|- SO^". At 100° the hydrogen-ion concen- tration has become very much less at all three concentrations, and at 156° in the 0.1 molal solution it is scarcely appreciable. This justifies the con- clusion that sulphuric acid itself at 156° and above is at moderate dilutions dissociated only into hydrogen-ion and hydrosulphate-ion ; for the disso- ciation of the latter ion would of course be much less in the solution of the acid than of its acid salt, owing to the presence in the former of the hydro- gen-ion coming from the dissociation of the first equivalent of hydrogen. Since under these conditions sulphuric acid dissociates as a monobasic acid, it is of interest to compare its ionization with that of hydrochloric acid at the same molal concentration, say at 0.04 molal. The ionization of sulphuric acid may be obtained by doubling the second values given in tables 114 and 115, that of hydrochloric acid by interpolation between the values given for other concentrations in table 115 and in table 41, section 56, Part V. The ionization values for the 0.04 molal acids are as follows : 100°. 156°. 218°. 306°. HOI 92 «96 90 90 86 84 68 74 H.HSO, This shows that the two acids have at these temperatures not far from the same ionization-tendency (with reference in the case of sulphuric acid to the primary dissociation, that is, that of the first equivalent of hydro- *This value is doubtless a little too high because of slight secondary ionization. Section 97. — Ionization of the Substances. s^j gen) ; and it may reasonably be assumed that the same is true at 18° and the intermediate temperatures. With the help of this principle, the secondary ionization of the sulphuric acid — that is, the ratio of the sulphate-ion concentration to the total sul- phuric acid concentration — can be calculated for the more dilute solu- tions and for the lower temperatures by means of the relation CSO4 Ch Ch2S04 -, ^^~ C ^ c where C represents the total molal concentration of the sulphuric acid, and the other symbols, the molal concentrations of the separate substances as indicated by the subscripts. This relation follows at once from a com- bination of the equations, C = C-a-.aOi + Chsoj + CSO4 and Cn = Chsoj + 3 CsOi, the latter of which is an expression of the fact that hydrogen-ion is produced by the two chemical reactions H2SO4 = H+ -|- HSO4- and H3SO4 = 2 H+ + SOr. We have first made a preliminary calculation of the ratio CsoJC by the above expression by using for Cs/C twice the mean of the pairs of values given in table 114 of the ratio of the hydrogen-ion concentration to the total hydrogen-concentration, and by taking for CH2SO4/C the values of the corresponding ratio for hydrochloric acid as derived from ionization data given in table 41, Part V. We have then on the basis of this result, which shows the approximate proportion of sulphate-ion and hydrosul- phate-ion in the solution, interpolated a more correct value of the hydro- gen-ion concentration between the two limiting values given in tables 114 and 115, which, it will be remembered, were obtained under the two limiting assumptions that the acid dissociates only into H+ and SOi^ and that it dissociates only into H+ and HSO4".* Then new, final values of the concentrations of the sulphate-ion and hydrosulphate-ion were obtained b}- repeating the calculation. The values derived through these considerations are all brought together in table 118. It will be understood, of course, that they are only rough approximations. The concentrations are milli-formula-weights per liter, in accordance with the formula represented by the subscripts. The symbol C represents the total concentration of the acid in milli-formula-weights of H2SO4 per liter. But in calculating the values of the ionization-con- stant given in the last column, the concentrations are all expressed in formula-weights (not milli-formula-weights) per liter. *Designating these two limiting values (multiplied by 2) by C^/C and C^/C, respectively, it can be readily shown by formulating the exact conductance equations that we get for the true value of Ch/C: Ch Ch I Chso< ( Ch~Ch ) Ch 2Cs04 I Ch~Ch \ C~CcVr"/~C Q \ c' ^' 274 Conductivity of Aqueous Solutions. — Part VIII. Table 118. — The ionization-relations of sulphuric acid. Temperature. Concentra- tion. 100 Ch c 100 Ch^so, c 100 Chso^ 100 C6o^ C 108 Ch. Cio^ \ C Chso^ 18 1 185 1 13 86 (12,000) 5 165 2 31 67 18,000 25 137 5 53 42 27,000 50 127 6 61 33 34,000 1 100 1 136 2 60 38 860 5 111 4 80 16 1,100 25 98 7 88 5 1,390 ! 50 95 9 87 4 (2,200) 156 1 106 3 88 9 110 5 97 5 93 2 100 ; 25 89 9 93 -2 1 j 50 88 12 88 j 218 1 5 96 3 6 98 -1 40 85 14 87 (-1) ••••<• 1 306 1 97 5 (93) (3)* 40 70 32 (66) (2)* •These values probably arise from experimental error. We may next consider the ionization-relations of the potassium hydro- gen sulphate. It follows from the principle that the primary ionization of the sulphuric acid is the same as that of hydrochloric acid that the concentration of the un-ionized sulphuric acid is always so small in the solutions of the potassium hydrogen sulphate that the calculation of the hydrogen-ion concentration made under the assumption that the former concentration (or yg) is zero is substantially correct, and therefore that the second or larger numbers given in table 117 are more nearly the true values for the hydrogen-ion concentration. In order to get fairly accurate values for the sulphate-ion and hydrosulphate-ion concentrations in solu- tions of the salt, it is, however, desirable to form an estimate of the concen- tration of the un-ionized sulphuric acid (H2SO4) and the un-ionized potas- sium sulphate (K2SO4). As the latter was entirely disregarded in the previous calculation, a more accurate value of the hydrogen-ion concentra- tion will also be thereby obtained. In deriving these final values we have proceeded as follows. We make the preliminary assumption that Cso* = Ch (taking for Cn/C the larger of the two values given in table 117), and that CHSO4 == (7y — Cso4. Applying then the mass-action principle* that in a mixture of two sub- stances with a common ion the un-ionized fraction of each is the same as *That this principle is also applicable to salts of these types, even though the change of their ionization with the concentration does not conform to the mass- action law, has been shown by Noyes (Z. phys. chem., 52, 634, 1905). Section 97. — Ionization of the Substances. 2/5 if it were alone present at such a concentration that its ions are at a con- centration equal to that of the common ion in the mixture, we determine the ratios ^^2804 _ ^^^^ Ckhso^ ^ reference to the ioniza- <- K2SO4 -f- C 8O4 CKHSO4 -{- ChsOi tion values given in table 27, Part IV, and in table 12, Part II, for potas- sium sulphate and for potassium chloride, respectively, at the same concen- tration of the total potassium.* In a similar way we obtained the ratio Ch2S0.j/(C"h2S04 -f ChsOi) by determining from the data given in table 118 the value of this ratio for sulphuric acid when present alone in a solution in which the hydrogen-ion concentration is the same as that in the solution of the acid-salt under consideration. Fi'om these ratios and the prelimi- nary values of CsOi and Chso^, final values of CK2SO4, Ckhso^, and Cn^soi are calculated. From these Ck is also obtained by means of the equation Ck -)-Ckhso.i + 2 Ckoso.! = C, where C is the molal concentration of the potassium hydrogen sulphate. It follows now from the two equations, Cn + Chsoi "h CKHsOi + 2 CH28O4 = C and CSO4 + CHSO4 + CKHSO4 + CH2SO4 + CK2SO4 = C, that Cso4 ^ Ch -|- CH2SO4 — CK„a()4 and Chso4 ^^ C — Ch — 3 CH2SO4 — Ckhso4. We have then calculated final values of Ch by the following equation, which expresses the molal conductance A of the salt in terms of the equivalent conductances and molal concentrations of the separate ions, CA = CkAk + ChAh + CHSO4AHSO4 + 2 Cso4Aso4. In this equation all the quantities except Ch are known or can be expressed in terms of Ch and known quantities with the help of the two preceding equations. The equation then becomes r^ (^ - -t^(Ah + ASO4 -|- AS04 — AHSO4) ^ A -r (Ak + Ansoi) + 2(Ck9S04 — Ch>s04) / . , V z (^ ASO4 — AHSO4 ; From the values of Ch/C so obtained we have finally calculated Csoi/C ♦Whether one considers the ionization at the same concentration of the potassium- ion or of the total potassium mal) from the electromotive force of the alkali-acid hydrogen cell ^ ; and (i) from the conductivity of the purest water thus far obtained.** Although these entirely independent measure- ments have all given for the ionization of water values of the same order of magnitude and have thereby furnished one of the most striking evi- dences of the Ionic Theory, yet for none of the values so obtained can an}' considerable percentage accuracy be claimed. It has therefore seemed advisable to make a special stud}- of this constant at ordinary temperatures by the same method that has been emplo}-ed at higher temperatures b}- Noyes and Kato (see Part A^I) and by Sosman (Part A'll), that is, by measuring the increase in conductance produced by adding to a partially h}drolyzed salt of a Mcak acid and a weak base an excess of the acid or of the base, whereby the hydrolysis is reduced. In calculating from such data the ionization of water a knowledge of the ionization-constants of the acid and the base and of the degree of ionization of the salt is also necessary. The salt selected for this purpose must be sufficiently h}'drolyzed to give rise to a marked change in the unhydrolyzed portion of it when the excess of acid or base is added. On the other hand, both the acid and base of the salt must be strong enough to permit their ionization-constants to be directly and accurately determined by conductivity measurements. An examination of the available substances previously investigated seemed to show that ammonium hydroxide was the most suitable base, and that *Arrhenius, Z. phys. Chem., 11, 822 (1893) . tShields, ibid., 12, 184 (1893). iArrhenius, ibid., 5, 19 (1890); Bredig, ibid., 11, 829 (1893). SWalker, ibid., 4, 334 (1889). IJWijs, ibid., 11, 492 (1893). IJOstwald, ibid., 11, 531 (1893); Nernst, ibid., 14, 155 (1894); Lowenherz, ibid., 20, 293 (1896). **KohIratisch and Heydweiller, ibid., 14, 330 (1894). 286 Conductivity of Aqueous Solutions. — Part IX. diketotetrahydrothiazole was the most suitable acid. This acid has also been called dioxythiazole and mustard-oil acetic acid, and has, according to CO — CH,^ the investisration of Hantzsch,* the structuref I S. The base ^ NH — co- has at 25° an ionization-constant of 18.1 X 10"" and the acid one of 0.181 X 10"°, and their salt a hydrolysis of about 4 per cent, as the meas- urements presented below show. This base is more easily obtained pure than any other base of similar strength ; and the acid can be readily pre- pared in quantity from thiourea and chloracetic acid. It is, however, so weak, that its salt is about ten times as much hydrolyzed as ammonium acetate (which is 0.4 per cent hydrolyzed at 25°) ; and yet it is strong enough to have a conductance which can be fairly accurately determined, though it lies near the limit in this respect. In detail, therefore, this investigation has consisted in the preparation and purification of the diketotetrahydrothiazole and the determination of its ionization by conductivity measurements at 0°, 18°, and 35° at various concentrations, in corresponding measurements with ammonium hydrox- ide, and in measurements at these three temperatures of the conduct- ance of the salt at 0.03 and 0.05 normal both in water alone and in the presence of about the equivalent amount and half the equivalent amount of the free acid and of the free base in separate experiments. In order to determine the conductance of the completely ionized acid and salt, measurements were also made with the latter at a concentration of 0.003 normal. 100. PREPARATION OF THE SUBSTANCES AND SOLUTIONS. The diketotetrahydrothiazole was prepared as described by Volhardj by heating together thiourea and chloracetic acid in aqueous solution. The product was purified by a large number of crystallizations from methyl alcohol and from water. No boneblack was used. The crystalli- zation from water was continued until the sample was perfectly white and no further change in conductance was produced, as will be shown in section 103. The last crystallizations were made from conductivity water in platinum vessels, and the crystals were filtered out and dried at 100° in a platinum Gooch crucible in purified air. A portion of the product so dried was finely powdered and kept in a desiccator over sulphuric acid for several weeks ; it lost only a few hundredths of 1 per cent in weight, showing that it was dry. The melting-point of the purified sample was found to be 133.4°. *Ber. d. chem. Ges., 20, 3129 (1887). tEven assuming that this substance exists in part in the desmotropic "enol" form, this would make no difference in the values of the ionization of water derived from the study of its equilibria; for the concentrations of the two forms must be under all circumstances proportional to each other, tJ. prakt. Chem. (2) 9, 6 (1874). Section loo. — Preparation of the Solutions. 28/ The solutions of the acid were always prepared just before the con- ductance was measured by dissolving weighed portions of it in a known weight of conductivity water in a Jena flask. The solutions were pre- pared and transferred to the conductivity vessel in contact with onl)- purified air. The water used for dissolving the acid, and in general throughout this investigation, had at 18° a specific conductance which always lay between 0.15 and 0.60 X 10"" reciprocal ohms. The solutions of the acid even when kept for several hours in the conductivity-vessel showed a change in conductance of not more than 0.1 per cent. The ammonium hydroxide solution used was an approximately 0.1 normal one made by diluting with conductivity water a special sample of strong ammonia water (spec, grav., 0.90) furnished by the Baker & Adamson Chemical Co. and certified to be free from amines, carbonates, and silicates. The solution was titrated by running a slight excess of it directly into a loiown weight of standard hydrochloric acid, and running back to the end-point with hydrochloric acid with the help of methyl orange. The solutions were all measured by weight, not by volume. The hydrochloric acid was itself standardized by precipitating a known weight of it with silver nitrate and weighing the silver chloride. The solution was kept in a two-liter "non-sol" bottle (furnished by Whitall, Tatum & Co.). To protect it from evaporation and contamination it was connected through another bottle of ammonium hydroxide solu- tion of the same strength with a long soda-lime tube through which air was admitted when samples were withdrawn. The solution was trans- ferred through delivery tubes into the conductivity vessel or into a Jena flask in which it was diluted or mixed with the acid solution, in contact with only purified air. In order to use comparatively fresh solutions for the measurements, a new stock solution was prepared in the same way in the course of the experiments, so that the solution employed was never more than ten days old. Determinations of the alkaline strength showed that during this period the change in it was less than 0.1 per cent. The conductance of this solution was found to be substantially identical with that of one prepared from liquid ammonia by Mr. R. B. Sosman. The solutions of the salt, both alone and with an excess af acid or base, were prepared by introducing into a Jena flask provided with a perforated ground-glass stopper and filled with purified air a weighed quantity of the solid acid, and then introducing without opening the flask the proper quantity of conductivity water and of the stock ammonium hydroxide solution to produce as nearly as possible any desired round concentrations. These were in general attained within 0.1 or 0.2 per cent, but the exact concentration was always considered. The content by weight of the various solutions obtained as above described was reduced to volume concentration by means of the density of the solution, which in the case of the acid or salt solutions was calcu- 288 Conductivity of Aqueous Solutions. — Part IX. lated from the densities of the solid acid and of the water or ammonium hydroxide solution, under the assumption that no change in the total volume occurs on mixing.* The concentration given in the tables below is always that at the temperature of the measurement. The atomic weights used were those referred to oxygen as 16.00 as given in the report of the International Committee for 1906.f All weights were corrected for the bouyancy of the air. 101. APPARATUS AND METHOD. The conductivity measurements were made with a slide-wire bridge by the usual Kohl- rausch method. The slide-wire was cali- brated and the resistance coils were com- pared with each other. The conductivity vessel used was one of pipette form devised by Mr. G. A. Abbott in this laboratory. It is shown in Fig. 19. It has the advantages that the solution can be introduced into it and kept in it entirely out of contact with the air, that the electrodes are fully protected against change in position, and that the vessel can be entirely immersed in the thermostat. The capacity of the vessel was about 35 c.cm. ; and the vertical electrodes were about 2 cm. square and 1.3 cm. apart. The electrodes were used tinplatinized in the measurements with the acid, so as to reduce contamination; but were platinized in the measurements with the better-conducting base and salt. The conductance-capacity of the vessel was deter- mined by measuring in it (when unplatinized) a freshly prepared 0.003136 normal or (when platinized) a 0.0500 normal solution of potassium chloride,^ and allowing for the conductance of the water employed. The vessel was immersed in well-stirred thermostats whose tempera- ture was kept constant within 0.01°. That at 0° was maintained by a mixture of water and finely crushed ice in large proportion. The ther- mometers used were compared with the laboratory standard. *The density of the acid at 25° was found to be 1.673 by weighing a large excess of it in a pycnometer under its saturated solution. That there was in fact no appre- ciable volume-change on mixing was shown by direct measurements of the density of known solutions of the acid and of its salt. fSee J. Am. Chem. Soc, 28, 1 (1906). JThe actual conductances of these solutions in the vessel after allowing for the conductance of the water were 0.0015095 and 0.03256 reciprocal ohms at 18°, which correspond to conductance-capacities of 0.17861 and 0.17775, respectively, using Kohlrausch and Maltby's equivalent-conductance values. The same value was obtained at the end of the measurements as at the start. Fig. 19. Section 103. — Conductivity and lonization-Constants. 28p The final bridge reading was not recorded until it had become con- stant, which it did in 15-30 minutes. It then remained constant, even over night, in almost all cases; but with a few solutions containing the salt with an excess of ammonium hydroxide there was a slight progres- sive increase in conductance, for which a small correction (never more than 0.35 per cent) was applied, depending upon the time which had elapsed before the reading and upon the temperature to which the cell had been exposed. 102. THE CONDUCTIVITY AND lONIZATION-CONSTANTS OF AMMONIUM HYDROXIDE AND DIKETOTETRAHYDROTHIAZOLE. Tables 120 and 121 contain the results of the conductance measure- ments with ammonium hydroxide and with diketotetrahydrothiazole. The first column gives the temperature; the second, the date; the third, the concentration in equivalents per liter of solution at the temperature of the measurement; the fourth, the conductance in reciprocal ohms as actually measured in the conductivity vessel, multiplied by 10°; the fifth, the same diminished by the conductance of the water; the sixth, the equivalent conductance (A) calculated by multiplying the values of the preceding column by the conductance-capacity (0.17861 for the acid and 0.17775 for the base) and dividing by the concentration given in the third column and by 10'; and the seventh, the ionization-constant (K) calculated by the expression K = -—— r- and multiplied by 10" -'^oC-'^o ^) The values of A(, (the equivalent conductance for complete ionization) used in the calculation of the ionization-constant were derived as follows. That for the OH" ion at 18° was found to be 173.0 by subtracting Kohl- rausch's value* for the sodium ion (43.55) from Noyes and Kato's value for sodium hydroxide (216.5, see Part VI). That for the NH^^ ion at 18° was found to be 65.4 by subtracting Kohlrausch's value for chloride ion (65.44) from Sosman's value for ammonium chloride (130.9, see Part VII). In this way the value for ammonium hydroxide was found to be 238.4 at 18°. Those for ammonium hydroxide at 0° and 25° were obtained from the corresponding equivalent conductances of the XH% and OH" ions at 18° by means of the temperature-coefficients for the conductivities of these ions derived b}- Kohlrausch.f The values so obtained are Anh4 = 39.3, Aoh = 117.7 and Ao(NHiOH) = 157.0 at 0° ; and Anh4 = 75.9, Aoh = 194.7 and A„,nh,oH) = 270.6 at 25°. The A^ values for the acid at each temperature were obtained from those for its ammonium salt by subtracting the equivalent conductance of the NII+4 ion *Sitzungsber. preuss. Akad. der Wissensch., 1901, 1026-1033. tibid., 1901, 10. These coefficients are: (Anh*) t = ( Anh4),3 [1 + 0.0223 (t — 18) -|- 0.000079 (t - 18)=] Aoh) , = Aoh) [1 + 0.0179 (t - 18) + 0.000008 (t - 18 A„) = (Ah) a [1 -f 0.0154 (t - 18) - 0.000033 (t - 18)=] 2po Conductivity of Aqueous Solutions. — Part JX. derived as just described, and adding that of the H+ ion. The A„-values for the ammonium salt were derived from direct conductance measure- ments which will be presented and discussed in section 103. For the equivalent conductance of the H+ ion at 18° the value (315) derived from the measurements of Goodwin and Haskell* upon very dilute acid solutions was adopted ; while at 0° and 25° the values 224.3 and 348.5, respectively, were obtained from this one at 18° by means of Kohlrausch's temperature-coefficients just referred to. Table 120.— Equivalent conductance and ionization-constant of diketotetrahydrothiasole. Temper- ature. Date. Equiva- lents per liter. Conductance X lO^. Equivalent conduct- ance. Ionization-constant X 10®. Observed. Corrected. Separate values. Mean values. 1906 May 24.. 0.2503 185.9 184.5 0.1316 0.0710 May 21.. 0.1251 131.0 129.7 0.1852 0.0703 0709 1 May 25.. 0.1251 132.3 131.2 0.1873 0.0720f May 22.. 0.0626 92.9 91.6 0.2613 0.07011 0.07121 - 0.0711 June 1.. 0.2503 185.7 184.7 0.1318 June 2.. May 30.. 0.2503 0.1251 187.1 130.6 186.1 128.9 0.1328 0.1840 0.0723 0.0694 0.0713 . June 5. . 0.0626 94.0 93.2 0.2659 0.0725J 18 May 24.. 0.2500 372.5 370.1 0.2644 0.1436 May 21.. 0.1250 266.1 263.9 0.3770 0.1460 0.1463] May 25.. 0.1250 268.0 266.2 0.3803 0.1487 May 22.. 0.0625 189.5 187.2 0.5349 0.14711 0.1435 - 0.1459 .June 1.. 0.2500 371.5 369.9 0.2643 June 2 . . 0.2500 373.3 371.6 0.2654 0.1447 0.1455 May 30.. 0.1250 264.8 261.9 0.3740 0.1437 June 5. . 0.0625 190.8 189.3 0.5410 0.1504J i "5 May 24.. 0.2496 463.7 460.7 0.3297 0.1780] 1 May 21.. 0.1248 330.5 328.0 0.4693 0.18041 1818 May 25.. 0.1248 333.1 331.0 0.4737 0.18381 ■ May 22.. 0.0624 237.5 234.8 0.6719 0.18501 • 0.1814 .June 1.. 0.2496 462.6 460.7 0.3297 0.17801 .June 2.. 0.2496 462.6 460.6 0.3296 0.17791 May 30.. 0.1248 331.5 328.1 0.4701 0.18101 "•■"'■^■^ .Tune 5 . . 0.0624 238.3 236.6 0.6772 0.1876J Table 121. — Equivalent conductance of ionization-constant of ammonium hydroxide. Temper- Date. Equiva- lents per Conductance X 106. Equiva- lent con- lonizat stant on-con- y. 106. liter. Observed. Corrected. ductance. Separate values. Mean values. ! 1906 July 22.. 0.09569 1,015 1,014 1.884 13.95 13.91 July 24.. 0.04540 696 695 2.722 13.88 18 July 22.. July 24.. 0.09557 0.04534 1,709 1,171- 1,708 1,170 3.177 4.584 17.21 17.09 17.15 25 July 22.. July 24. . 0.09542 0.04527 1,989 1,363 1,988 1,362 3.703 5.436 18.11 18.02 18.06 *Phys. Rev., 19, 386 (1904). Section 102. — Conductivity and lonirjation-Constants. 2^1 The measurements of May 30 to June 5, given in table 120, were made with a sample of the acid obtained by recrystallizing three times from conductivity water with the usual precautions the material used in these measurements of May 21-25. The agreement of the results with the two samples shows that the material underwent no change in the three crystallizations. Ostwald* obtained the value 0.24 X 10"' for the con- stant at 25° without using special precautions. Sosman (see Part VII) with solutions prepared both from liquid ammonia and from the pure ammonia water, obtained for the constant of ammonium hydroxide at 18°, as the mean of a large number of deter- minations at concentrations from 0.01 to 0.1, the value 17.15 X 10"", which is identical with that given in table 131. He obtained the value 17.9 X 16"° as the means of two determinations at 23°. This value agrees closely with the value 18.06 X 10"" here presented. Earlier investigatorsf obtained considerably higher results, partly owing to the incomplete elimination of impurities and to the use of other values of the equivalent conductance for complete ionization. The results given in the tables show that the constants of the two sub- stances do not vary considerably with the concentration. Sosman, using a much greater range of concentration, also found that the variation of the constant for ammonium hydroxide at 18° was very small. It will be observed that with rising temperature the ionization of the acid increases very rapidly, and that that of the ammonium hydroxide also increases, but to a much smaller extent. No reliable estimate of the accuracy of these constants can be made. It seems, however, not improbable that the equivalent-conductance values for the acid may be too high by one per cent, owing to the effect of impurities ; and also that its equivalent-conductance values for complete ionization may be in error by one per cent at 18° and 25°, and by even 2-3 per cent at 0°. Under these assumptions the error in its ionization- constant may be 3-4 per cent at 18° and 25°, and 5-7 per cent at 0°. In the case of ammonium hydroxide, although the values of the equivalent conductance at the higher concentrations are probably somewhat more exact than those for the acid, yet there is an even greater uncertainty in the values for complete ionization, so that the ionization-constants are probably of the same order of accuracy. *Z. physik. Chem., 3, 181 (1889). fBredig, Z. physik. Chem., 13, 394 (1894). Davidson, Ber. d. chem. Ges., 31, 1613 (1898). Hantzsch and Sebaldt, Z. physik. Chem., 30, 396 (1899). 2^2 Conductivity of Aqueous Solutions. — Part IX. 103. CONDUCTIVITY AND HYDROLYSIS OF THE AMMONIUM SALT OF DIKETOTETRAHYDROTHIAZOLE. The data relating to the conductivity of the pure ammonium salt are presented in table 132, which is arranged like tables 130 and 121 except that the specific conductance is given in addition to the equivalent con- ductance. Table 122. — Conductance of the ammonium salt of dike tote trahydro thiazo le. Temper- Date. Equivalents Condactance X lO^. Specific conduct- Equiva- lent con- ature. per liter. Observed. Corrected. ance X 108. ductance. 1906 July 28.. 0.05005 14,424 14,423 2,563.6 51.22 July 29.. 0.04997 14,401 14,400 2,559.4 51.22 July 12.. 0.020047 6,015 6,013 1,068.8 53.32 July 14.. 0.020035 6,016 6,014 1,069.3 53.37 Aug. 3.. 0.002143 686.5 685.2 121.8 56.82 18 .July 28.. 0.04999 22,895 22,893 4,069 81.40 July 29.. 0.04991 22,828 22,826 4,057 81.30 July 12.. 0.020021 9,566 9,563 1,700.0 84.91 July 14.. 0.020010 9,562 9,559 1,699.1 84.91 Aug 3.. 0.002141 1,092.2 1,090.0 193.7 90.50 25 July 28.. 0.04992 26,408 26,406 4,694 94.03 July 29.. 0.04983 26,355 26,353 4,684 94.00 July 12.. 0.019992 11,044 11,041 1,962.6 98.17 July 14.. 0.019979 11,033 11,030 1,960.0 98.16 Aug. 3.. 0.002137 1,265.6 1,263.0 224.5 105.04 It will be seen that the values of the equivalent conductance at about the same concentration, which were determined with solutions made up separately from the solid acid and the stock ammonium hydroxide solu- tion, agree in every case within about 0.1 per cent. For the purpose of facilitating the subsequent calculation of the hydrol- ysis, the specific conductance l has been expressed as a concentra- tion-function of the form C =^ oL -|-;8l3 which corresponds to the van't Hoff function (CA)* ^= KC(A^ — A), which is known to express approx- imately the variation of the equivalent conductance A with the concentra- tion C in the case of neutral salts. As this equation is to be used only for interpolation for a small distance from the values from which it is derived, any possible inaccuracy in the assumed form of the function could not introduce a significant error. Using the conductance values at 0.03 and 0.05 normal as the basis, the corresponding numerical equations are : C = 17.330 L -)- 43.34 L? at 0° C = 10.832 L -I- 22.95 Li at 18° C= 9.373 L-f 18.45 L? at 25° Section loj. — Hydrolysis of the Ammonium Salt. 2Q^ Table 123 contains the data for the ammonium salt in the presence of an excess of the free acid or base. The first five columns are self-ex- planatory. The sixth column contains the uncorrected specific conductance X 10" of the solution in reciprocal ohms obtained by multiplying the observed conductance by the conductance-capacity and by 10". The seventh column contains the corresponding specific conductance corrected by subtracting that of the virater and in some cases the small estimated increase due to progressive contamination during the period of the measurement (see section 101). The eighth column headed "Salt in solution" contains the same values after correcting them for the specific conductance of the ionized ammo- nium hydroxide, when this was present in excess. (The conductance due to the ionized acid when it was in excess was entirely inappreciable.) This conductance (lb) was computed by the equations: „ if bCnH4 oh KbCb , ^ -iM n / « I . s CoH = -p^ = ~;^ — ; and Lr = lO-* ton (Anh + Aoh) Lnh4 '^y in which Kb is the ionization-constant for ammonium hydroxide, C-b the excess of it present, and C is the concentration of the salt and y its degree of ionization. The ninth column gives the concentration (Co) at which the salt in water alone has the same specific conductance as that (given in the eighth column) of the salt in the presence of the acid or base; this concentration Co was calculated by the empirical relations between C and l given on the preceding page. The last column contains the values of the percentage hydrolysis (lOO/io) of the salt in water alone at the concentration Co. These values have been computed by means of the equation : , Co — C Cb — (Co — C) '" C^' Cb-2(Co-C) in which C represents the concentration of the salt in the mixture and Cb that of the added base (or acid). This equation results from combination of the two equations : c,{i — K) = c{i-h) (CXy = Ch(Ch + Cb) in which h represents the hydrolysis of the salt in the presence of the excess of base (or acid). The first of these, which states that the con- centration of the unhydrolyzed portion (which is equal to the sum of the concentrations of the ions and the un-ionized salt) is the same in the two cases, is a consequence of the definition of Co- The second of these 294 Conductivity of Aqueous Solutions. — Part IX. equations is the expression of the mass-action requirement that the product of the concentrations of the free acid and base be the same when the ion-concentrations are the same. Table 123. — Conductance of the salt with an excess of acid or base and its hydrolysis. Tem- pera- Date. Milli-cq aivalentg per liter. Specific conductance X 10^. Concentra- tion (Cq) \oi salt in water alone. Percent- age hy- Solution. Salt in ture. Salt. Acid. Base. Observed. Corrected. solution. (lOOAo) 1906 July 10. 20.025 10.95 1,099.8 1,096.8 1,095.5 20.555 2.71 July 11. 20.025 19.78 1,100.6 1,098.4 1,096.0 20.562 2.68 July 15. 20.068 19.96 1,100.5 1,100.3 1,100.3 20.644 2.87 July 16. 20.068 10.13 1.099.8 1,099.5 1,099.5 20.629 Mean . . 2.88 2.78 July 26. 50.06 24.60 2,622.9 2,621.7 2,620.4 a. d..... 51.22 0.09 2.37 July 27. 50.06 45.29 2,632.7 2,631.7 2,629.2 51.39 *2.66 July 30. 50.10 49.14 2,622.9 2,622.6 2,622.6 51.27 2.34 July 31. 50.10 24.45 2,623.3 2,623.0 2,623.0 51.27 Mean . . 2.40 2.37 18 July 10. 20.000 10.93 1,765.4 1,761.2 1,758.8 a.d 20.742 0.02 3.82 July 11. 20.000 19.75 1,767.6 1,764.6 1,760.1 20.751 3.76 July 15. 20.044 19.94 1,767.4 1,767.0 1,767.0 20.836 3.95 July 16. 20.044 10.12 1,766.4 1,765.9 1,765.9 20.821 Mean .. 4.04 3.89 July 26. 50.00 24.57 4,200.0 4,194.1 4,191.6 a.d 51.63 0.10 3.38 July 27. 50.00 45.23 4,215.3 4,210.3 4,205.5 51.80 *3.61 July 30. 50.04 49.08 4,201.3 4,200.9 4,200.9 51.74 3.41 July 31. 50.04 24.43 4,195.9 4,195.5 4,195.5 51.68 Mean .. 3.39 3.39 25 July 10. 19.968 10.91 2,042.2 2,039.6 2,036.6 a.' d.... . 20.784 0.01 4.25 July 11. 19.968 19.73 2,047.6 2,045.4 2,040.0 20.818 4.24 July 15. 20.013 19.91 2,050.9 2,050.4 2,050.4 20.921 4.52 July 16. 30.013 10.10 2,047.4 2,046.8 3,046.8 20.884 Mean . . 4.58 4.40 July 26. 49.92 24.53 4,873.9 4,861.7 4,858.7 a.d 51.80 0.15 3.94 July 27. 49.92 45.17 4,894.7 4,885.1 4,879.4 52.02 *4.22 July 30. 49.96 49.01 4,866.4 4,865.9 4,865.9 51.88 3.85 July 31. 49.96 24.39 4,859.9 4,859.4 4,859.4 51.81 Mean . . 3.86 3.88 a.' d 0.04 *Oinitted in the computation of the mean. It will be seen from the last column of table 123 that the values of a. d. (the average deviation of the separate hydrolysis values from the mean) are about 0.10 at 0° and 18°, and 0.15 at 25° for the more dilute salt solution. The deviations for the more concentrated salt solution are much less than these. It is to be remembered in this connection Section loj. — Hydrolysis of the Ammonium Salt. 295 that these hydrolysis values are derived from experiments in some of which an excess of acid, and in others of which an excess of base was present, and in which varying quantities of these were added, and that most constant errors would either have been eliminated in the difference in the measurements with the mixture and the pure salt, or would have shown themselves by producing opposite effects when the acid and base were in excess. Before calculating the hydrolysis-constant, it is necessary to deter- mine the ionization of the salt at the concentrations in question, and therefore to determine the equivalent conductance A.^ for complete ioniza- tion. To do this the equivalent conductance of the unhydrolyzed part of the salt has been calculated at the three concentrations at which measure- ments were made by dividing the specific conductance as given in table 123 by the concentration of the unhydrolyzed part C„(l — /i„) ; and evi- dently it is to this concentration that the so-obtained values of the equiva- lent conductance refer. The values for /!„ used at 0.02 and 0.05 normal were the means given in table 123. The value of h^ used for the more dilute solution was calculated from these by the mass-action for- mula given below. From these three values of A the values of the three constants n, K, and Ao in the empirical equation, (AC)" =^ K{Ag — A)C, were computed. The ionization of the salt was then obtained by dividing the A-values by this value of A^. Table 124 contains the so-derived values of the equivalent conductance and percentage ionization of the salt. The values of the exponent n were found to be 1.35 at 0°, 1.39 at 18°, and 1.35 at 25°, thus of about the same magnitude as for ordinary salts. The ionization will also be seen to be about the same as that of other salts of the same ionic type. Table 134. — Equivalent conductance and ioni;:ation of the unhydrolyzed ammonium salt. Temper- Equivalents Equivalent conduct- Percentage ature. per liter. ance. ionization. 0.04875 52.55 84.5 0.01950 54.81 88.1 0.003080 58.5 94.1 0.00 62.2 18 0.04816 84.38 85.0 0.01926 88.32 88.8 0.002055 94.3 94.9 0.00 99.3 25 0.04782 98.03 83.1 0.01913 103.54 87.0 0.002035 110.1 93.4 0.00 117.9 2^6 Conductivity of Aqueous Solutions. — Part IX. From the values of the hydrolysis and ionization given in tables 133 and 124, the hydrolysis-constant Km (equal to \|^ K^ ^K] ) can be readily calculated by the mass-action relation K = Kn, in which hg (i-^o)y represents the hydrolysis of the salt in water alone at any concen- tration Co, y is the fraction of the unhydrolyzed salt C,, (1 — h^) which exists as ions, and Kw, Ka. and Kb are the ionization-constants for water, the acid, and the base, respectively. This equation is readily derived by combining the three simple mass-action equations, ChCoh =i2'w, Ch Ca = -K'aCha, and Cb Coh = ^bCboh, substituting for Cb and Ca the expression Co(l — hf,)y and for Cha and Cboh the expression Cgho, and taking the square root. The values of the hydrolysis constant Ku thus calculated are given in table 135. The values at the two concentrations will be seen to differ by from 13 to 9 per cent. As those at the higher concentration are influenced to a less extent by impurities and contami- nation, a double weight has been assigned to them in deriving the final mean values. It is not improbable that these values are still too high; but it is unlikely that the error exceeds 5 per cent. Table 125. — The hydrolysis-constant for the ammonium salt. Temper- ature. Equiva- lents per liter. Hrdrolysis-constant. Separate values. Mean Talues. 18 25 0.05 0.02 0.05 0.02 0.05 0.02 0.0287 0.0324 0.0413 0.0456 0.0488 0.0529 1 0.0299 1 0.0427 1 0.0500 104. THE IONIZATION OF WATER. The ionization-constants of water (K-^ = Ch Coh) can be calculated from the hydrolysis-constants given in table 125, and the ionization- constants of the acid and base given in section 103'. Table 136 contains the values of this constant for water, and also those of its square-root, which last represent the concentration of the hydrogen and hydroxide ion in pure water (in equivalents per liter). Table 126. — The ionization-constant of water and the hydrogen or hydroxide-ion concentration. Temper- ature. Ionization- constant K„ X lO". Ion concentration. (J"Kw=C„=Co„)X10T. 1 18 25 0.089 0.46 0.82 0.30 0.68 0.91 Section 104. — Ionization of Water. 297 To compare these results with those previously obtained the various values for the hydrogen-ion or hydroxide-ion concentration in pure water have been brought together in table 127. Table 127. — The hydrogen-ion concentration (X ro') in pure water. Results of various investigators.* Investigator. Method of determination. 0°. 18°. 25°. Arrhenius Wijs Hydrolysis of sodium acetate by ester-sa- ponification 1.1 1.2 1.19 1.00 0.91 Catalysis of ester by Nernst Lowenherz Kohlranseh & Heydweiller . . Kanolt Electromotive force of gas cell 0.8 Electromotive force of Conductance of pure water 0.36 0.30 0.80 0.68 Hydrolysis *For references to their articles see section pg. It will be seen that the new values are uniformly lower than those of Kohlrausch and Heydweiller, but only by from 16 to 20 per cent. This approximate agreement is of interest not only in indicating the absence of any considerable error in the values of Kohlrausch and Heydweiller, in spite of the somewhat uncertain correction that had to be applied for the impurities in the water ; but also in proving that the ionization of water is nearly, if not quite, the same when pure, as it is when an ionized salt is present in it at a concentration of 0.02 to 0.05 normal. As the most probable values of the hydrogen-ion concentration in pure water it would seem best to adopt for the present the lower ones derived above ; for, although it is not impossible that these are in error by as much as 10 per cent, yet it is reasonably certain that the error lies in such a direction as to produce too high rather than too low results. This will be evident when it is considered that the effect of impurities in the water or the solutes would be to give rise not only to too high values for the ionization-constants of the acid and base, but also, by combining with the excess of either of them added in the hydrolysis experiments, to give too great an increase in the conductance and therefore too great a value for the hydrolysis. It will be seen from table 126 that the hydrogen-ion concentration increases with great rapidity with the temperature, being three times as great at 25° as at 0°. It is of interest to calculate from this increase the heat of ionization of water, and to compare its value with that obtained 2p8 Conductivity of Aqueous Solutions. — Part IX. for the heat of neutralization of strong acids and bases. The calculation has been made for the two temperature-intervals by the equation , K, Q T, where K.^ and K^, represent the ionization-constants of water at Ti and Tj, R is the gas-constant (1.986 cal per degree), and Q is the heat of ioniza- tion of one mol of water. The value of Q is thus found to be 14,500 calories at 9°, and 14,200 calories at 31.5°. The mean value of the heats of neutralization of potassium and sodium hydroxides by hydrochloric and nitric acids as recently determined by Wormann* is 14,340 calories at 9° and 13,590 calories at 21.5°. The agreement is a surprisingly close one, and shows that the ionization values at the three temperatures, if affected by errors, must be affected by them by the same percentage amount. 105. SUMMARY. In this article have been presented the results of measurements of the conductivity at 0°, 18°, and 25° of ammonium hydroxide, diketotetrahy- drothiazole, and of the salt of this base and acid, both alone and in the presence of an excess of the base or acid. From these measurements have been calculated the ionization-constants of the base and acid, the hydrol- ysis and hydrolysis-constant of the salt, the ionization-constant of water and the concentration of the hydrogen-ion or hydroxide-ion in it. The final results may be summarized as follows : Table 128. — Ionization-constants of ammonium hydroxide, of diketotetrahydro- thiazole, and of water. Tempera- ture. Ionization-constants. Concentration of hydrogen-ion in pure water. Ammonium hydroxide. Diketotetratiydro- thiazole. Water. 18 25 13. 91 XIO-** 17.15X10-" IS-OGXIO-** 0.0711X10-'' 0.146 XIO-" 0.181 X10-« 0. 089X10-" 0.46 X10-" 0.82 X10-" 0. 30X10-' 0. 68X10-' 0. 91X10-' The values for the hydrogen-ion concentration given in the last column are 16 to 20 per cent lower than those derived by Kohlrausch and Heyd- weiller from the conductivity of the purest water. From their varia- tion with the temperature the heat of ionization of water has been cal- culated, and found to be in close agreement with the directly measured heat of neutralization of strong acids and bases. *Drucle's Ann. Phys., 18, 793 (1905). Part X. Solubility of Silver Chloride, Bromide, and Sulpho- cyanate at 100°. By William Bottger. Part X. SOLUBILITY OF SILVER CHLORIDE, BROMIDE, AND SULPHO- CYANATE AT 100°. 106. OUTLINE OF THE INVESTIGATION. The solubility of many difficultly soluble salts at room temperature has already been determined by several investigators* by means of measure- ments of the electrical conductivity of the saturated solutions. The exten- sion of such measurements to much higfher temperatures is attended w^ith the difficulties that open vessels can not be used owing to evaporation of the solvent, and that glass vessels are inadmissible owing to the con- tamination of the solution resulting from them. The platinum-lined bombs with quartz insulation recently constructed in this laboratory and described in Part II, enable, however, such measurements to be made with readiness and accuracy. One of these being placed at my disposal by Professor Noyes, I took the opportunity of making a few solubility deter- minations at 100°, at which temperature the results have much practical interest, owing to the frequent use of boiling solutions in analytical and preparation work. Unfortunately the time available only permitted the investigation of three salts. The results obtained with these, though not so accurate as might have been secured if the bomb could have been rotated within the bath, as will be done in later investigations in this laboratory, seem, however, to deserve publication. 107. DESCRIPTION OF THE EXPERIMENTS. The solubility determinations were made in the same bomb that had been used just before by A. A. Noyes and Y. Kato (see Part VI), after certain repairs had been made in it. It was provided with an open cylindrical electrode of platinum-iridium. It was heated for the 100° measurements in the steam-jacketed xylene bath described in section 32, Part IV. The conductance-capacity was determined by measuring in the bomb at 18° the conductance of a 0.005 normal potassium chloride solution and was found to be 0.1490, which was nearly identical with an entirely independent result (0.1492) obtained about the same time by Mr. Kato. *R Kohlrausch and Rose, Z. physik. Chem., 12, 234; Holleman, ibid., 12, 125; F. Kohlrausch, ibid., 44, 197; W. Bottger, ibid., 46, 521. 301 ^02 Conductivity of Aqueous Solutions. — Part X. Since the determinations of solubility were to be made by measuring ;he conductance of the saturated solution in the presence of an excess )f solid salt, the question arose whether the latter would influence the :onductance-capacity appreciably, as it might possibly do by settling 3ut upon the cylindrical electrode or even by remaining in suspension. To answer this question, a 0.01 normal sodium chloride solution was neasured in the bomb both at 18° and 100°, first alone and then in the presence of 0.5 to 0.8 c.cm. (measured moist) of solid silver chloride. The conductance of the dissolved portion of the latter salt can b€ shown jy applying the principle of the common-ion effect to the solubility-value lereinafter presented (152 X 10"" mols per liter at 100°) to be only about L XIO"" reciprocal ohms even at 100°, and therefore to be negligible in ;omparison with the conductance of the sodium chloride. The specific :onductances multiplied by 10" observed in these experiments are given n the following table. Solution. 18° 99.8°. Initial. Final. 0.01 normal NaCl 0.01 normal NaCI-FO.5 , —0.8 c.cm. solid AgOl ' 1,024 *1,023 1,020 «1,030 1,025 *1,034 1,023 *1,020 *1,020 3,215 *3,213 3,215 *3,214 *3,215 *These second and third values were obtained by removing the bomb from the bath, shaking it, returning it, and allowing it to come to the original temperature. These results show that the effect of the solid salt on the conductance :ertainly does not exceed 0.4 per cent and it is not improbable that the differences of this magnitude observed at 18° were due to temperature variations, which were not entirely excluded in these first experiments ; Eor the differences at 99.8° where the temperature regulation was auto- matic seem to be scarcely appreciable. In any case the effect of the solid salt on the conductance-capacity is less than the other errors of the solu- bility detei-minations. The correction for the conductance of the water, which is important in such dilute solutions, was determined as follows, in oi"der to avoid making a new measurement in the bomb at 100° with each new sample Df water. Each of two separate samples was measured nearly simulta- neously at 46° in the glass apparatus with un-platinized electrodes which I had previously used for solubility experiments* and at 1D0° in the bomb itself after it had been thoroughly soaked out by heating with pure water at 100°. *Z. phys. Chem., 46, 530 (1903). Section io;.~Description of the Experiments. The observed specific conductances X 10" were as follows : 303 At 100°. At 46°. Ratio. Sample 1 Sample 3 Mean 1.98 3.48 1.10 1.37 1.80 1.93 1.88 All other samples were measured only at 46° ; and their specific con- ductances m the bomb at 100° were calculated by multiplying the values so obtamed by 1.9. The error involved in this method of computation, mcludmg that arising from unavoidable accidental contamination* from the air in filling the bomb, would rarely exceed 0.3 X lO^" reciprocal ohms. The error that might arise from the gradual leaching out of conducting material from the bomb itself was practically eliminated, since the various salts were never introduced into the bomb until it had been so thoroughly soaked out by heating to 100° with pure water that the conductivity increased by only 0.1 X lO"" reciprocal ohms on removing the bomb from the bath, shaking, and returning it. The silver chloride, bromide, and sulphocyanate, whose solubilities were determined, were prepared by adding with vigorous stirring a cold 0.1 normal silver nitrate solution to a nearly equivalent quantity of 0.1 normal solution of sodium chloride or hydrochloric acid, potassium bromide, and ammonium sulphocyanate, respectively, which was heated to about' 50°. The sodium chloride had been especially purified by precipitation in the usual manner with hydrochloric acid, but the chemically pure salts of trade were used in the other cases. The supernatant liquid was then immediately poured off, and the residue was washed for two weeks with hot water which was renewed several times each day. The salts were prepared and kept in a room illuminated only by red light. The solubility-determinations were made as follows. When the bomb was found to give oiif conducting material only within the above-men- tioned limit, from 0.5 to 0.8 c.cm. of the moist silver salt was placed in it and washed three times with pure water; then the bomb was filled up to within 5 to 8 mm. of the rim, taking every precaution to avoid contami- nation by impurities from the air, and it was finally closed. Only a few minutes later, during which time the glass vessel for measuring the con- ductance of the water at 46° was filled, the conductance of the contents of the bomb was measured at room temperature without shaking the bomb after it was closed. The bomb was then shaken violently to bring about a close contact between solid and liquid, and the conductance was again *The magnitude of such contamination is illustrated by the fact that three portions from the same stock-bottle successively introduced into the bomb showed at about 25° specific conductances of 1.17, 0.99, and 1.18 X 10-^ reciprocal ohms. ^04 Conductivity of Aqueous Solutions. — Part X. measured. In most cases this was repeated till only a very slight increase of conductance was observed.* The bomb was then put into the xylene bath heated by steam. When the temperature of the bath had reached its former value, readings were taken every five minutes, and as soon as no appreciable change in the conductivity occurred, the conductivity was measured with three different resistances in the rheostat. The bomb was then taken out of the bath, shaken violently about 100 times, replaced, and readings taken after heat- ing for 40 to 60 minutes. Since at the end of these operations the specific conductance had increased by about 1 X 10"°, the change was at first ascribed to incomplete saturation. If this were true, one would expect of course that upon repeated shakings and heatings these increases would become less and less. To test this view an experiment was made with silver chloride in which the observed conductances measured at 99.7° at the start, and after suc- cessive shakings and the stated periods of heating between each reading were as follows: Period of heating (min.) 62 135 56 55 Specific conductance X 10" 59.73 60.47 62.73 64.35 65.77 Increase per hour 0.72 1.08 1.63 1.68 Considering in connection with these results the fact that even at room temperature the saturation occurs almost instantaneously, it seems very probable that these increases are not due, or are only in small part due, to incomplete saturation; for if they were due to this, one would expect that the increase per hour would diminish instead of increasing. It is more probable that the effect is mainly due to a slight decomposition of the salt — perhaps a reduction by impurities in the water.f It might also *These data at the room temperature are not given in the table below, as they were not measured at any one temperature, their purpose being mainly to serve as an indication of accidental contamination in any experiment. As a result of all the observations it was found that the increases after shaking were small in comparison with those taking place immediately after pouring in the water, showing that satura- tion is attained very rapidly. This is illustrated by the following data. The conductance immediately after closing the bomb at room temperature (32.7°) was 2,754; and after shaking successively the number of times shown by the figures in parentheses it was: (2) 2.923; (2) 3.966; (3) 3.983; (2) 3.985; (4) 3.004; (4) 3.003; (10) 3.011; (10) 3.015; (100) 3.028; (100) 3.028. These numbers show, if we assume 3.03 as the final value corresponding to that temperature and 1.00 to be the conduct- ance of the water, that 86 per cent of the silver chloride goes into solution during the short period of pouring in the water and closing the bomb and 98 per cent after shaking the bomb 8 times. Whether the later increase of 2 per cent is a consequence of further solution of the salt or whether it is due to a rise of temperature brought about by the process of shaking is uncertain. tit was found in general on bringing the contents of the bomb back to room tem- perature that the conductance had increased by an amount which was greater the longer the duration of the previous heating. In one case the conductance of the saturated solution at 29.1° before heating was 3.84 X 10-' reciprocal ohms, while upon returning to that temperature after heating for 60 minutes it had become 4.16 X 10-". Section io8. — The Conductivity Data. ^05 conceivably arise from a gradual leaching out of soluble impurities, but this is disproved by experiments that will be described in the next section. The method of heating and shaking just described was used in experi- ments 1 to 5 (see table 129) with silver chloride and in all of those with silver sulphocyanate. A slightly different procedure was followed in some of the later experiments (6 to 9) with silver chloride and in those with silver bromide, in that the bomb was removed from the bath after the latter had reached about 99° and vigorously shaken before the first bridge-reading was taken; after which it was, as before, removed from the bath, well shaken, returned to it, heated again for 30 to 60 minutes, and a new reading taken. Even in this case the agitation took place somewhat below 100°, since the bomb cooled off a little, while it was out of the bath ; but it is probable that enough fine particles remained in sus- pension to secure saturation in the subsequent period of heating. In the last two experiments with silver chloride (10 and 11) the bomb was not shaken before the first reading at 100°, but was heated for an unusually long period of time (135 and 365 minutes, respectively) ; and afterwards the effect of rocking the bomb gently in the bath was tried. 108. THE CONDUCTIVITY DATA. The following table contains the results of the measurements. The headings are for the most part self-explanatory. All the conductivity values are those of the specific conductance expressed in reciprocal ohms and multiplied by 10^ The conductance of the water at 100° was cal- culated, as stated above, from that at 46° by multiplying by 1.9. The headings "first value" and "second value" under "Specific conductance of solution at t°" will be understood from the description of the proce- dure in the last section; the "second value" was always that obtained by removing the bomb from the bath after the "first value" was observed, shaking it vigorously, and heating it again for a considerable period. In the last column the time in minutes that the bomb was heated in the 100° bath before the reading for the "first value" was taken, is given under I, and the time between the "first" and "second values" is given under II. In the determinations with silver chloride the sample prepared from silver nitrate and hydrochloric acid was used in experiments 4 and 5, that from silver nitrate and sodium chloride in all the others. In experiments 6 to 9 the same portion of silver chloride was used, being treated successively with fresh portions of water, to see whether the apparent solubility would decrease owing to the leaching out at first of more soluble impurities. jo(5 Conductivity of Aqueous Solutions. — Part X. Table 129. — Specific conductance of saturated solutions near I00°. SILVER CHLORIDE. Experi- ment No. Dale. Specific conduct- ance of water. Temper- ature of experi- ment t°. Specific conduct- ance of solution at ^° Specific conduct- ance of salt at /°. Time of heating. At 46°. At 100° Lw First value Li Second value L2 ii— Lw La — ^Lw ■• II. 1 2 3 4 5 6 7 8 9 10 11 Mean . a. d... 1905 July 28.. July 29.. July 29.. July 31.. Aug. 1.. Aug. 9. . Aug. 9.. Aug. 9.. Aug. 10.. Aug. 10.. Aug. 11.. 1.33 1.25 1.50 1.30 1.20 1.86 1.58 1.67 1.75 1.25 1.62 2.58 2.38 2.85 2.47 2.28 3.53 3.00 3.17 3.33 2.38 3.08 100.1 100.0 99.9 99.7 99.9 100.2 100.2 100.2 100.2 100.2 100.1 60.76 60.40 60.54 59.72 60.27 61.72 60.82 61.69 62.20 60.16 '61.94 61.82 '62.16 ='6o!47 62! 35 61.35 62.47 62! 27 58.18 58.02 57.69 57.25 57.91 58.19 57.82 58.52 58.87 57.78 58.86 59.24 59.78 'ssioo 58.82 58.35 '59!i4 "59.19 80 75 55 80 60 60 55 60 70 135 265 40 60 60 "46' 30 60 "go 100.06 58.10 0.35 58.93 0.46 90 50 SILVER SULPHOCYANATE. 1 2 3 4 Mean . a. d... Aug. 3.. Aug. 3.. Aug. 4. . Aug. 4. . 1.30 1.47 1.10 1.26 2.47 2.79 2.09 2.39 100.1 100.1 100.1 100.1 17.23 '16.91 '17.24 "17.28 17.65 14.76 14.12 15.15 14.89 15.18 95 50 75 50 30 100.10 14.73 0.30 15.18 67 30 SILVER BROMIDE. 1 2 3 4 5 Mean .. a.d... Aug. 7. . Aug. 7. . Aug. 8.. Aug. 8.. Aug. 8.. 1.01 1.20 1.19 1.29 1.37 1.92 2.28 2.26 2.45 2.60 99.95 »99.95 100.1 100.1 100.1 10.36 10.89 9.91 "10.62 =10.34 =11.46 'i6!92 8.44 *8.61 7.65 8.17 7.74 '9.54 8.66 45 '60 55 60 70 '^25 "75' 100.06 8.00 0.30 8.66 56 75 ^On shaking again and heating for 45 minutes longer the value became 62.87, corresponding to an increase of 0.95 per hour. =For full data on the effect of repeated shaking and heating in this experiment see section II. •These values were obtained after rocking the bomb in the bath. The changes produced by it were, however, not large, except in one case, where the bomb had not been heated long enough. They amounted to -f 0.98 in expt 10 and -f- 0.16 in expt. 11 with silver chloride, to — 0.16 in expt. 2, + 0.13 in expt. 3, and -f 0.16 in expt. 4 with the sulphocyanate; and to -f- 0.19 in expt 4 and -j- 0.09 in expt. 5 with the bromide. *On shaking and heating for 40 minutes longer the value became 62.63 corresponding to an increase of 0.54 per hour. "On shaking and heating for 35 minutes longer the value became 12.19 and after another 60 minutes, 13.28, corresponding to increase of 1.25 and 1.09 per hour. "Omitted in calculating the mean since the measurements at room temperature showed con- tamination. ^Omitted in calculating the mean since the rate of progressive change was abnormally large. Section 109. — Conductance of the Saturated Solutions. jo^ 109. FINAL CONDUCTANCE VALUES FOR THE SATURATED SOLUTIONS. Attention may be first called to the results with the two separate samples of silver chloride. That prepared with hydrochloric acid and used in experiments 4 and 5 gave the mean value 57.58 at 99.80° while the sample made from sodium chloride gave 58.23 at 100.13°. Reduced to a common temperature of 100° by means of the temperature-coefficient 3.7 per cent per degree (see below) these values become 58.01 and 57.96, which are in close agreement. It may be next pointed out that the four experiments (6-9) made suc- cessively with the same portion of silver chloride do not show any pro- gressive decrease, the values being 58.19, 57.83, 58.53, 58.87, thus making it improbable that soluble impurities are enclosed within the solid salt and are gradually leaching out. It is also of some interest to compare the mean value from experiments 1-5 with that from experiments 6-9, since in the latter, but not in the former, the bomb was shaken after the temperature of the bath had been nearly attained. These two mean values are 57.81 at 99.93°, and 58.35 at 100.30°, which when reduced to 100° become 57.98 and 57.93, respectively, thus confirming the conclusion that saturation was attained in both series. It will be seen that the variable errors give rise to an average deviation of the separate values from the mean conductivity of the salts of about 0.3 X lO"** reciprocal ohms in all three cases. Far more serious, however, are probably the constant errors, which may arise from the failure to attain complete saturation in the "first values" at any rate, and from the contamination of the solution by the progressive decomposition of the salt. These two errors would affect the results in opposite directions. It is, however, probable from what has been said above that the former source of error is insignificant in comparison with the latter. The best method of treatment seems to be, therefore, to apply a correction for the progressive increase in conductance. Assuming that complete saturation was attained in the case of the first values l^ — w, then the increase (Lj — Lw) — (Li — L.„) is wholly due to progressive contamination, and assuming further that it is proportional to the time, we may obtain a better value by subtracting from Li — W the product of this increase by the ratio of the first period of heating* to the second period. In making this calculation, the mean increase per hour was first computed for each salt from all the experiments for which both "first" and "second values" are given in the table.f Correcting in this way the mean of the first ♦Decreased by ten minutes to allow for the time required to raise the bomb from ^''tThis^ was found to be 0.96 for AgCl, 0.84 for AgSCN, and 0.80 for AgBr. per hour. Compare the values given in foot notes 1, 4, and 5 to table 129, 3o8 Conductivity of Aqueous Solutions. — Part X. values in the table we get the following final results, which have also been corrected to 100° with the help of the van't Hofi equation* and the temperature-coefficient of the conductivity of silver nitrate.f Table 130. — Specific conductance of the satu- rated solutions at ioo°. Salt. Specific conductance X 10». AgCl 56.7 13.9 7.4 AgSCN AgBr It seems very improbable that the errors from any source in these final values exceed half the differences between them and the "first values" directly observed. Under this assumption the possible percentage errors are 1.2 for the chloride, 2.9 for the sulphocyanate, and 4.0 for the bromide. no. THE SOLUBILITY VALLES. To derive the solubility (in equivalents per cubic centimeter) from these conductance values, it is necessary to divide them by the equivalent conductance (A^) of the salt at zero concentration and at 100°. The Aq value for silver nitrate at 100° has already been determined to be 367 by Mr. A. C. Melcher; and since those for the three silver salts in question are known to differ from this by only 3 to 4:^4 per cent at 20°|, and the differences between the mobilities of various ions become less with rising temperature, no error of importance will be made by assuming the Ao-values for the three salts to differ from that for the nitrate at 100° by half the percentage amount by which they differ from it at 20°. The Ao-values at 100° calculated under this assumption are 373 for AgCl, 359 for AgSCN, and 375 for AgBr. The solubility values at 100° computed in this way and expressed in milligrams and in equivalents per liter are given in the following table, For comparison the values previously found at 20° and the ratio of the ^ dS/S Z" '~~~ ^-p ^2RT^' w^'^'"^ ^ '^ the solubility and L the molal heat of solution, whose values are cited in the next section. --;=- is thus found to be at 100° 2.8 per cent for AgCl, 4.0 per cent for AgSCN, and 3.6 per cent for AgBr. tThis temperature-coefficient has been found by Mr. A. C. Melcher to be 0.88 per cent at 100°. Combining this with the temperature-coefScient of the solubility, we get for the temperature-coefficient of the conductance of the saturated solutions 3.7 per cent for AgCl, 4.9 per cent for AgSCN, and 4.5 per cent for AgBr. tSee Bottger, Zstchr. phys. Chem., 46, 596 (1903). The values at 20° are 1217 for AgNOs, 125.5 for AgCl, 127.1 for AgBr, and 116.1 for AgSCN. Those for the three latter salts differ from that for the nitrate by + 3.1 + 4.4, and — 4.6 per cent respectively. ' Section no.— The Solubility Values. ^op solubility at 100° (S,,^) to that at 20° (5,„) are given in parallel columns The percentage errors in these 100° solubility values are of the same mag- n tude as those m the 100° values of the specific conductances (See end of section 109.) ^ Table 131.- -Solubility of silver chloride, snlpho- cyaiiate, and bromide. Milligrams Equivalents ' Equivalents oalt. per liter per liter at ' per liter at I '^'"'° at 100°. I 100°<10«. I 20°X10». I SmiS-m. logs T^ = -H Kohlrauscli Z. phys. Chem., 50, 35C (1905). I have corrected his values tn 9(1° by means of his own temperature-coefficients. correctea liis values to iO iLottger, Z. phys. Chem., 46, 602 (1903). The increase of solubility with the temperature is much less in the case of silver chloride than of the other two salts. It is of some interest to apply to these results the integrated form of the van't HofT equation : £2 __L r, — T^ S^ ~ 2R TJ',^ Since there are undoubtedly considerable errors in the very small solu- bility at 20° of the sulphocyanate and bromide, the best method is to use the formula in calculating this solubility {S^) from that at 100° {S,) with the help of the heat of solution (L). The values of the heat of pre- cipitation as determined by Thomsen- at about 18° by metathesis, which are equal to the heat L absorbed by the dissolving of one equivalent, are 15,850 cal. for AgCl. 22,400 cal. for AgSCN, and 20,100 cal. for AgBr. The so calculated values of the solubility X lO"* at 20° are : 8.1 for AgCl, 0.62 for AgSCN, and 0.47 for AgBr. The agreement with the observed values is as good as could be expected in the case of the last two salts, but is not very satisfactory in the case of silver chloride. It is possible, of course, that the assumption involved in the integration that the heat of solution remains constant through so wide a temperature-interval is attended with considerable error. Attention may also be called to the relatively large solubility of silver chloride at 100°, which amounts to 21.8 milligrams per liter. This shows clearly that the statement made in several text-books on quantitative analysisf that this substance may be washed with hot water is a mis- leading one. *See Ostwald's Lehrbuch, II, 1, 335, 439. fClassen, Ausgewahlte Methoden der analytischen Chemie, 1,3; Presenilis, Anleit- img zur quant, chem. Analyse (6te Aiifl.) 1, 298-299; Jannasch, Praktischer Leit- faden der Gewichtsanalyse, 1, 10. Part XI. The Equivalent Conductance of the Hydrogen-Ion Derived from Transference Experi- ments WITH Nitric Acid. By Arthur A. Noyes and Yogoro Kato. Part XL THE EQUIVALENT CONDUCTANCE OF HYDROGEN-ION DERIVED FROM TRANSFERENCE EXPERIMENTS WITH NITRIC ACID. 111. OUTLINE OF THE INVESTIGATION. In an article published four years ago by A. A. Noyes and G. V. Sammet* there were described some transference determinations made with -jV, bV and sV normal hydrochloric acid at 10°, 20°, and 30°, which when combined with the equivalent conductance of chloride-ion (using the value of Kohlrausch) yielded for hydrogen-ion a much higher equiva- lent conductance than that which had been derived from the conductivity of acids at high dilutions. Thus the value for hydrogen-ion at 18° derived from the transference experiments was 330, while that of Kohlrausch derived from conductivity was 318. This serious divergence appeared greater than the possible errors in the transference determinationsf ; and it seemed as if it must be due either (1) to an error in the extrapolated values of the equivalent conductance of acids at zero concentration, (2) to the formation of complex-ions or some other abnormality of the hydro- chloric acid, or (3) to a marked difference in the relative velocities of the hydrogen-ion and the anion, at moderate and at very low concentrations. To test the first of these possibilities a study of the effect of the impurities in the water upon the conductance of very dilute hydrochloric and nitric acids was made in this laboratory by H. M. Goodwin and R. Haskell, t the results of which showed that, after eliminating the effect of impurities as far as possible, a value for the equivalent conductance of hydrogen-ion at extreme dilution (315 at 18°) even lower than that previously derived by Kohlrausch (018) was obtained. In view of these results it did not seen possible that the divergence could be due to the first-mentioned cause. The present investigation was therefore undertaken, in order to test the second explanation, or that being excluded, to establish the correctness of the third one. For it was thought that independent transference experiments with another acid, if they yielded results concordant with those with hydro- chloric acid, would serve both to exclude any specific error that might arise from complex-ion formation or other individual peculiarity of that *J. Am. Chem. Soc, 24, 944-968; 25, 165-168 (1902-3); Ztschr. phys. Chem., 43, ^^lyi,;"^„„„g'r;jnental results of Noyes and Sammet have recently been fully con- firmed by those of Jahn, Joachim and Wolff (Z. phys. Chem., 58, 641 (1907). JPhys Rev 19, 369-396 (1904) ; Proc. Am. Acad., 40, 399-415 (1904). Reviewed in'Z. phys. Chem., 52, 630 (1905). ^^^ ^14. Conductivity of Aqueous Solutions. — Part XI. acid and to confirm the experimental accuracy of the transference data, and that they would thus establish the fact that a marked change in the relative migration-velocity of the ions of acids takes place on passing to very low concentrations. Nitric acid was selected as the second acid, since it is of quite a diflferent chemical character.* Another purpose of this investigation, bearing directly on the third suggestion mentioned above, was to extend the transference measurements with both acids to a dilution of about 0.002 normal. 112. PREPARATION AND STANDARDIZATION OF THE SOLUTIONS. The chemically pure nitric acid of trade was freed from lower oxides of nitrogen by diluting it with two-thirds its volume of conductivity water and drawing a current of purified air through it. It was care- fully tested (using 5-10 c.cm.) for chloride with silver nitrate, for sul- phate by evaporation with barium chloride, for ammonia with Nessler reagent, and for nitrite by diluting and adding starch and potassium iodide. These impurities could not be detected at all, or were present only in entirely insignificant quantity. Diluter solutions (from 0.06 to 0.0006 normal) were made up with water having in all cases a specific con- ductance lying between 0.9 and 1.2 X 10"® reciprocal ohms at 18°, and were titrated with the help of phenolphthalein against a 0.1 normal solu- tion of barium hydroxide, which had been repeatedly crystallized and was proved to be substantially free from chloride, and also from silica, calcium, strontium, or other metals than barium (by precipitating with sulphuric acid and evaporating the filtrate to dryness in a platinum dish, when a scarcely weighable residue was obtained). The strength of the barium hydroxide solution was determined gravimetrically both by pre- cipitating with sulphuric acid after neutralizing with hydrochloric acid and by evaporating to dryness with pure nitric acid and weighing the resi- due of Ba(N03)2 after heating to 160° - 180°. The two methods gave for the content of the solution in milli-equivalents per kilogram iiiq ggf and l^^'Z^f respectively; the value adopted was 110.64. Afterwards two other solutions of barium hydroxide were prepared and titrated against nitric acid solutions which had been standardized against the first barium hydroxide solution. Solution No. 2 contained 0.11904,f and solu- tion No. 3 contained 0.05859| equivalents per kilogram of solution. The five solutions of nitric acid varying from about 0.06 to 0.006 *A single transference experiment has already been made with this acid at 25° at 0.05 normal concentration by Bein (Z. phys. Chem., 27, 44. 1898). tl86.83 gm. of this solution (the total amount used in three concordant experi- ments) neutralized 388.08 gms. of HNO3 Sol. No. 2. $118.19 gm. of this solution (used in five concordant experiments) neutralized 1048.90 gms. of HNOa Sol. No. 5. Section 112. — Preparation of the Solutions. 315 normal, which were standardized for use in this work against these barium hydroxide solutions showed as a mean in each case of 5 or 6 determina- tions a content in milli-equivalents per kilogram of solution as follows : No. 1 No. 2 No. 3 No. 4 No. 5 Content 59.22 57.42 18.436 6.809 6.605 A. D. 0.01 0.00 0.003 0.001 0.001 The very dilute solutions (approximately 0.002 normal) of nitric and hydrochloric acids employed could hardly be titrated with sufficient accu- racy by this method. The concentrations both of the original solutions and of the portions after electrolysis were therefore determined by measuring their conductance by the usual Kohlrausch method in a cylindrical cell with horizontal electrodes, and dividing the corresponding specific con- ductance by the equivalent conductance of the acid in question at this concentration and temperature. Goodwin and Haskell* have recently determined the equivalent conductances at 18° in 0.002 normal solution to be 371.3 for HNO3, and 375.0 for HCl at 18°, from which follows with the help of Deguisne's temperature-coefficients:! 383.4 for HNO3 and 387.4 for HCl at 20°, which are the values we have used in calculating the original concentrations. The actual conductance measured in the conductivity vessel, the specific conductance, and the concentration in milli-equivalents per liter calculated therefrom were as follows: Nitric acid solution Hydrochloric acid solution No. 6. No. 7. 1 No. 1. No. 2. Actual conductance X 10" Specific conductance X 10° Milli-equivalents per liter 2,142 847.3 2.210 ,094 828.4 2.161 1,975 781.3 2.017 *2,136 845.0 2.181 *The value found before the first experiment with this solution was 21355, that between the fourth and fifth experiments was 21372, showing that there was no considerable change from contamination during the course of the work. The conductance-capacity of the conductivity vessel was 0.3956 for all the measurements presented in this article.^ Hydrochloric acid solution No. 1 was made by diluting quantitatively by weight (with water of con- ductivity 0.9 X 10"") a 0.13737 normal solution which had been stand- ardized by weighing the silver chloride obtainable from it; the concen- tration calculated from the dilution was 2.015 in close agreement with that derived from the conductivity (2'.017). Solution No. 2 was pre- pared from the same stock solution, which was itself made by treating pure salt with pure sulphuric acid, redistilHng the strong acid obtained, and diluting it; it was proved to be free from non-volatile matter and from sulphuric acid. *Phys Rev., 19, 381, 383 (1904). These values like all of ours given below were not corrected for the conductance of the water. tKohlrausch and Holborn, Leitvermogen der Elektrolyte (1898), p. 199. tA 009954 normal potassium chloride solution measured m it showed as an aver- age of several determinations a conductance of 3111.3 X 10-« reciprocal ohms. 3i6 Coiiductkity of Aqueous Solutions. — Part XI. 113. DESCRIPTION OF THE EXPERIMENTS. The apparatus, consisting of two connecting U-tubes, was almost iden- tical with that used by Noyes and Sammet, and the procedure followed in the transference experiments was nearly the same. Referring the reader therefore to their article* for the main features, we will here describe only the modifications adopted in our work. In order to avoid all danger from leakage, the two U-tubes were joined by drawing over their ends two thicknesses of light black tubing, tightly wiring this on, and entirely covering- the joint with melted paraffin. The anode consisted of a circular platinum plate, convex downward, soldered with gold to a platinum wire. The cathode was a straight platinum wire which dipped into the solution always less than 1 cm., so that b}- having the current dense the reduction of the nitric acid was as far as possible prevented. Since the solution weakened around the cathode and concentrated around the anode, to avoid stirring, the cathode arm was filled with liquid nearly to the top, while the anode arm was filled onh' a few centimeters above the bend and the elec- trode was placed just below the surface. To keep the solution at this level the anode arm was fitted with a rubber stopper carrying a delivery tube which dipped into an outside vessel of water whose level could be varied. Given in outline, the method of carrj-ing out the transference experi- ments consisted in passing a suitable current for three hours and fifteen minutes (except when otherwise noted in the table) through the stand- ard nitric or hydrochloric acid solutions in the apparatus just described, detemiining the quantit}- of electricity by means of two silver coulometers placed in series with it, one on either side, dividing the electrolyzed solu- tion into a cathode, an anode, and three middle portions, and titrating each of these with barium hydroxide (or, in the case of the 0.003 normal solutions, measuring the conductance at 20°) to determine the concen- tration-changes. From the analyses of the cathode and anode portions two separate values of the transference-number were obtained, and by the analysis of the middle portions it was made certain that no error arose through convection. The method of procedure at the end of the electrolysis was to transfer by means of a pipette the three middle portions to tared wide-mouth Erlenmeyer flasks with rubber stoppers. Then the two U-tubes were separated from each other, stoppered, well cleaned and dried outside, and weighed. The solutions in them were then, after thorough mixing, poured as completely as practicable into tared flasks, again weighed, and finallv titrated, allowance being made in the calculation for the small portion that remained in the tubes, which were themselves cleaned, dried, and *J. Am. Chem. Soc, 24, 946 (1902) ; Ztschr. phys. Chein., 43, 51 (1903). Section 113.— Description of the Experiments. ^ly weighed empty. In the titration of all the portions, the quantity of barium hydroxide solution added was determined by again weighing the flasks containing them after exact neutralization with the base. In those cases where the titration was replaced by a measurement of the con- ductance, each portion was poured in succession into a cylindrical con- ductance-cell with horizontal platinized electrodes 2.5 cm. apart and measured as accurately as possible, using three resistances in the rheostat. The principal error to be feared was that which might arise in the analysis of the cathode portion through the reduction of some of the nitric acid by the electrolytic hydrogen. To reduce this to a minimum the cathode was, as already stated, made as small as possible. Since careful analytical tests* showed (except in one experiment. No. 2, where the cathode was known to be badly arranged) no nitrite or ammonia in the cathode portion or nitrous vapors in the hydrogen evolved, there is good reason to believe that the error from this source was not serious in most of the other experiments. The effect of this error, it may be noted, would be to cause an apparent increase in the transference number of the anion when calculated from the cathode change. In case of the 0.002 normal hydrochloric acid solution investigated there was the possibility of an opposite error from the liberation of chlorine at the anode, which would have resulted in too small a transference number as calculated from the anode change. With so very dilute a solution and the low current-density used, there was probably little danger of this; but to detect any such effect, two different forms of anodes were employed — a short platinum wire in experiments 1-5 (see table 122) and a platinum disc in experiments 6, 7, 9, and 10. As the mean results (167.8 and 168.8) with the two electrodes with such different surface- areas agreed almost completely, it seems hardly possible that there was a serious error from this source, especially in the latter experiments.f In order to determine what error, if any, might arise in the very dilute solutions from contamination during the experiment, a "blank" experi- ment was made, in which the solution was treated in absolutely the same way as usual except that no current was passed. The stock solution of ♦These tests were made by adding to 10 c.cm. of the cathode portion after its neutralization a few drops of pure sulphuric acid and some starch solution contain- ing potassium iodide ; by adding to 10 c.cm. of the neutralized portion a few drops of Nessler reagent ; and by conducting the hydrogen evolved at the cathode through a tube containing filter paper moistened with a solution of starch and potassium iodide. All these tests gave a slight positive indication in the one experiment mentioned above, but in no other case, though they were tried in most of them. fThe cathodes were also varied in form (since the cathode results were consid- erably higher than the anode results), though there seemed to be no possibility of an abnormal reaction. A platinum disc was used in experiments 1-5, a spiral wire in 6-8, and a short straight wire in 9-10. The form of electrode had no influence, however. In experiment 8 a silver anode was used. 3i8 Conductivity of Aqueous Solutions. — Part XI. hydrochloric acid used (No. 2) had a conductance of 31372 and the por- tions withdrawn at the end of the experiment had conductances as follows : K* 21336 ; Mk, 21355 ; M, 21349 ; Ma, 21349 ; A, 21356. There was on an average a decrease of 0.1 per cent. Although this would cause a not inconsiderable divergence of the cathode and anode trans- ference numbers, yet it would not affect their mean appreciably ; therefore no correction was made for it (except that the use of 21360 as the initial value eliminated it in great measure in the experiments with this solution.) 114. THE EXPERIMENTAL DATA. The data of the experiments and the calculated transference values for the 0.06 — 0.007 normal nitric acid solutions are given in tables 132 - 134. The ftrst column contains the number of the experiment; the second, the number of the acid solution used; the third, letters representing the dif- ferent portions submitted to analysis, K signifying the cathode solution, Mk the adjoining middle portion, M the next portion, Ma the portion adjoining the anode, and A the anode portion itself; the fourth, the weight in grams of the separate portions; the iifth contains the number of grams of barium hydroxide solution used in neutralizing the portions after the electrolysis; the sixth, the initial content, expressed in equiva- lents and multiplied by 10°, as calculated from the weight of the portion and the standardization value ;f the seventh, the final content calculated from the barium hydroxide used; the eighth, the change in content of the separate portions; the ninth, the total change in content, which includes the changes in the portions adjoining the cathode and anode; J the tenth, the milligrams of silver precipitated in the coulometers; and the eleventh, the calculated transference numbers for the anion multipUed by 1000.§ *For the meaning of these letters see the next paragraph. tSee section 113, BaO^Hi Solution No. 1 was used in experiments 1 to 6; Solu- tion No. 3 in experiments 7 to 26 ; and Solution No. 3 in experiments 27 to 32. JExcept where the change in the adjoining portion was opposite in sign to that in the electrode portion. §The way in which these were calculated may be illustrated with the help of the data obtained in the first experiment. The cathode portion submitted to analysis weighed 214.08 grams and was found to require 107.72 gm. of the Ba02H2 solution containing 0.11064 milli-equivalents per gram, so that the final content of the portion was the product of these last two quantities or 11.918 milli-equivalents. To deter- mine the original content the weight of the portion is multiplied by the original con- centration of the solution (0.05922 milli-equiv. per gm.), which gives 12.678 milli- equivalents. The decrease in content in the cathode portion is, therefore, 0.760 milli-equivalents. Adding to this the decrease in the adjoining middle portion (0.005) and dividing by the number of milli-equivalents of silver (523.0/107.93) precipitated in the coulometer, the transference number is found to be 0.1579. The srnall correction for the change in weight of the electrode portions by the electrol- ysis and transference is applied later. Section 114. — The Experimental Data. ^iq Table 132. — Transference data for 0.058 or xV normal nitric acid at 20**. Exper- Solu- iment I tion No. No. 2 i 1 10 11 Por- tion. I Weight of portion. BaOgHg solution used. Initial content. Final content. K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A M Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A 214.08 74.55 212.29 186.16 303 . 87 224.01 186.40 185.03 108.02 298.46 245.61 126.48 163.15 137.35 268.43 304.16 109.63 182.99 155.70 273.97 281.68 134.58 134.20 139.90 221.38 304.32 127.83 136.01 132.70 244.75 267.30 128.27 140.92 131.81 236.68 256.11 148.68 141.13 132.89 274.66 295.01 105.16 148.18 147.77 281.13 258.40 135.90 143.28 139.93 253.26 34^.53 148.88 162.04 139.38 256.25 107.72 39.86 113.50 99.67 169.51 107.59 99.65 99.01 57.86 171.71 116.57 67.56 87.31 73.59 158.32 147.75 58.62 97.86 83.48 161.19 137.57 72.08 71.83 75.01 131.64 149.65 68.43 72.74 71.50 143.75 122.93 66.50 73.07 68.51 138.33 120.13 77.01 73.15 69.05 155.27 141.78 54.54 76.88 76.75 157.05 124.30 70.51 74.35 72.63 141.29 167.97 77.20 84.05 72.33 143.14 6 12,678 4,415 12,575 11,025 17,995 13,266 11,039 10,957 6,397 17,675 14,545 7,490 9,662 8,134 15,897 18,012 6,492 10,837 9,221 16,224 16,681 7,970 7,947 8,285 13,110 ".8,022 7,570 8,055 7,859 14,494 15,349 7,365 8,091 7,568 13,590 14,705 8,537 8,103 7,630 15,770 16,939 6,038 8,008 8,485 16,144 14,837 7,803 8,227 8,034 14,542 19,725 8,548 9,304 8,003 14,713 11,918 4,410 12,558 11,028 18,755 11,904 11,026 10,955 6,402 19,002 12,898 7,451 9,660 8,142 17,517 16,348 6,501 10,828 9,231 17,834 15,221 7,975 7,947 8,299 14,565 16,558 7,572 8,048 7,911 15,906 13,601 7,358 8,085 7,580 15,305 13,292 8,521 8,094 7,640 17,180 15,687 6,035 8,506 8,493 17,376 13,753 7,802 8,237 8,036 15,633 18,584 8,543 9,300 8,003 15,838 change 8 Total change Ag in coulo- meters. Trans- ference number X103. 10 11 — 760 5 17 3 + 760 — 1,362 13 2 + 5 + 1,337 1,647 39 2 + + 1,630 1,664 + 765 + 763 ■1,375 +1,332 —1,6 9 9 + 10 + 1,610 — 1,460 + 5 ± + H + 1,455 — 1,464 + 2 7 + 52 + 1,412 — 1,748 — 7 — 6 + 12 + 1,715 — 1,413 16 +1,628 —1,664 523.2; 157.9 523.9 919.5 919.7 1,139.5 1,129.3 1,118.6 +1,620 1,460 1,118.8 1,019.9 +1,469 1,464 +1,464 —1,755 +1,727 —1,429 +1,239 —1,085 157.4 161.4 156.3 161.1 155.6 160.6 1,020.1 1,013.8 156.3 154.5 155.4 156.0 1,012.9 1,201.3 156.0 157.7 1,201.3 988.3 155.0 157.2 + 10 + 1,410+1,430 989.4 — 1,252—1,255 861.8 — 3 — 3 + 7 + 1,332 — 1,084 — 1 i + 2, + 1,0911+1,093 757. 6i 155.7 — 1,141—1,1471 783.31 158.1 861.4 758.2 155.2 156.0 155.2 154.5 +1,135 783.0 155.0 320 Conductivity of Aqueous Solutions. — Part XL Table 132. — Transference data for 0.058 or xV normal nitric acid at 20° — Continued. Exper- iment No. sV™- Wei£htof portion. Iff' 1 Initial Final used """=-«■ , """="'• 1 Ctiange in content. Total cliange in content. Agin coulo- meters. Trans- ference number X103. 1 2 3 4 5 6 7 8 9 10 11 12 2 K Mk M Ma A 275.18 154.33 150.66 132.84 304.76 133.84 80.06 78.12 68.94 167.07 15,801 8,861 8,650 7.627 17,499 14,808 8,858 8,644 7,628 18,485 — 993 — 3 — 6 + 1 + 986 — 996 687.1 156.5 + 987 686.8 155.1 Table 133. — Transference data for 0.0184 or -jV normal nitric acid at 20°. Exper- iment No. 1 Solu- tion No. Por- tion. Weight of portion. solution used. Initial content. Final content. Change in content. Total change in content. Ag in coulo- meters. Trans- ference number X103. 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 3 3 3 3 3 3 3 3 K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Mk A K Mk M Ma A 288.64 142.34 180.71 150.21 321.64 305.45 151.88 129! 16 308.11 334.04 157.46 164.29 133.13 363.95 353.27 161.93 175.48 136.96 299.07 342.27 154.70 171.63 145.82 347.01 280.38 145.40 159.65 135.00 307.95 340.61 127.96 159.91 152.38 355.91 287.80 102.36 111.64 131.39 423.23 40.98 22.01 27.93 23.24 53.39 42.31 23.51 '2o!6i 52.70 46.44 24.34 25.42 20.62 61.59 49.64 25.06 27.13 21.23 51.23 46.04 23.89 26.57 22.60 60.64 36.50 22.50 24.70 20.97 54.44 45.45 19.77 24.74 23.65 62.33 39.08 15.79 17.26 20.30 70.95 5,319 2,623 3,329 2,767 5,927 5,628 2,799 2,380 5,677 6,155 2,901 3,027 2,453 6,706 6,509 2,984 3,233 2,524 5,511 6,307 2,851 3,162 2,687 6,394 5,166 2,679 2,941 2,487 5,674 6,276 2,358 2,947 2,808 6,558 5,303 1,886 2,057 2,421 7,799 4,879 2,620 3,325 2,767 6,370 5,037 2,799 2,382 6,273 5,529 2,897 3,026 2,455 7,332 5,909 2,983 3,230 2,527 6,099 5,481 2,844 3,163 2,690 7,219 4,345 2,678 2,940 2,496 6,480 5,410 2,354 2,945 2,815 7,419 4,653 1,880 2,055 2,417 8,446 -^40 — 3 — 4 +443 —591 —443 300.7 159.0 +443 -591 300.8 402.0 159.0 158.7 + 2 +596 —626 — 4 — 1 + 2 +626 —600 — 1 + 3 +588 —826 — 7 + 1 + 3 +825 —821 — 1 — 1 + 9 +806 —866 — 4 — 2 + 7 +861 —650 — 6 — 2 — 4 +647 +598 —630 401.8 420.8 160.6 161.6 +628 —601 421.0 400.5 161.0 162.0 +591 —833 400.5 564.6 159.2 159.2 +828 —822 564.7 552.8 158.3 160.5 +815 —870 553.0 588.7 159.1 159.5 20 +868 —656 588.8 441.8 159.1 160.3 +647 441.7 158.1 Section ii^. Table lM.~Transference data —The Experimental Data. 321 1 1 .. Por- tion. Weight portion. i solution used. acia at ao" Ejipei imen No. - Solu- tion No. Initial Final content. content. 6 1 -r Change in content Total change in content. Ag in coulo- meters. Trans- ference number X103. 1 2 3 4 s 7.03 8.84 \ 7.65 ! 29.12 1 14.24 7.57 9.14 7.20 28.75 17.51 7.00 8.09 6.54 27.60 15.20 7.03 9.36 6.38 35.71 16.63 7.60 8.00 7.33 24.03 14.68 7.73 7.67 6.43 26.49 35.02 14.90 18.77 14.99 56.11 31.75 35.19 16.68 n . 37 54.39 36.61 14.34 16.63 14.64 56.33 39.75 13.64 18.07 13.49 53.52 21 22 4 4 K Mk: M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk 129! 36 159.75 132.01 372.55 370.41 135.75 162.43 124.36 379.59 383.23 123.40 142.82 113.52 408.87 339.32 123.67 162.28 111.23 376.62 353.55 133.83 140.73 127.78 359.34 348.65 139.89 139.53 115.36 393.06 391.96 133.43 167.47 132.85 419.49 369.56 136.30 148.75 116.62 394.42 407.05 138.28 148.07 129.11 416.34 407.80 112.65 160.23 119.82 413.34 ' 881 1,087 ! 899 2,537 i 3,533 934 ' 1,106 847 2,584 2,609 840 973 771 3,770 2,311 842 1,105 757 2,564 2,401 911 '836 1,053 911 3,467 1,696 901 1,088 857 3,432 2,085 833 963 778 3,285 1,810 836 1,102 759 3,061 1,978 905 — 45 — 35 + 12 +930 —837 — 23 — 18 + 10 9 J 10 636.4 11 i +942 —850 636.5 578.4 1 159.8 158.6 23 4 1 "1 +838 —524 — 7 +848 1 578.5 \ —531 1 352.9 I 158.3 160.3 — 9 + 7 + 515 —501 — 6 — 3 + 2 +497 -^23 — 6 — 6 + 3 +413 —556 — 3 — 9 + 4 +557 —538 — 8 — 6 + 1 +517 —583 — 10 — 5 1 ■ ■ '! 24 35 4 4 +523 —507 352.7 337.3 159.5 163.2 +499 —429 337.4 281.7 159.6 164.3 ' 958 1 953 870 1 873 2,447 : 2,860 2,303 ' 1,747 934 ' 931 923 913 763 766 26 27 1 +416 —559 283.0 377.5 159.3 159.7 M Ma A 5 1 K i Mk M 3,596 3,589 881 1,106 877 3,771 3,444 900 983 3,153 2,051 873 1,100 878 3,288 1,861 890 978 +561 —546 378.0 353.71 I 160.3 1C6.7 ! M. 1 1 28 29 5 1 K 1 Mk I M j Ma ' A 5 K Mk M i Ma ! A .5 j K ' Mk ' M 5r« +518 —593 353.5' 158.1 397.3' 161.1 770 1 777 J + 7 3,605 ' 3,187 1 +583 3,688 : 2,143 —543 847 ■ 840 ' — 7 978 974 1 — 4 853 858 : + 5 2,750 3,294 -f 544 3,693 3,339 j —364 744 j 740 1 - 4 1,058 ' 1,059 + 1 791 791 -1- + 589 1 397.5) 160.0 —.550 ; 371.2 159.9 ' 1 1 1 *30 + 549 j 371.2' 159.6 —368 236.2 168.2 ' j \. 1 3.724 3.078 - 4-.-?.-4 1 4-354 23R.3 161. S *In this Experiment (No. 30) the period during which the solution was electrolyzed was greater than the usual time (3^ hours'), namely, 6 hours. 322 Conductivity of Aqueous Solutions. — Part XI. Table 134. — Transference data for 0.0067 or y^ normal nitric acid at 20° — Continued. Exper- iment No. j^^ 1 tion. 1 solQtion. BaO,H, solation used. Initial Final content, j content. 1 ""•"•■ ' consent. Agin coulo- meters. Trans- ference number X103. 1 2 3 4 5 6 7 8 9 10 11 *31 *32 5 5 K Mk M Ma A K Mk M Ma A 286.25 143.83 148.08 107.04 382.47 409.57 119.64 164.62 131.90 410.17 36.52 16.11 16.59 12.07 49.94 34.24 13.41 18.49 14.96 58.11 2,551 950 978 707 2,526 3,705 790 1,087 871 2,140 944 972 707 2,926 2,006 786 1,083 877 —411 — 6 — 6 +400 —699 — 4 — 4 + 6 +695 -^17 275.6 163.3 +400 —703 275.8 472.0 156.6 160.7 2,709 3,404 +701 472.1 160.3 *In these experiments (Nos. 31 and 32) the solution was electrolyzed 454 hours and 6 hours, respectively. Table 135. — Transference data for 0.0022 normal nitric acid at 20°. Exper- Solu- Weight of portion. Actual Change in Change Total Ag Trans- iment No. tion No. Portion. conduct- anceX10«. conduct- ance X10». in content. change in content. in cou- lometers. number X103. 1 2 3 4 5 6 7 8 9 10 *33 6 K 349.79 1,498 —644 —2,336 —3,345 154.5 163.8 Mk 97.13 2,133 — 9 — 9 M 151.75 2,139 — 3 — 5 Ma 118.86 2,156 + 14 + 17 A 389.53 2,707 +565 +2,282 -i-3,299 154.5 160.6 34 7 K 349.70 1,813 —381 —1,019 —1,031 66.8 165.1 Mk 119.33 2,092 — 2 — 3 M 2,086 — 8 Ma 123.57 2,095 + 1 + 1 A 359.49 2,358 +264 + 984 4- 985 66.7 159.3 35 7 K 359.94 1,562 —532 —1,986 —1,988 131.3 Mk 106.04 2,092 — 3 — 3 M 134.48 2,089 — 5 — 7 Ma 113.76 2,104 + 10 + 13 A 393.43 2,571 +477 +1,946 4-1,958 131.2 161.0 36 7 K 350.57 1,528 —566 —3,058 —3,073 135.5 165.1 Mk 104.87 2,080 — 14 — 15 M 132.59 2,090 — 4 — 5 Ma 115.59 2,105 + 11 + 13 A 386.20 3,603 +509 +3,039 +3,052 135.5 163.4 37 7 K 134.6 Mk 125.23 2,086 — 8 — 10 M 134.42 2,095 + 1 + 1 Ma 139.43 2,104 + 10 + 14 A 376.86 2,606 +513 +2,001 4-3,015 134.6 161.6 *In this experiment (No. 33) the electrolysis was continued for 4Vs hours instead of for 3ji hours as usual. Tables 135 and 136 present the results obtained with the more dilute solutions where the concentration was determined by conductance meas- urements. The first four columns are the same as in the preceding tables. Section 114. — The Experimental Data. 323 Table 136. — Transference data for 0.0031 normal hydrochloric acid at 20° Exper- Solu- ! imcnt tion 1 Portion. No. No. Tir ■ L. t Actual P"'"""- lanceXlO". Change in conduct- anceXlOa. Cliange Total change in cou- lometers. Trans- ference number X 103. *7 *8 10 K Mk M Ma A K Mk M Ma A K Mk M Ma K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma A K Mk M Ma K Mk M Ma A K Mk M Ma A 384.26 125.64 135.42 126.10 389.93 313.49 132.60 131.29 112.29 385.67 372.66 121.36 135.37 130.33 385.12 115.65 143.10 126.67 430.37 388.28 122.78 138.55 122.73 424.00 420.70 121.58 148.97 102.76 458.17 443.00 122.55 143 . 52 127.24 476.09 436.04 107.32 142.92 118.21 458.82 107.75 160.12 104.29 478.33 438.20 114.76 143.57 104.46 471.81 1,250 1,959 1,971 2,000 2,658 1,360 1,969 1,973 1,989 2,455 1,466 1,970 1,970 1,985 1,295 1,935 1,959 1,995 3,577 1,497 1,966 1,970 1,975 2,383 1,546 2,116 2,127 2,163 2,664 1,761 2,133 2,136 2,141 2,473 1,863 2,126 2,129 3,078 1,819 3,135 2,133 2,142 2,430 1,835 2,131 2,132 2,136 2,411 —725 — 16 — 4 + 25 +683 —615 — 6 — 2 + 14 +480 —509 — 5 — 5 + 10 —680 — 40 — 16 + 20 +602 —478 — 9 — 5 + +408 —590 — 20 — 9 + 27 +528 —375 — 3 + + 5 +337 —374 — 10 — 7 — 58 —317 — 1 — 3 + 6 +394 —301 — 5 — 4 + +275 8 —3,863 — 21 — 5 + 32 +3,736 —1,980 — 8 — 3 + 16 +1,902 —1,949 — 6 — 7 + 13 —2,690 48 — 23 + 26 +2,661 —1,906 — 11 — 7 + +1,777 —3,549 — 25 — 14 + 38 +3,485 —1,706 — 4 + + 7 +1,648 —1,227 — 11 — 10 — 70 —1,494 — 1 — 5 + 6 +1,444 —1,355 + +1,333 -2,883 +2,768 —1,988 +1,918 —1,955 -2,738 +2,687 —1,917 +1,777 —2,574 +2,513 —1,710 +1,655 —1,238 -1,495 +1,450 —1,361 +1.333 178.6 178.9 133.9 123.9 120.2 119.8 171.0 170.9 115.0 114.8 161.0 161.1 105.8 105.8 78.0 77.7 93.7 92. ti 85.0 84.9 10 174.3 167.1 173.3 167.2 175.8 173.0 169.7 180.1 167.0 172.5 168.5 174.4 168.8 171.6 174.1 168.8 173.0 169.3 *In experiments 5, 7, and 8 the ^j— ^;^,,^;;i7^;^77^;^^iii^;jJta^only 2H liows- ^2^ Conductivity of Aqueous Solutions. — Part XI. The fifth contains the actual conductance X 10' ; the si.vth, the difference between this value and the initial conductance X 10° as given at the end of section 112 ;* the seventh, the corresponding change in content of the whole portion, expressed in 10"' equivalents, obtained by multiplying this difference by the conductance-capacity of the vessel (0.3956), dividing by the equivalent conductance values 382.1 for HNO3 and 385.8 for HCl,t and multiplying by the volume of the portion (obtained from its weight by multiplying it by 1.0018) ; and the eighth, the total change of content or the sum of the changes in the electrode portion and the adjoin- ing portion. The ninth column contains the milligrams of silver deposited in the coulometers; and the tenth, the transference number for the anion X 10^. 115. SUMMARY OF THE TRANSFERENCE NUMBERS. The following table contains a summary of the transference numbers derived from the preceding experiments together with the means derived therefrom. In finding the separate means of the cathode and anode values a few abnormally high or low values (designated by an asterisk) have been omitted.f To these means in the case of the two most concen- trated solutions a correction has been applied to remove a small error introduced by the method used for the calculation of the separate values,§ and the results are designated "corrected means." These cathode and anode means have then been combined in the case of the three stronger nitric acid solutions under the assumption that each has a weight inversely proportional to the square of its average deviation (A. D.). Since the cathode values show in all three cases much greater variations, this procedure gives to the anode values a much greater weight, which would be a priori desirable since they are not subject to the possible error arising *These initial values are : 2142 for HNO3 Solution No. 6 ; 2094 for HNO3 Solu- tion No. 7 ; 1975 for HCl Solution No. 1, and 2136 for HCl Solution No. 2. fThese values are those of diJdC at 0.002 normal, where i, represents the speci- fic conductance and C the equivalent concentration. We derived them through a careful consideration of all the results obtained by Goodwin and Haskell with both acids at 18° between the concentrations of 0.001 and 0.005 normal. The values were first derived at 18° and were found to be 370.0 for HNOa and 373.5 for HCl, and these were then increased with the help of Deguisne's coefficients so as to make them correspond to 30°. It is scarcely possible that the errors in these values exceed 0.3 per cent. JThe high cathode values in experiments 2, 3, and 4 were probably due to reduc- tion by the electrolytic hydrogen, which was proved to have taken place in experi- ment 2. The cathode value in experiment 22 was omitted since the middle portion showed a large change in content. §Namely, in calculating the original content the total weight of the electrode por- tion was simply multiplied by the initial content per gram. That weight had, how- ever, been increased, over what it would have been originally, at the anode by the weight of the transferred nitric acid and had been decreased by the electrolysis out Section iij. — Summary of the Transference Numbers. 5^5 from the reduction of the nitric acid around the cathode. It is in fact very probable that both the larger variations and the greater magnitude of the cathode values are due to this cause. In spite of this source of error it is to be noted that the mean cathode value exceeds the mean anode value by only 0.9, 0.6, and 1.1 per cent, respectively, in the case of the three more concentrated solutions. Taking into account the fact that almost all other errors aflfect the two results in opposite directions we believe the final A. D. values give a fair measure of the probable precision of the final results, which is from 0.2 to 0.3 per cent for the 0.06 to 0.007 normal nitric acid solutions. In the case of the 0.002 normal solutions of both acids the divergence of the cathode and anode mean values is much greater, and it seemed best to assign an equal weight to each without reference to the value of its average deviation ; for the divergence probably arises in the main from a slight contamination of these very dilute solutions during the experi- ment, which would affect the cathode and anode values oppositely and about equally. The final A. D. values, which expressed as percentages are 0.7 per cent for the nitric acid and 1.0 per cent for the hydrochloric acid, are again a fair measure of the maximum error of which there is any reasonable probability. of it of the water corresponding to the hydrogen and oxygen evolved : and at the cathode it had been decreased by the weight of the transferred nitric acid. By considering the effect of this on the result, it will readily be seen that when any acid of equivalent weiglit a, transference number n, and original content c in equivalents per gram of solution is electrolyzed as in this case with the production of hydrogen and oxygen, and the calculation is made as above (multiplying the total weight of the portion by c) then the anode transference-number should be increased by the fractional amount (An — 9)c/» and the cathode transference num- ber should be increased by the fractional amount AC. In this case, with the strong- est (0.058) normal solution, the corrections, applied (since A ^63, »; = 0.156, and c^ 0.000058) are -f 0.03 per cent on the anode value and +0.36 per cent on the cathode value. With the 0.0184 normal solutions the corrections are one-third of these percentages. . The corresponding correction was not applied by Noyes and Sammet to their results with hydrochloric acid. It would have the effect of increasing their final value at 0.05 normal (165,69) by just 0.17 per cent (to 165.96), while at the lower con- centrations the correction would be scarcely appreciable. A more simple way of calculating transference numbers from the experimen- tal data is to refer the initial content to the weight of water present instead of to that of the whole solution, and to calculate correspondingly the weight of water in the portion after the electrolysis by subtracting from its total weight the weight of solute found in it; but even then a correction must be applied to the anode portion for the water electrolyzed out of it. The present basis of all such transference determmat.ons is of course the assumption that the water itself does not migrate. 326 Conductivity of Aqueous Solutions. — Part XI. Table 137.- —Summary of the transference values 0.058 Nonnal HNOs at 20°. 0.0184 Normal HNOs at 20°. 0.0067 Normal HNOs at 20°. Experiment No. Cathode. Anode. Experiment No. Cathode. Anode. Experiment No. Cathode. Adode. 1 157.9 *161.4 *161.1 *160.6 154.5 156.0 157.7 156.0 157.2 154.5 158.1 156.5 »157.4 156.3 155.6 156.3 155.4 156.0 155.2 155.0 155.2 155.7 155.0 155.1 13 14 15 16 17 18 19 20 159.0 158.7 161.6 162.0 159.2 160.5 159.5 160.3 159.0 160.6 161.0 159.2 158.3 159.1 159.1 158.1 21 159.8 158.2 159.5 159.6 159.3 160.3 158.1 160.0 159.6 161.8 •156.6 160.3 a 22.. .. »158.6 160.3 162.2 164.3 159.7 •166.7 161.1 159.9 •168.2 163.3 160.7 3 23 4 24.. 5 25 6 26 7 27. . 8 28 9 29 Meani Corrected mean a.d A. D. 160.10 160.29 1.00 0.35 159.30 159.33 0.71 0.25 10 30 11 31 12 32. . Mean Corrected mean a. Id A. D. 156.49 157.05 1.10 0.36 155.53 155.58 0.41 0.12 Mean ( a.d A. D 161.44 1.36 0.48 159.68 0.69 0.21 Final mean Final A. D. 159.64 0.34 Final mean Final A. D. 149.96 0.44 Final mean Final A. D. 155 .73 .27 0. J022 Norm il HNOs at 20°. 0.0021 Normal HCl at 20°. Experiment No. Cathode. Anode. Experiment No. Cathode. Anode. 33 163.8 165.1 163.5 165.1 160.6 159.3 161.0 163.3 161.6 1 174.2 173.3 175.8 173.0 *180.1 172.5 174.4 171.6 174.1 173.0 •167.1 •167.2 •169! 7 •167.0 168.5 168.8 iesis 169.3 34 2 35 3 36 4 37 5 164.4 0.7 0.4 161.2 1.0 0.5 6 a, d 7 A. T>'. '.'.'.'.'.'.'.'.'.'..'. 8 Final mean Final A. D 162.8 1.2 9 10 Mean A. D 173.5 0.3 tl68.8 0.1 Final mean 171.1 1.7 Final A. D.. 1 fThe mean of all the anode values is 168.3 but it seems best to omit the first four, in which experiments an anode of small surface was used, and which are somewhat lower perhaps oy^ing to the evolution of a small quantity of chlorine. 116. SUMMARY AND DISCUSSION. The final results of the transference experiments described in this article, as well as of those carried out by Noyes and Sammet* with 0.05 — 0.006 normal hydrochloric acid at 20°,t are brought together in table 138. In this table are also given the values of the equivalent conductance of *Ztschr. phys. Chem., 43, 63 (1903) ; J. Am. Chem. See, 24, 958; 25, 167 (1902-3). tCorrected for the inaccuracy in their calculation as described in a preceding foot- note. Section ii6. — Summary and Discussion. ^27 hydrogen-ion calculated from each transference number and from the most probable values for nitrate-ion and chloride-ion (64.6 and 68 5 respect- ively) at 20° and extreme dilution.* In the last row of the table 'are given the corresponding values for zero concentration as derived from Goodwin and Haskell s conductivity experiments.f Table n%.~Final values of the transference-numbers and the equivalent conductanee of hydrogen-ton. Equivalen Transference-number Equivalent conductance X 103. of hydrogen-ion from experiments witli HN08. HCI. HNO3. HCl. HNOs. HCl. 0.058 0.051 155.7 166.0 350.3 344.3 0.0184 0.017 159.6 167.5 340.3 340.5 0.0067 0.0056 160.0 167.1 339.1 341.4 0.0023 0.0031 162.8 171.1 333.2 331.8 166.0 174.5 334.6 324.0 It will be seen from table 138 that, except at the highest concentration (0.055 normal), there is substantial agreement between the values of the equivalent conductance of the hydrogen-ion derived from the independent transference experiments with the two different acids, and that the (nearly constant) value for the concentration-interval between 0.018 and 0.006 normal is nearly 5 per cent larger than that derived from conductivity measurements at extreme dilution. The reality of this divergence, first discovered by Noyes and Sammet, confirmed as it is on the conductivity side by the investigation of Goodwin and Haskell and on the transference side by the recent determinations of Jahn, Joachim, and Wolff, and by these new experiments with nitric acid, can, we believe, no longer rea- sonably be doubted. It must therefore be concluded that the transference number of the anion of acids, and therefore the ratio of the velocity of the anions to that of the hydro gen-ion, is several per cent larger at very small concentration (0.001 normal and less) than at moderate concentrations (0.05 to 0.005 normal). Thus a change in the relative velocities takes place even after the concentration of the solute has become so small that as a medium the solution scarcely differs from the pure solvent. The fact *The value here given for the CI is that derived by Noyes and Sammet from Kohlrausch's conductivity data and the existing transference data for potassium chloride. That for the NOb ion we have obtained by subtracting from that for the CI the difference for these two ions at 20° given by Kohlrausch (Sitzungsber. konigl. preuss. Akad. der Wissensch., 1901, 1031). These values have then simply been multiplied by (l — »)/«. „ ^ tt^t^ , , . ^ tThese investigators found for A„ at 18° 377.0 for HNO3 and 380.1 for HCl. The corresponding values at 20° calculated with Deguisne's coefficients are 389.3 and 393 5 respectively. Subtracting from these the values for the NO3 and CI ions (64 6 and 68.5) one obtains the values for the hydrogen ion given in the table. 328 Conductivity of Aqueous Solutions. — Part XI. that higher transference numbers were obtained with the 0.002 normal solutions than with the more concentrated solutions of both acids confirms the conclusion drawn from the comparison with the conductivity data. The values obtained at 0.003 normal show, moreover, that even at this very low concentration the velocities have not yet become identical with those at zero concentration. This change of the transference number may, of course, arise either from an acceleration of the anion or from a retardation of the hydrogen- ion at very high dilution, or from both causes combined. The facts that salts do not as a rule show any change in their transference numbers after a moderate dilution is reached and that their ionization-values cal- culated from freezing-point lowering and other molecular properties agree with those corresponding to the conductance ratio (A/A„)* make it proba- ble, however, that it is the fast-moving hydrogen-ion that is mainly, if not wholly, aflfected.f It is under this (possibly incorrect); assumption, namely, that neutral ions have the same velocity at moderate and at very low concentrations, that the values, given in table 138, of the equivalent conductance of hydrogen-ion at various concentrations were derived. The fact that the values of the equivalent conductance of hydrogen-ion are nearly constant for the interval of concentration 0.006 - 0.018 seems to indicate that these are the normal ones, and that the variations at lower concentrations arise from some secondary eiifect of a general character, determined perhaps by the smallness of the ion-concentration itself. The results obtained at the highest concentration (0.05 to 0.06 normal) differ in the case of the two acids, which makes it seem probable that the variation in the stronger solution is due to some different cause, probably one of a specific chemical nature, from that which gives rise to the change at high dilutions. As to the bearing of these results on the calculation of ionization- values, it may be said that in the case of largely ionized acids at moderate concentrations it seems in the light of now existing knowledge most appro- priate to divide the observed equivalent conductance of the acid by a A,, value obtained by adding to the equivalent conductance of the anion that for the hydrogen-ion obtained by the transference experiments above described at the concentration in question. On the other hand in the case of any acid solution in which the io/t-concentration is less than 0.001 nor- mal the older value (324 at 20° or 315 at 18°) for hydrogen-ion is to be preferred. ♦See A. A. Noyes, Z. phys. Chem., 52, 634. tit is therefore probable that the decrease in the conductance of strong acids always observed at very high dilutions is not wholly due to impurities in the water. Section it6. — Summary and Discussion. j^p It is of interest to compare the ionization of hydrochloric acid com- puted in the manner just stated with that of neutral salts of the same ionic type, like potassium and sodium chlorides. At the concentration 0.05 normal the ionization-value derived from Kohlrausch's value (360) of the equivalent conductance of the acid at 18° is found to be 0.948, provided the equivalent conductance of hydrogen-ion is taken at 31.5 as derived from the conductivity of the acid at small concentrations ; but it becomes 0.900 when the equivalent conductance of hydrogen-ion is taken 6.2 per cent larger than this, in accordance with the transference results. At this same concentration the ionization-values for potassium chloride and sodium chloride, as derived from their equivalent conductances, are 0.891 and 0.878. The approximate agreement of these values with the new one for hydrochloric acid seems to justify the extension to largely ionized acids of the principle that salts of the same ionic type have at the same concentration roughly the same degree of ionization. Part XII. General Summary of the Results. By Arthur A. Noyes. Part XII. GENERAL SUMMARY OF THE RESULTS. It seems desirable at the close of this extended series of papers to sum- marize the more important results which have been attained, both in order to make them more readily available to readers who may not be interested in the details of the experiments, and in order to show more' clearly, by bringing together all the more significant results, the general conclusions which can be drawn from them. In order to carry out these investigations a new form of conductance vessel capable of withstanding high pressures and not liable to con- taminate dilute aqueous solutions even at high temperatures had to be constructed at the start. The vessel or "bomb" which was developed as a result of several years' experimenting and which has been used successfully with only minor modifications for all the measurements above presented will be readily understood in its essential features by reference to figure 1 on page 10, and from the following brief description : It consists of a cylindrical vessel A of about 125 c.cm. capacity provided with a cover B which is held in place by means of a large nut C, all these parts being made of steel. The bomb is lined through- out with sheet platinum. The cover is made tight by a small packing- ring of pure gold wire which fits into a small V-shaped groove. The body of the bomb serves as one electrode. The other electrode is brought in through the bottom of the bomb, being insulated inside by a piece of quartz and outside by mica layers M. The quartz-piece Q is in the form of a cylindrical cup about 2 cm. in external diameter and 3.7 cm. in height, the bottom of it being covered on the inside by the circular platinum-covered top of the electrode, which was usually well coated with platinum black. In the cover is a narrow cylindrical chamber provided with an auxiliary insulated electrode r„, which serves to show the height of the liquid in the chamber and indirectly the volume of the liquid in the bomb. The cover also contains a small platinum tube T^ through which the air may be exhausted from the bomb. In most of the experiments made with the more dilute solutions, the bomb was modified, so as to reduce contamination, by removing the cup and flat electrode within it, and replacing these by a cylindrical platinum- iridium electrode usually about 10 mm. high and 7.2 mm. in diameter, which was supported on a vertical quartz cylinder, through the center of which the electrode rod passed downwards (see fig. 13, page 63). 333 2S4 Conductivity of Aqueous Solutions. — Part XII. For the measurements at 18° and 100° and in some of those at 128° and 156° the bomb was immersed in a liquid xylene or pseudocumene bath, but at the higher temperatures it was heated in the apparatus shown in fig. 2, page 12, in the vapors of boiling liquids (brombenzene at 156°, naphthalene at 218°, isoamylbenzoate at 260°, bromnaphthalene at 3'81°, and benzophenone at 306°). In the later experiments the heater and the electrical connections were so arranged that the bomb could be rotated (see fig. 14, page 64), thus causing thorough stirring of the contents. By means of this apparatus conductance measurements have been made up to 306° at all or nearly all the temperatures just mentioned with sodium chloride, potassium chloride, silver nitrate, potassium sulphate, barium nitrate, hydrochloric acid, nitric acid, sulphuric acid, acetic acid, ammo- nium hydroxide, ammonium chloride, sodium acetate, and ammonium acetate; at the temperatures up to 218° with magnesium sulphate, and sodium hydroxide; and from 18° to 156° at intervals of 25° or 28° with nitric acid, phosphoric acid, sulphuric acid, potassium hydrogen sulphate, and barium hydroxide. With most of these substances the measurements have been made at four or more different concentrations varying between 0.1 and 0.002 normal. The final values of the equivalent conductance of these substances will be found in the tables of the preceding parts on the following pages : Potassium and sodium chlorides 47 Silver nitrate, barium nitrate, potassium sulphate, magnesium sulphate 103 Acetic acid and sodium acetate 137-8, 225 Ammonium hydroxide and ammonium chloride.. 174,225 Hydrochloric acid 137, 262 Sodium hydroxide 174 Nitric acid, phosphoric acid, sulphuric acid, potas- sium hydrogen sulphate, and barium hydroxide 262 These conductivity results have interest from a theoretical standpoint mainly in two respects — first, with reference to the equivalent conduct- ance of the ions or their specific migration-velocities; and second, with reference to the degree of ionization of the various substances. The values at the different temperatures of the equivalent conductance (A(,) extrapolated for zero concentration or complete ionization were obtained with the help of a function of the form -— = - — X'i(CA)"-^, A(, A which corresponds to the equation C(Ao — A) = K(CA)", by plotting 1/A against (CA)""^, varying the value of n till a linear plot was obtained, and then extrapolating for zero concentrations.* All the so-derived values of A,, for the largely ionized electrolytes are summarized in the following table. The substances are arranged primarily according *A discussion of this method of deriving the Ao-value will be found in section 17 (Part II, page 50). Summary. 335 to the ionic type and secondarily in the order in which the A^, values at 1'"^ increase. In adjoining columns are given also the mean temperature- coefficient AAo/A^ for the successive temperature-intervals and the ratio A„(S)/A„(Kci) of the equivalent conductance of the substance in question to that of potassium chloride at the same temperature. Table 139. — Equivalent conductance at zero concentration. Temper- ature. Sodium acetate. Sod ium chlori de. Silver nitrate. '^o ^^0 '^o(S) ^o(KCl) K A/ '^o(S) "^o(KCl) ^0 ^o(S) ^o(KCl) 18 78.1 2.53 0.60 109.0 3.09 0.84 115.8 3.06 0.89 100 285 2.95 0.69 362 3.44 0.87 367 3.62 0.89 156 450 3.40 0.72 555 3.31 0.89 570 3.39 0.91 218 660 0.80 760 3.33 0.92 780 2.94 0.95 281 3.00 970 4.40 0.96 965 4.00 0.96 306 924 0.82 1080 0.96 1065 0.95 18 Potassium chloride. Ammonium chloride. Sodium hydroxide. 130.1 130.7 1.01 216.5 1.67 3.46 3.47 4.60 100 414 3.77 415 3.80 1.00 594 4.30 1.43 156 625 3.23 628 3.43 1.00 835 3.63 1.33 218 825 2.86 841 1.02 1060 1.29 281 1005 4.60 3.81 306 1120 .... 1176 1.05 18 Barium nitrate. Potassium sulj hate. Barium hydroxide. 116.9 0.90 132.8 1.02 222 1.71 3.27 3.93 5.16 100 385 3.84 0.93 455 4.64 1.10 645 3.58 1.56 156 600 3.87 0.96 715 5.64 1.14 847 .... 1.36 218 840 4.44 1.02 1065 6.27 1.29 .... .... .... 281 1120 7.20 1.11 1460 10.6 1.45 .... • ■ . > .... 306 1300 1.16 1725 1.54 18 Phosphoric acid. Nitric acid. Hydrochloric acid. 338 4.78 2.60 377 5.61 2.90 379 5.76 2.91 100 730 3 57 1.76 826 3.95 1.99 850 4.20 2.05 156 930 1.49 1047 2.95 1.67 1085 2.90 1.73 218 1230 1.49 1265 1424 1.81 1.53 1.27 306 .... .... 33^ Conductivity of Aqueous Solutions. — Part XII. The results given under Ao(S)/A„(koi) in table 139 show that the values of the equivalent conductance for complete ionization in the case of all the di-ionic substances investigated become more nearly equal as the temperature rises, the approach toward equality being rapid between 18° and 218°, but comparatively slow at the higher temperatures. This shows, of course, that the specific migration-velocities of the ions are themselves more nearly equal, the higher the temperature. Complete equality has not, however, been reached even at 306°, but the divergence exceeds 6 per cent only in the cases of hydrochloric acid, sodium hydrox- ide, and sodium acetate, which have ions which at 18° move with excep- tionally large or small velocities. The behavior of the tri-ionic salts, potassium sulphate and barium nitrate, is especially noteworthy. Their equivalent conductance increases steadily with rising temperature and attains values which are much greater than those for any di-ionic uni-univalent salt. Thus at 306° the value for potassium sulphate is about 1.5 times as great as that for potas- sium chloride. This behavior, which at first sight appears abnormal, is in reality in conformit}' with the principle that the velocities of ions sub- jected to the same electric force approach equality with rising tempera- ture; for, assuming that the resistance of the medium becomes the same for all ions, the velocity of a bivalent ion, owing to its double electric charge, should become twice as great as that of a univalent ion under the same potential-gradient; and correspondingly, the equivalent con- ductance of a completely ionized unibivalent salt should become 1.5 times that of a completely ionized uni-univalent salt. What is remarkable is, therefore, not the greater values at high temperatures, but the approxi- mate equality at room temperature of the equivalent conductances of bivalent and univalent ions, especially of the elementary ones which might be expected to have not far from the same size. This equality may be due, as has been suggested by Morgan and Kanolt,* to a relatively large hydration of the bivalent ions. With respect to the form of the temperature-conductance curve, it will be seen from an examination of the values of AA(,/Af that the rate of increase of conductance is in case of all the neutral di-ionic salts greater between 100° and 156° than it is between 18° and 100° or between 156° and 218°, t and therefore that the curve is first convex, later concave, and then again convex toward the temperature axis, with two intermediate points of inflexion. In the case of the acids and bases, however, and therefore of the hydro- gen-ion and the hydroxide-ion, the rate of increase of the equivalent *J. Am. Chem. Soc, 28, 572 (1906). fWith respect to this last temperature-interval sodium acetate forms an exception. Summa/ry. 3,7 conductance steadily decreases with rising temperature, so that the curve IS always concave toward the temperature axis. With the tri-ionic salts on the other hand, the rate of increase steadily increases, owing to the great increase in the equivalent conductance of the bivalent ion; the curve is therefore always convex toward the temperature axis. It is of interest to note that the fluidity, or the reciprocal of the viscosity, of water shows nearly the same increase as the conductance of the di-ionic salts, at any rate up to 156°, which is about the limit to which previous determinations of the viscosity have extended. Thus, using for the viscosity {7,) the data of Thorpe and Rodger and of de Haas* and taking the mean values of A„ for the five uni-univalent salts included in this research, the product ijA(, has the values 1.19 at 18°, 1.01 at 100°, and 1.01 at 156°. When it is considered that the conductance values increase five-fold, this variation in the ratio will be seen to be of secondary significance. With respect to the variation of the equivalent conductance (A) with the concentration (C), it has been found that between the concentrations 0.1 and 0.003 or 0.0005 nonnal the results at all temperatures with all the salts, both di-ionic and tri-ionic, and also with hydrochloric acid, nitric acid, and sodium hydroxide, are expressed by the function C(A(, — A) = K(Ca)" provided that to the exponent n a value (varying with the differ- ent substances) between 1.40 and 1.55 is assigned. This is clearly shown by the summar}^ of the n values given in table 140. These were derived Table 140. — Values of exponent n in the function C(Ao — A) =:=X(CA)'>. Substance. 18°. 100°. 156°. 218°. 281°. 306°. KCl 1.42 1.40 1.40 1.48 1.50 1.48 NaCl. . . . 1.43 1.48 1.50 1.50 1.47 1.46 AgNOa . . 1.53 1.52 1.50 1.50 1.52 1.52 NaCjHgOs. 1.45 1.45 1.42 1.36 .... .... HCl. . . . 1.45 1.38 1.40 1.47 HNO, . . . 1.43 1.45 1.45 .... NaOH . . . 1.50 1.50 1.50 1 Ba(0H)2.. 1.55 1.45 1.45 1 K,S04 . . . 1.42 1.42 1.42 1.42 1.42 1.42 BalNOa).. 1.50 1.50 1.50 1.50 1.50 1.50 MgSO.. . . 1.43 .... ... * 1 . • • • .... *Sep Landolt-Bornstein-Meyerhoffer, Physikalisch-chemische Tabellen, pp 76-77. Sdttar^orprtLsir^hl'o^™^ between 0" and 156» jj5 Conductivity of Aqueous Solutions. — Part XII. by a graphical method (see section 17, page 50) which involved no assumption in regard to the value of Ao, this being regarded as a third constant to be determined from the data themselves. In general, the value of H could be found within 0.02 or 0.03 units. It is evident that, if the conductance-ratio A/A„ can be taken as a meas- ure of the ionization (y), the latter changes with the concentration in the case of all these substances in accordance with an entirely similar expo- (CyV- nential law, namely, in accordance with the function ^^=773 — '■ — := const., '-(,■'• — y ; in which n has values varying with different substances only between 1.40 and 1.55. In a previous article* emphasis was laid on the remarkable fact that at ordinary temperature the form of the functional relation between ioni- zation and concentration is the same for salts of different ionic types. These results show that this is also true at high temperatures, and, more- over, that even the very large variation of temperature here involved and the large consequent change in the character of the solvent affect only slightly, if at all, the value of the exponent in this purely empirical rela- tion. Thus an additional confirmation is given to the important conclu- sion that the form of the concentration-function is independent of the number of ions into which the salt dissociates. This seems to show almost conclusively that chemical mass-action has no appreciable influence in determining the equilibrium between the ions and the un-ionized part of largely dissociated substances. How complete this contradiction with the mass-action law is, is seen when it is recalled that for di-ionic and tri-ionic salts this law requires that the concentration of the un-ionized substance be proportional to the square and cube, respectively, of the concentration of the ions, while the experimental data show that it is proportional to the f power of that concentration, whatever may be the type of salt. It has also been shown in the preceding articles (pages 49 and 139) that the functions A,, — A ^ KO' and Ao — A = K{CAy, which contain only two arbitrary constants (A^ and K) satisfactorily express the results with potassium chloride, sodium chloride, hydrochloric acid, and sodium hydroxide at any rate up to 218° between the concentrations of 0.1 and 0.002 or 0.0005 normal. Since, however, the data at still smaller concen- trations, as determined by Kohlrausch and others at 18°, do not conform to the requirements of these functions, they apparently do not give by extrapolation a correct value of A„, and correspondingly the ratio A/Aj, *Noyes, The Physical Properties of Aqueous Salt Solutions in Relation to the Ionic Theory, Congress of Arts and Science, St. Louis Exposition, 4, 317 (1904) ; Technology Quarterly, 17, 300 (1904) ; Science, 20, 582 (1904) ; abstract in Z. phys. Chem., 52, 635. Summary. 339 derived from them is not a true measure of the ionization. It has therefore not seemed worth while to make a study of the appHcability of these func- tions to all the siibstances investigated. The equivalent conductance and ionization of the slighUy ionized sub- stances, acetic acid and ammonium hydroxide, on the other hand, changes with the concentration at all temperatures even up to 306°, in accordance with the mass-action law. It is interesting to note that phosphoric acid, an acid of moderate ionization (60 per cent at 18° and 39 per cent at 156° at 0.01 normal concentration), has intermediate values of ;/ (1.8-1.9), which, however, approach more nearly the theoretical value (2.0) than the empirical one. In order to show the relations between degree of ionization, the charac- ter of the substances, and the temperature, the percentage ionization of all the substances investigated at the different temperatures in 0.08 and 0.01 normal solution is shown in table 141. The substances are arranged in the order in which the ionization at 18° decreases. The values in the case of sulphuric acid show the percentage of the total hydrogen which exists in the form of hydrogen-ion, without reference to whether it arises through the primary dissociation into H+ and HSO4" or the secondary one into H+ and 50^= ; the values are only approximate ones based on an estimate of the relative extent to which these two stages in the dissociation have taken place, as described on page 867. The values for magnesium sulphate are only rough approximations, owing to its being largely hydrolyzed. The ionization at 0.08 normal for all of the salts and for hydrochloric and nitric acids is also shown graphically in figure 30. Fig. 20. — Change of ionization with temperature. too HCI KCI AgNOa 1 ' .,_^ 60 NaCjHjOj • — == -— ■ ^ $~=r- KjSO* 70 =^ ^ HCI 3 60 "c ^ -. ' 50 50 S) MgS04 ^ k- 40 2 "0 c 8a(N03)2 e 30 ^ ^^ 20 20 " ^ 10 10 10 4 6 8 IC l< 11 ■0 If wpe It atur to e 22 J^o Conductivity of Aqueous Solutions. — Part XII. Table 141. — Percentage ionization. Substance. Concen- tration. 18°. 100'=. 156°. 218°. 281°. 306°. 0.01 0.08 0.01 0.08 0.01 0.08 0.01 0.08 0.01 87 84 83 47 59 0.08 72 69 64 31 38 0.01 82 81 80 79 77 76 37 47 0.08 60 33" 64* 63" 57 23 ' 35* 0.14 o.ii HCl HNO3 NaOH KCl NaCl NH4CI .... AgNOa . . . NH^C^HsOi,. NaC^HsO,. . Ba(0H)2 . . K^SO^ BaCNOa)^. . HjSO^ .... MgSO,.... H3PO4 HOjHaO, . . NH,OH . . . 0.01 0.08 0.01 0.08 0.01 0.01 0.08 0.01 0.08 0.01 0.01 0.08 0.01 0.01 0.08 0.01 0.08 0.01 0.08 0.01 0.08 0.01 0.08 0.01 0.08 0.01 0.08 0.01 0.08 0.01 0.08 97.1 96.8 96.2 94.2 93.6 93.7 93.3 91.9 91.2 93 87.2 86.7 83 66.7 60 4.17 4.05 93.2 92.6 87.3 85.7 83.3 81.1 83" 73.2 70.1 66* 45.5 31 1.50 1.45 95.0 95.2 95.7 91.1 92.7 92.2 91.8 88.7 88.8 85 80.3 83.6 56 52.4 42 3.24 3.59 89.7 89.0 82.6 83.2 80.2 77.6 70 64.8 66.9 48" 31.9 19.5 1.17 93.6 93.4 94.3 89.7 92.1 91.2 88.8 87.1 88.0 85. 75 80 49 35 29.4 2.26 2.46 87'.2 85.3 79.7 81.2 75.8 75.6 65" 58 62* 45 " 19" 12.5 0.82 92.2 92 89.8 90.2 90.1 86.3 82.2 63 74 46 13 1.26 1.36 82.5 75 77.3 77.7 70.8 68.5 45 " 53 42* 7' 0.46 0.47 As will be seen from table 141 the ionization steadily decreases with rising temperature in the case of every substance investigated. To this principle stated as an entirely general one the only exceptions seem to be water itself up to about 270° and many slightly ionized acids and bases up to about 40°, as illustrated by the ionization-constants for acetic acid and ammonium hydroxide tabulated below ; but above this temperature, even such acids and bases also decrease steadily in ionization.* The decrease in ionization will, moreover, be seen to be nearly the same for all the largely ionized salts of the same ionic type, so that such salts, ♦Compare also the results of Euler (Z. phys. Chem., 21, 266, 1896) and of Schal- ler (Z. phys. Chem., 25, 517, 1898). Summary. ,.j which have roughly the same ionization at 18°, are also not far from equally lomzed at much higher temperatures. The decrease in percentage ionization per ten degrees (- 10»Ay/At) at the concentration 0.08 normal has for the neutral salts the following average values : Table U2.— Decrease of ionisation with the temperature. Type of Salt. Values of (-lOSAy/AO between | 18° and 100° 100° and 156° 156° and 218° 218° and 281° 281° and 306° Dl-ionic Tri-lonic 0.33 0.34 0.55 0.94 0.68 1.23 1.09 2.30 2.84 3.20 Thus the rate of decrease in ionization is small between 18° and 100° for either type of salt ; but it becomes greater at the higher temperatures, especially in the case of the tri-ionic salts ; and for the highest temperature- interval (281° -306°) it is extremely rapid for both types of salt. The decrease in ionization of hydrochloric acid, nitric acid up to 156°, and sodium hydroxide is about the same as that of the di-ionic salts ; thus the average value of ( — lO^Ay/A^ at 0.08 normal for hydrochloric and nitric acids is 0.38 between 18° and 100°, 0.63 between 100° and 156° ; and for hydrochloric acid 0.76 between 156° and 218°. Between 156° and 306° nitric acid decreases in ionization much more than the other sub- stances of the same type. The physical property of the solvent which is most closely related to its ionizing power is, as has been shown by Thomson and by Nernst, its dielec- tric constant. It is therefore of some interest to compare its variation with the temperature with that of the ionization of salts. Unfortunately, the dielectric constant of water has been determined only between 0° and 76°. Drude* has, however, derived for this interval a quadratic equation, from which a value at 100° may be calculated, probably without great error. The values of the dielectric constant obtained from this equation are 81.3 at 18° and 58.1 at 100°, and the ratio of these is 1.40. The question now arises, what function of the ionization should be com- pared with this ? It seems clear that, from a theoretical standpoint, it is simplest to consider the ratio ^ ^\]~'^'\ of the concentrations of un-ion- ized salt which prevail in solutions that at the two temperatures {t, and t^) have the same concentration of the ions (that is, solutions for which Cy = C yj • for in such solutions the electric force between the ions, and therefore 'their tendency to unite to form un-ionized molecules, in so far as this has an electrical origin, must be inversely proportional to the dielec- *Wied. Ann. Phys., 59, 50 (1896). 34^ Conductivity of Aqueous Solutions. — Part XII. trie constant. The above ratio is evidently equivalent, since C^yz = Cj-yi, to the ratio J^ZT)/^' where, however, y^ and y^ refer to the slightly- different concentrations Cj and C^ (Q being equal to C^yjy^). Now for the four uni-univalent salts given in table 141 the mean values of the percentage ionization at 0.08 normal is 84.4 at 18° and 80.9 at 100°, or by interpolation, 80.6 at 100° at 0.08 X 1.042 normal (that is, at CiYi/yz) ; whence the value of the ratio just referred to is found to be 1.30. The value of the corresponding ratio for the two tri-ionic salts at 0.08 nor- mal is in the same way found to be 1.38.* While the former of these values differs considerably from the ratio (1.40) of the dielectric constants, yet all the values lie in the same neighborhood. Indeed, the agreement is as close as could be expected considering the character of the data involved. Finally, even though it seems theoretically to correspond to a less com- parable condition in the solution, yet, in view of the valence principle dis- cussed just below, it is of interest to note the values of the simpler ratio, X--Q " y of the concentrations of the un-ionized substance at two tem- peratures at the same total concentration, instead of the same ion-concen- tration. At 0.08 the value of this ratio for 100°/18° is 1.22 for the four uni-univalent, and 1.21 for the two uni-bivalent salts, thus considerably less than the ratio of the dielectric-constants. The degree of ionization of the different substances may be next con- sidered in relation to the ionic type to which they belong and to their chem- ical nature. It has already been pointed out that even up to the highest temperatures neutral salts of the same ionic type have roughly the same percentage ionization, the differences not exceeding 8 per cent in any case investigated. The strong acids, hydrochloric acid and (up to 156°) nitric acid, and the strong bases, sodium and barium hydroxides, also conform in a general way to this principle, though their ionization seems to be several per cent greater than that of the corresponding salts ; it is worthy of men- tion, however, that this greater value may be due to an increase in the equivalent conductance of the hydrogen-ion or hydroxide-ion with the concentration of the solute, as is indicated to be the case by the transfer- ence results with these acids presented in Part XI and again referred to below. It is also remarkable that the rough proportionality which had previ- ously been shown to exist at ordinary temperaturesf between the un-ion- *The mean values of the percentage ionization for these two salts at 0.08 normal are 71.7 at 18° and 65.8 at 100°, or by interpolation 64.8 at 100° at 0.08 X 1-09 normal. tFor a discussion of this principle, see the author's article on The Physical Prop- erties of Aqueous Salt Solutions. . . ., loc. cit. Summary. ^^ ^ ized fraction of a salt at any concentration and the product of the valences of Its ions has now been proved by the measurements of Noyes and Mel- cher to persist up to the highest temperatures, where the degree of ioniza- tion has become much less. This is shown by the following summary, which is a reproduction of table 29 on page 110. Under A are given the mean values of the percentage of un-ionized salt, 100(1 — y), for the neutral salts of each type at the concentration 0.04 molal and for the uni- univalent salts at 0.08 molal ; and under B are given the ratios of these values to the product of the valences (vivj of the ions. Mola 18° 100° 1 156° 218° 281° 306° liter. A 12 15 28 55 B 12 15 14 14 A 15 18 34 68 B 15 18 17 17 A 17 21 40 81 B A 20 25 51 93 B 20 25 25 23 A 25 31 65 B 25 31 32 A 31 39 74 B 31 39 37 1X1 1X1 1X2 2X2 0.04 0.08 0.04 0.04 17 21 20 20 It will be seen that the principle continues to hold, especially when the comparison is made at the same equivalent concentration, even when the ionization has become very small ; thus it is only 26 per cent for the uni- bivalent salts at 306° and only 7 per cent for the bibivalent salt (magne- sium sulphate) at 218°. The ionization tendencies of phosphoric acid, acetic acid, and ammonium hydroxide, and the effect of temperature on them are best shown by the summary of their ionization-constants which is given in table 143.* The values for phosphoric acid were determined by Noyes and Eastman (see page 269), those for acetic acid by Noyes and Cooper (page 142) and by Sosman (page 228) ; and those for ammonium hydroxide were determined by Noyes and Kato (page 178), by Sosman (page 228), and by Kanolt (page 290). The concentration involved in the constant is expressed in equivalents per liter, and the constants themselves have been multiplied by 10". It is evident from these results that the ionization-constant for ammo- nium hydroxide increases considerably in passing from 0° to 18°, then remains nearly constant up to 50°, and finally decreases with increasing rapidity as higher temperatures are reached, attaining at 306 a value which is only about one-two-hundredth of that at 18 ; and that at all temperatures the values for acetic a dd^ar^not ^ery different from those ■^ 7~L Z V o^Jrl thf valrips varv considerably with the concentration *In the case of pho!Ph«"<^aadAe value™ co^ ^^^ concentration-function was in correspondence with *^,^^^* *\V"^„„^red by the mass-action law. The values iTe'X\l.\lo's! 'XAtLl^^r^^^^^^^ f^ormula-weights (H3Pa) per liter. 344 Conductivity of Aqueous Solutions. — Part XII. Table 143. — lonization-constants of phosphoric acid, acetic acid, and ammonium hydroxide. Temperature. Phosphoric acid. Acetic acid. Ammonium hydroxide. 13.9 10400 1812 17.2 25 9400 ■ ■ * > 18.0 50 7000 18.1 75 4800 • • . > 16.4 100 3400 11.1 13.5 125 > > > > . . . ■ 10.4 128 2230 .... .... 156 1420 5.42 6.28 218 .... 1.72 1.80 306 0.139 0.093 for ammonium hydroxide. Phosphoric acid is seen to have a much larger ionization, which, however, decreases steadily and very rapidly with rising temperature. The interpretation of the results obtained with sulphuric acid is com- plicated by the fact that the ionization doubtless takes place in two stages; but a method has been described on pages 371-3 by which it is possible to determine the hydrogen-ion concentration within fairly nar- row limits from the conductance alone, without knowledge of the extent to which the separate stages occur. The method is of general applica- tion to dibasic acids ; and, if the ionization-constant for the first hydrogen be known, as is true with many of the organic acids, the method could be used for computing that of the second hydrogen from the conductance at high dilutions where the secondary ionization is appreciable. The ratio of the hydrogen-ion to the total hydrogen in the case of sulphuric acid is thus found to vary in 0.08 normal solution from about 66 per cent at 18° to 48 at 100° and 35 at 306°. Similar calculations of the hydrogen-ion concentrations have been made in the case of potassium hydrogen sulphate. These show that in 0.1 molal solution at 156° the hydrogen-ion concentration is not more than 3 per cent; and this justifies the conclusion that the secondary ionization of sulphuric acid (into hydrogen-ion and sulphate-ion) in its own moderately concentrated solutions is also insignificant at this temperature and higher temperatures. Interpreted with the help of this conclusion the con- ductivity data for the acid show that the primary dissociation (into hydrogen-ion and hydrosulphate-ion) is about the same as that of hydro- chloric acid at temperatures between 100° and 306° ; and it is reasonable to suppose that the same is true at lower temperatures down to 18°. Summary. ^ac With the^help of this principle the ionization of the hydrosulphate-ion at 18°, 100°, and 156° in the solutions both of the acid and acid salt has been computed; the final results will be found in tables 118 and 119 on pages 274 and 376. This ionization is thus found to be large at 18° ; but it decreases very rapidly with the temperature. Thus in a 0.1 molal potassium hydrogen sulphate solution equal quantities of sulphate-ion and hydrosulphate-ion are present at 18° ; while at 100° there is only 15 per cent, and at 156° only 4 per cent, as much sulphate-ion as hydro- sulphate-ion in the solution. Only rough values of the ionization-constant of the hydrosulphate-ion into hydrogen-ion and sulphate-ion can be given, since they vary very much with the concentration; some idea of its magnitude is furnished by the following values which hold at about 0.01 molal (or 0.002' molal at 156°); 18500 X lO"" at 18°, 1220X10-° at 100°, and 115 X lO"" at 156°, whereas the ionization-constant for acetic acid at 18° is 18 X lO"". From the change of the ionization-constant with the temperature, the heat absorbed (Af7) by the reaction HSO^ = H+ + 50,= has been found to be given by the expression: AC/ =14,170 — 65 T, where T represents the absolute temperature. From this it follows that the value at 18° is —4750 calories, and at 100°, —10,070 calories, while from Thomsen's heat-of-neutralization measurements and otu" ionization data at 18° the value — 5020 calories is derived. In addition to the measurements with unhydrolyzed salts just dis- cussed there have been presented in the preceding Parts of this publica- tion measurements of the conductance of certain salts of weak acids or bases both in water alone and in the presence of an excess of the acid or base. Various methods of calculating the hydrolysis from the change in conductance produced by the acid or base have been described (see pages 143, 186, and 230) ; and values of the hydrolysis of the salts in ques- tion have been obtained. From these, by combination with the ionization- constants of the acid and base, the ionization of water has been calculated. The salts so investigated are sodium acetate at 318° by A. A. Noyes and H. C. Cooper; ammonium acetate at 100°, 156°, 218°, and 306° by A. A. Noyes and Yogoro Kato and by R. B. Sosman; and the ammonium salt of diketotetrahydrothiazole, a very slightly ionized organic acid, at 0°, 18°, and 25° by C. W. Kanolt. The final conductance results will be found on pages 186, 188, 233 and 295. Table 144 contains a summary of the computed values of the per- centa<^e hydrolysis of ammonium acetate in 0.01 normal solution, of the ionization-constant of water (defined by the equation i^w^Cn.Con), and of the concentration (Ch or Coh) of the hydrogen-ion or hydroxide- 34^ Conductivity of Aqueous Solutions. — Part XII. ion in pure water in equivalents per liter. (The value for ammonium acetate at 18° is not based on direct measurements, but is calculated from the results of Kanolt with the ammonium salt of diketotetrahydrothiazole.) Table 144. — Hydrolysis of ammonium acetate and ionization of water. Hydrolysis of lonization- Hydrogen-ion Temperature. ammonium constant of concentration in acetate. water. pure water. t 100a K^ X lo" C„ X lo' 0.089 0.30 18 (0.35) 0.46 0.68 25 .... 0.82 0.91 100 4.8 48. 6.9 156 18.6 223. 14.9 218 52.7 461. 21.5 306 91.5 168. 13.0 It will be seen that the hydrogen-ion concentration in pure water increases with extraordinary rapidity between 0° and 100°; namely, by about 3 fold between 0° and 25° and 7>4 fold between 25° and 100°. Between the latter temperature and 218° the ionization increases more slowly, afterwards passes through a maximum (which appears to lie between 250° and 375°), and finally decreases. When it is considered that the ionization of weak acids and bases, as shown by the data for ammonium hydroxide, acetic acid, and phosphoric acid, decreases rapidly with rising temperature, and that this acts in the same direction in increasing the hydrolysis of salts as does an increase in the ionization of water, it will be evident that the tendency of salts to hydrolyze is enor- mously greater at high temperatures, as is well illustrated by the values given for ammonium acetate. The great increase in hydrolysis is also exemplified by the hydrolysis values for sodium acetate and ammonium chloride in 0.01 normal solution that can be calculated from the preceding data; these salts, which at 18° are 0.02 per cent hydrolyzed, are found to be 1.6 per cent at 218° and 3.4 to 4.1 per cent hydrolyzed at 306°. The fact also deserves mention that the values of the concentration of the hydrogen-ion in water at 0°, 18°, and 25° as derived from these hydrolysis experiments are only 16 to 20 per cent lower than those obtained directly by Kohlrausch and Heydweiller* from the conductance of their purest water; thus proving that the ionization-constant of water is at any rate roughly the same when it is pure as when an ionized salt is present in it at a concentration of 0.02 to 0.05 normal. *Z. phys. Chem., 14, 330 (1894). Summary. ^a7 From these ionization-constants (Xw) approximate values of the internal-energy-increase AU attending the reaction H,0 = H+ -f OH" (the so-called heat of ionization) can be computed by the familiar equa- tion* derived from the Second Law of Energ-etics: " ^ ~ clT ~ RT^ This is best done by integrating it under the assumption that AC/ is a linear function of the temperature as expressed by the equation At/ = Af/o + aRT. The integral then has the form : 1 ^2 , T^ AC/„ T^ — T, log^^-alog^ = -^» ^^ From the values of the ionization-constant K at 0°, 25°, and 100°, the values of the constants At/o and a have been found to be 28460 and — 24.923, respectively. Therefore, the general equation for the energy- increase attending the ionization becomes : AC/ = 28460 — 49.5 7, and that for the ionization-constant becomes : logio(10"if ) = 84.450 — —^ — 24.923 log^o T. The values of the energy-increase in calories and of the ionization-constant of water as calculated by these expressions are given in table 145. *This equation ceases to be even approximately exact at high temperatures where the vapor-pressure of water becomes very large. The exact expression, which may be derived through the consideration of an appropriate cyclical process, is as follows : where A{/ is the energy-increase and AF is the volume-increase that attends the ionization of one mol of water under the pressure p — P, which is substantially identi- cal with the vapor-pressure p, since the osmotic pressure P is in this case negligible in comparison. Approximate values of Af/ up to 140° have been computed by Tammann (Z. phys. Chem., 16, 144. 1894) which show it to be equal to about —26 ccm at 140° ; and since it is shown to be increasing at a rate roughly proportional to the compressibility of water, it probably has a value m the neighborhood of — 40 c cm at 218°. Assuming this to be the case, the last term m the above equation can, with the help of the existing vapor-pressure data, be shown to have a value of about — 170 calories at 218°, while the value of At/ as computed by the linear equation is 4155 at 218°. Thus at temperatures above 200° this last term begins to form a sub- stantial part of the whole. 34S Conductivity of Aqueous Solutions. — Part XII. Table 145. — Internal-energy-increase attending the ionization of water and its ioniza- tion-constant calculated by an empirical equation. Temperature. Energy-increase lonizatioD-constant AU x^ X 10". 14950 0.088 18 14055 0.46 25 13710 0.81 50 12470 4.5 75 11230 16.9 100 9995 48. 128 8610 114. 156 7325 217. 318 (4155) (512) These values of the ionization-constant at 0°, 25°, and 100° necessarily agree with the directly determined ones given in table 144. It is of inter- est to note, however, that this is also true of the calculated value at 156°, which shows that up to this temperature the assumed equations hold true, and that therefore the values interpolated for the intermediate tempera- tures between 0° and 156° are doubtless substantially correct. Even at 218° the difference between the observed and calculated values (461 and 512), though doubtless real, is not very large; it lies in such a direction as to indicate that the energy-change Af7 is decreasing at a more rapid rate at temperatures above 156° than at the temperatures below it. This is also shown by the fact that the ionization-constant at 306° is much less than at 218°, while according to the linear equation the value of At/ should become zero, and therefore that of the ionization-constant K should become a maximum, very near the former temperature, namely, at 302°. The real maximum- value of the constant seems to lie between 250° and 275°. Above this temperature All assumes a negative value; and therefore the neutralization of completely ionized acids and bases would be attended by an absorption of heat. It may also be mentioned that at the lower temperatures, the calculated values agree well with the heats of neutralization directly measured by W6rmann,f who found for hydrochloric and nitric acids when neutralized with potassium and sodium hydroxides as mean values 14,710 calories at 0° and 13,410 calories at 25°. It seems worth while to call attention to a possible theoretical explana- tion of the fact that water, unlike all other substances thus far investi- gated, continues to increase in ionization up to so high a temperature as 250° to 275°. This phenomenon may well arise from the facts that water fDrude's Ann. Phys., 18, 793 (1905). Summary. ,jq at low temperatures is a highly associated liquid containing only a small proportion of H,0 molecules, and that this proportion increases rapidly with rising temperature. Therefore, even though the fraction of H,0 niolecules dissociated into H+ and OH" ions may decrease steadily, yet the actual concentration of these ions continues to increase until a large proportion of the complex water molecules have been depolymerized. This explanation was suggested by Dr. H. T. Kalmus of this laboratory. Among the other results of these investigations, it deserves to be mentioned that, incidentally to the conductivity determinations, the specific volume of several solutions at 218°, 281°, and 306° was measured. That of the 0.002 normal solutions which can be regarded as identical with that of pure water, was found to be 1.187 at 218°, l.SSr at 281°, and 1.437 at 306°. By interpolating graphically from these results the value 1.305 is obtained for 270°. Ramsay and Young* found 1.188 at 218° and 1.300 at 270°, the highest temperature to which their measurements extended. In addition to the conductivity researches at high temperatures, an investigation made by A. A. Noyes and Y. Kato of the ion-transference attending the electrolysis of solutions of hydrochloric and nitric acids at 20° has been described in this publication (in Part XI). The investiga- tion was along the same lines as the one previously described by Noyes and Sammet.f Its main object was to determine what the value of the equivalent conductance of hydrogen-ion is and whether it varies to an important extent with the concentration. The results will be found summarized in the table on page 337. It will be seen that the transference number of the anion in both nitric acid and hydrochloric acid decreases greatly as the concentration increases, and by a corresponding amount for the two acids up to 0.02 normal. This fact strongly indicates that hydrogen-ion, unlike the ions of neutral salts, increases in equivalent conductance or specific migration-velocity with increasing concentration, the magnitude of the increase being nearly five per cent between zero concentration and 0.02 normal. In deriving from conductivity data ionization values for largely ionized acids, it seems, therefore, most appropriate to divide the equivalent conductance at the concentration in question, not as usual by the equivalent con- ductance extrapolated for zero concentration, but by a value obtained by adding to the equivalent conductance of the anion that of the hydrogen- ion as derived from transference experiments at the same concentration. It is of interest to note that when this is done for hydrochloric and nitric acids at 20° their ionization is found to be nearly the same as that l^'^AJchL.^Soc., 2?' 95"; 2i''l6^(1902-3) ; Z. phys. Chem., 43, 63 (1903). tJ. Am. Chem 350 Conductivity of Aqueous Solutions. — Part XII. of neutral salts of the same ionic type instead of being several per cent larger as is the conductance-ratio A/Ao taken in the usual way. Reference may also be made to the measurements of Dr. Wilhelm Bottger, presented in Part X, of the solubility of some difificultly soluble salts. This constitutes only the beginning of a more extended investiga- tion of the solubility of substances at high temperatures by means of con- ductance measurements. Results have thus far been obtained at 100° with silver chloride, bromide, and sulphocyanate, whose solubilities expressed in equivalents per million liters at 100° and 20° have been found to be as follows: Temper- ature. AgCl AgSCN AgBi 100 20 Ratio 153 10.8 14 39 0.83 46 20 0.5 40 In the preceding pages have been summarized the generalizations to be drawn from the results of these investigations, in regard to the beha- vior of the various types of chemical substances in aqueous solutions through a wide range of temperature. In conclusion, it seems, however, desirable to draw attention again to a theoretical principle of even more general import, which has been already presented in a previous article by the author as a conclusion apparently justified by a study of the then existing data; for this principle has now received a further con- firmation through the demonstration of the fact that certain purely empirical laws relating to the ionization of salts in water still continue to be valid, even when the physical condition of that solvent is greatly altered by a large change in its temperature. This principle is that the ionization of salts, strong acids, and bases is a phenomenon primarily determined not by specific chemical affinities, but by electrical forces aris- ing from the charges on the ions; that it is not afifected (except in a secondary degree) by chemical mass-action, but is regulated by certain general, comparatively simple laws, fairly well established empirically, but of unknown theoretical significance; and that, therefore, it is a phenomenon quite distinct in almost all its aspects from the phenomenon of dissociation ordinarily exhibited by chemical substances, including that of the ionization of weak acids and bases. The most important facts leading to this conclusion are the approxi- mate identity of the ionization-values for salts of the same ionic type; Summary. ,£-j the existence of a simple approximate relation between the value of the un-ion,zed fraction and the product of the valences of the ions; the small ettect of temperature on the ionization of salts and a parallelism between the magnitude of that effect and the efifect upon the dielectric constant of water; the validity of an exponential relation between ionization and concentration, which differs from that required by the mass-action, and which IS approximately the same at all temperatures and for different lomc types of salts; and the fact that the optical properties and other similar properties of dissolved salts (when referred to equal molal quan- tities) is independent of this concentration and therefore of their ioniza- tion, so long as the solution is even moderately dilute. The molecular explanation of these facts and the more general con- clusions drawn from them would seem to be that primarily the ions are united somewhat loosely in virtue of their electrical attraction to form molecules, the constituents of which still retain their electric charges and therefore to a great extent their characteristic power of producing optical effects and such other effects as are not dependent on their existence as separate aggregates. Secondly, the ions may unite in a more intimate way to form ordinary uncharged molecules, whose constituents have com- pletely lost their identity and original characteristics. These two kinds of molecules may be designated electrical molecules and chemical mole- cules, respectively, in correspondence with the character of the forces which are assumed to give rise to them. Now in the case of salts and most of the inorganic acids and bases, the tendency to form chemical molecules is comparatively slight, so that the neutral electrical molecules greatly predominate. On the other hand, in the case of most of the organic acids, the tendency to form chemical molecules is very much greater, so that as a rule these predominate. The facts, moreover, indi- cate that chemical molecules are formed from the ions in accordance with the principle of mass-action,* but that electrical molecules are formed in accordance with an entirely distinct principle, whose theoretical basis is not understood. It is to be expected that with neither class of substances will the pre- dominating type of molecule be alone present ; and that minor deviations from the mass-action law in tlie case of moderately ionized substances, *The best evidence of this is that furnished by the change of the conductivity of sliffhtly ionized electrolytes with the concentration ; but distribution experiments also indicate it Thus it is probable that as a rule the chemical molecules alone distribute into the gaseous phase or into organic solvents and that therefore the concentration of the substance in such phases is a measure of the concentration of those molecules in the aqueous solution; and the few experiments thus far published indicate that the latter is at least approximately proportional to the product of the concentrations of the ions. (Compare the experiments on picric acid by Rothmund and Drucker, Z phys. Chem., 46, 826. 1903.) 35^ Conductivity of Aqueous Solutions. — Pa/rt XII. and from the usual empirical law in the case of largely ionized substances, may well arise from the presence of a small proportion of molecules of the other type. In the former case, we may indeed with some confidence predict quantitatively that that proportion of electrical molecules will always be present which corresponds for the type of substance in question to the concentration of its ions in the solution. ^ A fuller experimental investigation of the properties <.A dissolved salts, especially of those of polyionic types, and of the phenomena of the solu- bility effect and the distribution into a gaseous or another liquid phase of ionizing substances, if combined with a thorough and persistent study of all the available data, gives promise of suggesting a fuller theoretical explanation of this remarkable behavior of largely ionized substances in aqueous solution. Even if such a theoretical interpretation should not be discovered, one may at least hope to determine with greater accuracy and certainty the laws of the equilibrium between the ions and un-ionized mole- cules, and between the two forms of the latter, in case their existence shall be more fully substantiated. It is my conviction that at any rate we have here to deal with a new kind of equilibrium phenomenon, and not simply with some deviation of a secondary nature, arising, for example from a somewhat abnormal osmotic pressure, or a change in the migration veloci- ties of the ions, as has been assumed by most authors. In conclusion I desire to express to the authorities of the Carnegie Institution my great indebtedness for the assistance rendered me in the prosecution of these researches; for without such aid the progress made would have been discouragingly slow. Research Laboratory of Physical Chemistry, Massachusetts Institute of Technology^ Boston, June, 1907.