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DISSERTATION SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY IN CONFORMITY WITH THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY —BY- HARRY PRESTON BASSETT 1904 EASTON, PA. : THE CHEMICAL PUBLISHING COMPANY. I904. TABLE OF CONTENTS. Acknowledgment e tº e º e º ſº tº º ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Historical sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Principal investigators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Hittorf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tº º e e s e s e º 'º e º e e º a dº tº e º e º 'º 6 Kohlrausch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Lodge e e º 'º e g º e º e º º e º e º e º g º e º e º e º e º & © º e º e º ſº º e º 'º e º e º º gº tº e º ºs e g c & & IO Loeb and Nernst. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II Jones and Mather. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 3 Bein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6 A. A. Noyes tº e e º ºs e º dº e º e º ºs e e º e o e º ºs e g º e º e º 'º e º 'º e º ºs e e º ºs e º tº tº e º ſº tº º 2I Jahn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Steele and Denison . . . . . . . . . . . . . . . . . . . . . tº a e º ºs e s e º e e s is a e º e º e e º e 23 Experimental work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Conductivity apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Conductivity measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3O Silver nitrate in water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Silver nitrate in ethyl alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3O Silver nitrate in methyl alcohol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3I Silver nitrate in mixtures of ethyl alcohol and water . . . . . . . . . . . 3I Silver nitrate in mixtures of methyl alcohol and water . . . . . . . . . . 32 Relative velocity of ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Description of apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Preparation of solutions . . . . . . . . . . . . . . . . . . . . - - - - - - - - - - - - - - - - - - 4L Calibration of apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Measurements of relative velocities. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Silver nitrate in water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Silver nitrate in ethyl alcohol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Silver nitrate in methyl alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Silver nitrate in mixtures of methyl alcohol and water. . . . . . . . . . 49 Ionic velocities and conductivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Relative temperature coefficients of ionic velocities. . . . . . . . . . . . . 53 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Biographical sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 | 4:... [335 ACKNOWLEDGMENT. The author desires to express his great indebtedness to President Remsen, to Professor H. N. Morse, and to Profes- sor H. C. Jones for both class and laboratory instruction. Also to Professor J. S. Ames and Professor W. J. A. Bliss for instruction received from them. This investigation was undertaken at the suggestion of Professor H. C. Jones and has been conducted under his guidance. Determination of the Relative Velocities of the Ions of Silver Nitrate in Mix- tures of the Alcohols and Water and on the Conductivity of Such Mixtures. HISTORICAL SKETCH. The early investigators noticed that when an electric cur- rent was passed through an electrolyte, changes in concentra- tion were produced. This phenomenon was made manifest in some brilliant ex- periments by Davy,' but the first attempted explanation was offered by Berzelius and Hisinger.” No further progress was made in solving this problem un- til the time of Faraday,” who noticed that if a current is passed through a solution of copper sulphate, using copper poles, the solution around the cathode becomes lighter blue, while that around the anode becomes darker blue in color. This same phenomenon was observed by Gmelin' two years later. Pouillet” observed a similar phenomenon in a gold solution. Ten years later Smee” still advocated the theory put for- ward by Faraday, and published many experiments to prove this theory. He came to the conclusion that when a solution of a metallic salt was subjected to the influence of a current, water was decomposed and the oxygen and hydrogen passed in different directions, and the hydrogen at the instant of de- composition on the negative pole acted upon the copper sul- phate and other metallic salts in the same manner as iron or zinc would in the same solutions. 1 Gilbert Ann. Bd., 28, 26; Phil. Trans., 1807, p. 28. 2 Ann. d. Chem., I, I74. * * Pogg. Ann., 32, 436 (1834). * 16td., 44, 5 (1838). * Compt. rend., 20, 1544 (1845). * Phil. Mag., 17, 196 (1840). * 6 Daniell and Miller,' working jointly, put forward the con- ception of the interchange of ions. From the results of their investigation they came to the conclusion that the usual con- ception was wrong. They devised an apparatus which was divided into three cells by two porous walls. In this they electrolyzed copper and zinc sulphates. They proved in this investigation that the two ions of each of these two salts evi- dently traveled with different velocities, but they could not interpret their results. They also worked on other metallic salts, but the conclusion that they drew from the results found in the copper and zinc solutions did not hold in the other C2S6S. The subject was left here until Hittorf undertook his elaborate series of experiments and showed that these changes in concentration were caused by a difference in the velocities of the anion and cation (in copper sulphate the anion so, traveling faster than the cation Cu). *. Hittorf, in his investigation, went back to the explanation put forward by Grotthuss. He showed that by analysis of . the solution around the electrodes, the ratio between the ve- locities of the two ions could be calculated. In his work he devised several forms of apparatus depend- ing upon the nature of the salt under investigation. In prin- ciple, however, they were very similar, consisting of a verti- cal tube divided into cells by porous diaphragms, the cathode being inserted in the upper cell and the anode in the lower cell. The form of apparatus used by him has some very objec- tionable features. The membranes are liable to be acted upon by the electrolyte during the electrolysis, and produce some very serious errors. Hittorf also determined the ratio between the velocities of the ions of a large number of salts and studied the effect of changing the conditions of the experiment. He first studied the effect of changing the strength of the current. By using currents of several different strengths he was able to show * Phil. Trans., I., 1844; Pogg. Ann., 64, 18 (1845). * Pogg. Ann., 89, 177 (1853); 98, I (1856); 103, I (1858); iod, 337, 513 (1859). 7 that the relative velocities of the ions was independent of the strength of the current. - The next question to settle was the effect of concentration of the solution on the relative migration velocities. To set- tle this question he investigated solutions of copper sulphate ranging from normal to twentieth-normal. He found from these determinations that the migration ve- 1ocity of the & ion was, with respect to the SO, ion, in- creased as the dilution increased until a certain dilution was reached, beyond which it became constant. He also proved in this connection that in some cases the velocity of the cation decreased with increase in dilution, of which a notable exam- ple is silver nitrate. The third condition which Hittorf thought might affect the velocity of the ions was the effect of temperature. From his work on such salts as copper sulphate between 4°C. and 20° C., he concluded that the temperature coefficient was zero. After the work of Hittorf very little was done in this field until the work of F. Kohlrausch’, in which he showed that a very important relation exists between the velocities of the ions and the conductivity of solutions. Kohlrausch came to the three following conclusions : I. If dilute solutions of various salts be prepared, having their strengths proportional to the chemical equivalents of the salts, then the specific conductivities of these solutions are all of the same order of magnitude. 2. In dilute solutions, under a given electromotive force, each of the ions moves through the liquid with a fixed velocity, dependent on its own chemical nature, and inde- pendent of that of the other ion. This he termed the law of independent migration. 3. The influence of change in temperature upon conduc- tivity tends, as dilution increases, to a limiting value, the temperature coefficient being the same within narrow limits. In Kohlrausch's investigation he determined the specific conductivities of solutions of varying strength, from satura- 1 Wied. Ann., 26, I and I45 (1879). 2 /šid., 26, 194 (1885). 8 tion to dilution of a few per cent, and from observations thus obtained deduced by extrapolation the conductivity in more dilute solutions. - In his determination of the conductivity of salt solutions he measured the constant (u + v), the sum of the velocities of the anion and cation which approaches a constant value in very dilute solutions, so that he was able to assign to certain ions values for c and a, which are known as specific ionic velocities. Kohlrausch calculated the values for the specific velocities of different ions, from measurements of the conductivities of salt solutions, and their migration constants, on the supposi- tion that all the molecules of the salt present in solution are actively concerned in carrying the current. He supposed that the ratio of the numbers of the active and the inactive mole- cules represents in reality the average ratio of time during which each molecule is active to the time during which it is inactive. According to this, every molecule is in turn active, but at any instant only a certain portion of the molecules are active. This is, of course, equivalent to supposing a certain fixed fraction of the whole number of molecules to be active as far as exerting osmotic pressure, but when the velocity of the ions is concerned it is quite different. Kohlrausch saw that in any given solution of a salt, the average velocity is dependent on the driving force or fall of potential on the specific velocities and the coefficient of ioni- zation or (C + A) = 7 x (c-H a), where C + A are the aver- age velocities and c-H a the specific velocities. He found by comparing the conductivity of solutions of definite dilution, that two electrolytes having a common anion and different cations, have the same difference in conductivity as two elec- trolytes having a common anion and the same cation as the first two electrolytes. He also pointed out that the same re- lation holds for a common cation. In both cases the differ- ences are practically the same within the limits of experimen- tal error. Then, from the above relation the conductivity of a solution at infinite dilution is the sum of two constants, one depending on the anion and the other on the cation. 9 Since the conductivity of a solution at infinite dilution deals with comparable numbers of ions, this value must depend upon the velocity with which they move; thus this constant is then proportional to the velocity of the cation and anion. If we represent by c the velocity of the cation, and by a the velocity of the anion /4, - c + a. If expressed in words, the velocity with which any ion travels is a constant for a given solvent and a given potential gradient, and is independent of the nature of the other ion or ions with which it is present in the solution. This law, as is readily seen, only holds for very dilute solu- tions, as it is only in very dilute solutions that the value of ſu, can be obtained directly by experiment. Ostwald', however, has shown that the law of Kohlrausch is of more general application and can be used with concen- trated as well as with dilute solutions. If the solutions are concentrated they will not necessarily be completely dissociated, and, therefore, the amount of disso- ciation must be taken into account. The law of Kohlrausch then becomes ſu, F a (c -- a), a representing the amount of dissociation. In these investigations by Kohlraush and Ostwald they have demonstrated that the molecular conductivity of an electro- lyte increases with the dilution, and reaches at a definite limit a maximum value. This value, as shown above, is the sum of the two independent constants, which are in fact the veloci- ties of the ions at infinite dilution in terms of the conductivity units. It is, then, obvious that the law of Kohlrausch can be used to determine the velocity of ions. This value, Jug, can be determined directly by the conduc- tivity method for measuring the molecular conductivity, and we can determine the ratio between these two velocities by Hittorf's method for determining the relative migration num- bers. From the two equations 1 “Lehrbuch der allgemeinen Chemie,” Vol. II., p. 672. : ". º : . * * : i * * : : IO ſu. = C + A (I) C # = x. (2) where A and C represent the velocities of the ions at infinite dilution and cla is the ratio found by Hittorf's method. By this method the velocity of the ions must be the same, whether determined for one substance or for any other substance in which it may occur. This point was tested by Kohlrausch for several ions, and their velocities were calculated for sev- eral salts and found to be the same in every case. Up to this time numbers given by Kohlrausch for the abso- 1ute velocity of different ions were deduced on theoretical grounds ; and the only verification to which they have been subjected was by showing that from them the observed con- ductivities and migration coefficients of a number of solutions can be calculated. The first direct measurement of the mean velocity of ions was made by Lodge', who observed the progress of a layer which moved through a gelatin Solution and thus marked the advance of the ion whose velocity he wished to determine. The values obtained experimentally by him agreed well with those calculated by Kohlrausch. The method of Lodge, however, was open to objections: since the influence of the gelatin was quite unknown, the as- sumption was made that all ions, if affected at all, would be influenced to the same extent ; further, since the observed velocity is conditioned by the fall of potential, i. e., it is nec- essary that the fall should be regular and that it should be known before C can be determined. Lodge did not fulfil these conditions in his experiments. He assumed that in the tube, which was 40 cm. long, and with a difference of poten- tial of 40 volts between the ends, the fall in potential was I volt per centimeter. In fact the contents of the tube, origi- nally homogeneous, became heterogeneous by the passage of the current, and thus the fall in potential could not remain regular. That the fall was not very irregular is shown by 1 Brit. Ass'n Report, 1886, p. 393 ; 1887, p. 387. * • * s . * > * = . • * g e : º & e * g © e g & © © & e 2. "s e s : g ſº, • ‘s g II his values for the hydrogen ion, which compare fairly well with those calculated by Kohlrausch. Up to this time no form of apparatus had been devised which did not use either a porous diaphragm or a gelatin So- lution. Loeb and Nernst’ devised a form of apparatus which did away entirely with the porous diaphragm used by Hittorf. Their apparatus was of the form of a Gay-Lussac burette with the electrode around which the solution became more concen- trated placed in the lower portion. In their investigation they worked upon eight silver salts, also determining their conductivity and calculated their ionic velocity according to the principle laid down by Kohlrausch with the view of still further testing the modern view of elec- trolysis. From their results the values were practically constant and gave satisfactory evidence for the truth of the theory, the number varying only within narrow limits. They also calcu- lated the values for the velocities of the other ions, and studied the effect of temperature on the velocity of the ions and found that rise in temperature slightly diminished the relative ve- locity of the swifter ion; all ions thus tended to move with the same velocity. Their method is subject to several sources of error. There is no means of separating the solutions after electrolysis to be removed for analysis, and no means to prevent diffusion. Again, it is better to measure the current by some direct method. The methods of Kistiakowsky” and also of Bein” are quite similar to that of Loeb and Nernst. Both have made slight modifications in the apparatus, but the same objections which apply to the apparatus of Loeb and Nernst hold in these cases. Kistiakowsky used his method to advantage to determine the ions of some complex salts, and in this connection did some very interesting work. Whetham,” avoiding the use of a gelatin solution, also all l Ztschr. phys. Chem., 2, 948 (1888). 2 Ibid., 6, 97 (1890). * Wied. Ann., 46, 29 (1892). 4 Phil. Trans., A. 337 (1893). I 2 porous diaphragms, measured the velocity of the moving boundary between two aqueous solutions. In his method he used two salts that had a common ion. A bounding layer between the salt solutions was observed, and absolute instead of relative measurements made. Any uncertainty as to the regularity of the fall of potential was avoided by the selection of such pairs of solutions which had equal or nearly equal specific conductivities. He employed a vertical tube and observed the margin between a colored and a colorless solution. His results agreed very closely with those calculated from the conductivity measurements for the same concentration. This method, however, as stated above, is very limited in its application on account of the difficulty of finding pairs of solutions that fulfil all the necessary conditions. It is also further limited by the necessity for the employment of a col- ored solution as indicator, since it is impossible to find an in- dicator with a suitably colored anion which will not give a precipitate with such salts as those of the alkaline earth and the heavy metals. The next work on this subject was done by Schrader." He undertook to investigate aqueous solutions containing mix- tures of two electrolytes, such as potassium iodide and chlo- ride, and in this manner determined the ratio between the ionic velocities of chlorine and iodine. He then compared these results with those obtained by Hittorf. He worked upon quite a number of salts, but his principal work was done with solu- tions of copper and cadmium salts. In his investigation he devised a form of apparatus that was different from that used by previous investigators, to overcome some of the defects to which they were subject. His apparatus was essentially a modification of that used by Kistiakowsky, but bent in such a form that he could draw the liquid off from either electrode for analysis. There still remained many serious defects in the forms of apparatus, in spite of the fact that many investigators had worked upon this problem. 1 Ztschr. Elektrochem., 3, 498. I3 All of these methods depend upon essentially the same principle, that is, the passage of a known amount of current through a solution of the electrolyte, and the subsequent separation and analysis of the solution around the electrodes, yet, the results obtained under similar conditions differ con- siderably. In the work of previous investigators they have either separated the solutions around the electrodes by por- ous diaphragms, or have relied upon the difference in specific gravity resulting from the electrolysis to secure a separation, and to secure this result have placed the anode and cathode at different levels in their apparatus. Some of the most serious objections have been overcome in a form of apparatus devised in this University by Jones and Mather." The conditions which they wished to fulfil in the construction of this apparatus were as follows: I. That it should be symmetrical in form in order that the current could be passed in either direction. 2. That it should be large enough to contain a sufficient quantity of liquid to allow a large change in concentration. 3. That it should be provided with a means of separating the two solutions around the electrodes after the electrolysis. 4. That diffusion should be overcome as far as possible. The apparatus which they devised to fulfil these condi- tions may be described as follows: It consists of two limbs united near the upper end by a U-tube, the bottom of which does not quite come to the lower ends of the limbs. At the center of this U-tube is a stop-cock of large bore. The lower ends of the limbs are closed with ground-glass stoppers, through which holes are bored and the electrodes inserted. The upper ends of the limbs above the U-tube are contracted to a comparatively small bore and graduated in millimeters in order to level the solution. This apparatus is then connected to a brass frame which, by means of a tube and clamp screw, can be secured in an upright position to a rod on the table or in the bath. This is then calibrated in order to determine the ratio between the contents of each side. With this apparatus they could completely separate the 1 Amer. Chem. Journ., 26, 473 (1901). I4. solution around one electrode from that around the other and accurately determine the increase in concentration on one side and the decrease in concentration on the other. The current in their investigation was measured by means of a silver voltameter. They had, however, some difficulty in securing an accurate adjustment of level after the electrolysis in the first form of apparatus, and, therefore, modified it somewhat. The form of apparatus employed in these first determina- tions was a modification of that finally adopted, which is de- scribed above. In the form used at this time the limbs were of full size throughout the entire length, with the stoppers at the top. The electrodes were at the end of glass tubes which were inserted through the stoppers and extended to the bot- tom of the limbs, and in order to secure adjustment of the level of the liquid in the two limbs it was necessary, at the close of the experiment, to raise slightly the stopper in order to permit the entrance of the air. This no doubt did not se- cure a very accurate adjustment of level in the two limbs, and this discrepancy was recognized by the investigators, who then devised the final form, as stated above. This investigation, as will be seen from above, dealt chiefly with the improvement of the apparatus, the experiments be- ing limited to solutions of silver nitrate in water and ethyl alcohol, and silver acetate in water. In the investigation of these salts in the different solvents results were obtained which compared well with each other, although some difficulty was encountered in the investigation of silver acetate in aqueous solutions when the solutions were very concentrated, which was probably due to the formation of complex ions. They also tried the effect of allowing the electrolysis to proceed for different intervals of time, and from their results no difference could be detected in the rela- tive velocities of the ions. In their investigation of silver nitrate in ethyl alcohol, they came to practically the same conclusions as Lenz," who WaS the only investigator that had worked upon alcoholic solu- 1 Mem. Petersb. Ak. 30, No. 9, (1882). I5 tions of salts up to this time. His work was done some fifteen years before. From their results they calculated the absolute velocities of the ions according to the law laid down by Kohlrausch, as far as data were available for the conductivity at infinite dilu- tion of the solutions employed. At the end of this investigation the following conclusions were drawn : I. That the wide differences observed between the veloci- ties of cation and anion, at O’C., becomes less as the tempera- ture rises, the velocities tending to become equal, as had been observed by others. 2. That the effect of decrease in concentration is in the same direction as that of increase in temperature. 3. That the velocities are largely dependent upon the nature of the solvent. Since this investigation, quite a number of papers have ap- peared upon this problem. Gordon", since the time of Mather’s work, has investigated the variations of temperature on cadmium salts in aqueous solutions. He states that the electromotive force of the ele- ment Cd CdSO, Aq CuSO, Aq Cu increase with tem- perature, indicating a diminution in the concentrations of the cadmium ions, which may be due to the formation of molecu- 1ar aggregates. This was proved in the case of the halogen cadmium salts. On this assumption, the transference ratio should not be greater at higher than at low temperatures, i.e., the ratios of the weights of cadmium which has actually passed from the anode liquid to the quantity deposited on the cathode, or dissolved from the anode. Hopfgartner” did some work similar to that of Schrader mentioned above, but it does not have any direct bearing upon the subject under investigation in this paper. Kummel”, however, has shown that the limiting values for the migration constants of zinc and cadmium salts can be di- l Ztschr. phys. Chem., 25, II5 (1898). 2 Ibid., 23, 469 (1897). 3 Wied. Ann., 64, 655 (1898). I6 rectly determined with the haloid compounds when the dilu- tion is 1/100 to 1/500 normal, and that these values are also in keeping with the Kohlrausch law. In his investigation it appeared that the sulphates gave complex ions and, therefore, do not give results consistent with the Kohlrausch law for the dilutions stated above. His method, however, is similar to that of Lodge. The most elaborate investigation on this problem since the time of Hittorf was carried out by Bein." He describes in all, five forms of apparatus with various means of separating the cathode solution from the anode solution. In one or two of these forms he makes use of a pinch-cock to separate them. In another form he used the method devised by Loeb and Nernst, while in still another form he separates the liquids by means of a mercury column. It can be said that most of the forms of apparatus devised by him are very complex, proba- bly more complex than is necessary. + The work of previous observers is also discussed at consid- erable length with special reference to the influence of diffu- sion on the values obtained. The method used by the author consists in the analysis of the anodic, mean, and cathodic liquids, various forms of appa- ratus being employed, according to the dilution of the electro- lyte and the temperature required. All these are described and numerous figures are given. For sodium and hydrogen chlorides, the values were found to be almost independent of the concentration but vary with the temperature. The transference numbers for anions are given by the ex- pressions HC1 m, = o. 157 -H O.OOO9t; NaCl n, - o.622 -H o.oOO74f. For potassium chloride the values are : 7tu F O. 503 and 71.6 F O.5I3. They were obtained and appeared to be independent of con- centration, at least between the limit of one-fifth and one- hundredth normal. I Ztschr, phys. Chem., 27, 54 (1898); 28, 439 (1899). 17 For lithium chloride the values n, - o.624 and nº = o.621 were obtained in one-hundredth normal solutions, while n,s = o.672 and nor = o.61o for one-fifth to one-twentieth nor- mal solutions. For ammonium, rubidium, caesium, and thallium chlorides the values O. 507, O.515, O.508, and O.516 were respectively obtained at about 20°. Calcium chloride gave results similar to those obtained for lithium chloride the transference ratio changing but slightly with dilution at high temperatures. For barium chloride no = O.559 and nor = O.515 in solutions containing o.o.4 per cent chlorine. For cadmium chloride n, = O.568 and nor = O.473 in solutions with O.2 per cent chlorine, but at higher concentration the temperature change was much less. Silver acetate gave the values n, F O.413 and nas = O.439, which, however, do not agree with the results of Nernst and Hittorf. Sulphuric acid gave numbers in accord with the expression my - O. I60-H. O.OOI5t, and these also differ from Hittorf's values. For copper sulphate the values vary slightly with concen- tration and temperature, and apparently gave a good maxi- mum of O.632 at 15°. Silver nitrate gave the value n., E. o. 517, changing but slightly with temperature. The remaining determinations were made at temperatures of about 20° to 25° with the fol- lowing results : Salt. %2. Strontium chloride O. 560 Magnesium “ O.615 Manganese “ O.613 Cupric ( & O. 595 Cobalt { { O. 585 Thallium sulphate O.528 Magnesium “ O. 54I Sodium carbonate O.6Oo Potassium ‘’ O.435 Sodium hydroxide O.799 ‘‘ bromide O.625 Potassium iodide O.505 I8 Salt. %2. Nitric acid o. 172 Sodium nitrate O.629 Oxalic acid º O.2I4 Ammonium hydroxide O. 562 Calcium { { o,786 Potassium permanganate O.559 Succinic acid O. 239 Some determinations were also made by him in the case of solutions of concentrations from three to four times normal. The values obtained differ very considerably, however, from those at low concentrations and exhibit a much more marked temperature change. He also reviews the various values for transference ratios of salts obtained by different methods and is led to the general conclusion that the relative velocity of the cation is in all cases less when a dividing membrane is used than when no such division is employed. This difference is most marked for animal membranes, and is small or negligible for porous clay divisions or parchment paper. In order to test the correctness of this conclusion, the transference ratios of hydrogen, sodium, lithium, calcium, and cadmium chlorides were determined with various septa of (I) clay, (2) parchment paper, (3) fish bladder, or (4) gold beaters' skin, and in all cases the velocity of the cation is diminished by use of the last two membranes. The values obtained by Hittorf and others with membranous septa are collected and compared with those obtained by the author. This influence of the membrane does not appear to depend on its general permeability, and the probable cause is briefly discussed. It may be due to a chemical activity of the mem- brane, which would hence possess the character of an acid or to polarization induced by the current in the membrane. In either case the result is that membranes actually behave as partial semipermeable divisions. The next work to be considered on this problem is that of O. Masson', who has devised a new form of apparatus for measuring absolute velocities. He recognized the doubtful validity of Lodge's method and the narrow scope of Whet- 1 Ztschr, phys. Chem., 29, 501 (1899); Phil. Trans, , 192 A, 331. I9 ham’s and thus was led to devise a new method of measuring directly the velocity of ions. Two flasks, each provided with a lateral opening, are connected by a graduated, horizontal tube containing a mixed solution of gelatin and the salt to be investigated. The flasks contain suitable solutions into which the electrodes dip. These anode and cathode solutions must both be distinctly colored, the colored ion being the cation in the anode solution, and the anion in the cathode solution. Further, the colored ions must migrate at a specifically slower rate than the corresponding ions of the salt in the tube. A suitable anode solution is copper sulphate with a copper anode. A suitable cathode solution is sodium chromate with a platinum cathode. When a current passes, the progress of the cation (for ex- + ample K) in the colorless gelatin solution is accompanied by ++ an equal advance of the blue Cu ions; the anions (for exam- ple C1) are similarly followed by the yellow CrO, ions. The contents of the tube thus become blue at one end, colorless in the middle, and yellow at the other end. The relative length of the blue and yellow parts gives the ratio of the velocities + of cation K and anion C1. From this ratio the migration num- bers can be calculated and compared with the values found by Hittorf. The method depends essentially on the supposition that the progress of the colored ions is determined by the velocity of the colorless ions in front. Analysis showed that the bound- ing plane between colored and colorless zones is very sharp. The relative length of the blue and yellow parts remains con- stant throughout one experiment and is the same for different experiments at the same concentration. The ratio of the ionic velocities for the same salt is the same when potassium ferrocyanide or potassium tartrate is substituted for sodium chromate. Theory, too, excludes any mixture of the ions, provided that the colored are specifically slower than the col- orless ions which precede them. \ 2O The migration numbers for the anion obtained from the ratio of the ionic velocities are, in the case of sodium, potas- sium and ammonium salts, smaller than those found by Hit- torf, whose values, however, hold for more dilute solutions than those used by the author. Contrary to Hittorf's observation, the migration number for the CTion seems to decrease slightly with increasing con- centration. The relative velocities of the ions are compared with Kohl- rausch’s numbers, and a fair agreement is found. The abso- lute velocities are smaller than in aqueous solution. Kohlrausch," about this time, published an investigation upon the velocity of ions in dilute aqueous solutions up to one-tenth normal, working in all cases at 18°C. He showed that for solutions of one-twentieth to one-tenth of the normal concentration the conductivities of compounds composed of univalent ions, or of univalent ions in union with bivalent ions, may be calculated from the ionic velocities, which, in this case, depend for each univalent ion on concentration only. This does not hold for compounds composed of bi- valent ions only. For these compounds the velocities vary in each case with increasing concentration, in the same regu- 1ar manner from the velocities in solutions of infinite dilution, so that if I is the velocity in a solution of concentration n, and l, the velocity at infinite dilution l = 1. onº's where Q is the constant for all ions. If the conductivity is given in cm−1 ohm-º, and the concentrations in gram-equivalents per liter, Q has the value 213. This, however, does not hold for the hydroxyl ions of the bases or the hydrogen ions of the acids, as the decrease in velocity with rising concentration is far more marked in these cases. The fall in the velocities of the bivalent ions is also not quite the same when these ions are in union with univalent ions, as when in union with other bivalent ions. All ions in solutions of infinite dilution have velocities en- tirely independent of the other ions with which they are asso- ciated. 1 Ann. phys. Chem., (II.), 66, 785 (1898). 2I Among the later investigations on the subject is that of Steele." The method employed by him is in principle the same as that of Masson in that the velocity of movement of a layer between two solutions is measured, the measured ion being followed in all cases by an indicator ion of specifically slower velocity. Like the method of Masson it is also a method of comparison. In a given experiment the velocities of the boundaries at the anode and cathode end of a homoge- neous solution are compared, both being driven by the same, unknown, potential fall per centimeter. The method differs, however, from Masson’s in two essential respects ; first, the measurements are made in water and not in gelatin, and sec- ond, the employment of a colored ion as indicator is not nec- essary. All that is required is that a solution of the indicator containing about the same number of gram-molecules per liter as the measured salt solution should differ from the latter in density and refractive power. The choice of indicators is thus very largely increased. Still this method fails to deter- mine accurately X U, and X V, since it has not as yet been found possible to measure U directly, although this may be calculated very approximately. The essential feature of this method consists in the impris- onment of the aqueous solution to be measured between two partitions of gelatin containing the indicator ion in solutions, thus preventing displacement of the liquid during the course of the experiment. - The results obtained from his experiments confirm those previously calculated. The only apparatus which differs to any considerable extent from that used by previous experimenters has been devised by A. A. Noyes.” It consists of U-tubes attached by rubber tubing, the electrodes being inserted into the long arm of the tubes, and these filled with a solution to only a few centime- ters above the bend. After electrolysis he divided the solu- tion into three separate portions. With this apparatus Noyes has done some very accurate work. He made use of this ap- 1 J. Chem. Soc., 79, 4I4 (190I). * Ztschr, phys. Chem., 36, 61 (1901). 22 paratus especially in the determination of the relative veloci- ties of the ions of such salts as potassium chloride, sodium chloride, etc. In these experiments he used platinum elec- trodes, and titrated the alkali and acid as they were formed around the electrodes by means of burettes inserted into the stoppers. So far no work has been done in dilute solutions and it was important that this point especially should be investigated. The next work on this problem was done by Jahn' and a num- ber of students working under him in the University of Berlin. They used an apparatus differing from any previously em- ployed but resembling in some points that used by Noyes. Their apparatus consisted of a vessel of the form of an Erlenmeyer flask connected with a U-tube which made con- nection with a larger part of the apparatus, which could be varied in size according to the dilution of the solution to be used. The anode, which was inserted into the part of the ap- paratus which could be changed, consisted of the metal, silver, copper, cadmium, etc., according to the salt under in- vestigation or dissolved in the acid formed, while the cathode consisted of mercury which made connection with the circuit by means of a copper wire protected by a glass or rubber tube, the mercury being covered by a copper sulphate solution. By means of this apparatus they determined the transference numbers of the following acids and salts : hydrochloric and nitric acids, sodium, lithium, barium, and cadmium chlo- rides, potassium, sodium, and cadmium bromides, silver ni- trate, cadmium iodide, cadmium and copper sulphates. In the determination with hydrochloric acid an amalgama- ted zinc rod was used as the anode, while in the case of nitric acid the anode consisted of a silver rod which had previously been amalgamated. - In the determination of the migration velocities with the alkali and alkaline earth salts, the amalgamated zinc rod was used. In every case they made an analysis, both of the anode solution and the neutral layer. In their investigations on silver nitrate, the cadmium salts, * Ztschr, phys. Chem., 37, 673 (1901). 23 and copper sulphate, they used the metal carefully purified for the anode, and in the determinations were able to deter- mine the difference in concentration by making an analysis for the metal itself. In this investigation they also deter- mined the effect of dilution upon the relative velocities, and found that in many cases, such as in the cadmium salts, they did not become constant until dilution between 200 and 300 were reached. They compared their results with those ob- tained by Bein and Hittorf and they agreed very well, with the exception of lithium chloride, which agreed much better with the results obtained by Kuschel. From all the work done up to this time there still is a limit in the dilution at which it becomes impossible to measure the transport numbers. Even in the work of Jahn and his pupils, Noyes and Bein, the dilutions are limited. In Jahn’s work he could not get very accurate results above a dilution of N/150, and this range is not sufficient to measure the con- stant transport numbers of many salts, especially the diad and triad salts of which only a few have probably been deter- mined. Steele and Denison' undertook to measure the trans- port numbers of salts at dilutions comparable with those at which accurate conductivity measurements are made, and also to test whether at such dilutions the transport numbers would become constant. They selected the salts of calcium for their experiments because good measurements of their conductivities had been made at dilutions of n = o.oOo.I. Thus to work at dilutions comparable with the conductivity measurements they would have to work with solutions vary- ing between N/250 to N/400, it not being practicable to work at much greater dilutions on account of the impossibility of purifying such large quantities of water which would be re- quired for the experiments. In such dilute solutions as those referred to above they showed that it was obvious, that, in order to get an appreciable quantity of the salt carried by the current, a large volume of solution would have to be electro- lyzed or, by using small volumes, the experiment would have to be carried for a long time to get an appreciable change in 1 J. Chem. Soc., 81, 456 (1902). 24. concentration. Of the two alternatives the former was chosen, because in using the latter method the experiment would be in danger of being lost on account of a backward diffusion caused by the differences in concentration in the middle layer. However, by selecting the former alternative and employing the usual method, the apparatus would be of unmanageable size. With these facts in view they devised an apparatus which admits of the electrolysis of almost unlimited volumes of liquids. The apparatus used by them consisted of a W-shaped tube which was connected with a reservoir to which fresh quanti- ties of solution could be added as that in the apparatus was drawn off at the bottom of the limbs in the W-shaped tubes. The acid and alkali formed were neutralized by the addition of small quantity of N/2 alkali and acid respectively. The addition of this also overcame the concentration changes which would necessarily be formed and cause diffusion back into the tube. By using an apparatus constructed in this manner they could draw off each side separately, and then re- fill the apparatus from the reservoir, and allow electrolysis to proceed, until several liters of solution had been passed through the apparatus. In their investigation they deter- mined the transport numbers for cupric chloride, copper sul- phate, and cupric nitrate, as well as for potassium chloride. The current was measured by a silver voltameter. The values which they found for potassium chloride agree satisfactorily with all the best values obtained by other in- vestigators in this field, and also confirm Kohlrausch's as- sumption as to the constancy of the transport number for salts of this class with increasing dilution. Steele', after this investigation carried out by himself and Denison, proceeded with the investigation, using the apparatus formerly used by himself and described above in this paper. In this investigation the transport numbers of such salts as barium chloride and magnesium sulphate were determined. He came to the following conclusions concerning the results obtained : 1 Phil. Trans., 198 A, (1901). 25 1. The transport number is not independent of the concen- tration. This had already been pointed out by others. 2. The specific ionic velocity of the cation varies with the particular salt under investigation. 3. The current measured by the galvanometer is not the same as that calculated from the observed velocities. The explanation that the specific ionic velocities vary with the concentration, and vary more for some ions than for others, he attributed to the formation of complex ions in solution, but this means a motion of at least a portion of the undissociated salt along with the ions, and consequently the concentration of the solution at the margin is altered, and this interferes with the regularity of the potential fall, the velocity of the margin being correspondingly affected. With these points unsettled, Abegg and Gauss' undertook to investigate these points raised by Steele. They investigated the influence of the initial concentrations of the neighboring electrolytes and recommended that in Steele's method the concentration of the indicator jelly should be at least equivalent to that in the mid- dle electrolyte. They attributed the differences between the results obtained by Hittorf's method and those obtained by the direct method of Steele to the influence of cataphoresis on the moving boundaries, and showed that when a correction for this influ- ence is applied, the transport number for chlorine is the same as that found by Hittorf. The effect of electrical endosmose having been shown in only one case, Denison,” studying at the University of Breslau, undertook to investigate a number of salts and measure accurately this endosmose, and, if possible, to ascer- tain its effect on the transport numbers. The method used by him was practically that used by Steele. A few changes were made in the apparatus by which he could measure the endosmose and also obtain a constant voltage. He shows very clearly that in salts of the alkali metals, with the exception of lithium, if proper allowance is l Ztschr. phys. Chem., 40, 737 (1902). * Ibid., 44, 575 (1903). 26 made for the endosmose, very accurate results can be obtained. He found the same exception with lithium chloride as had been found by previous investigators, for instance, it exhibits an increase in the transport number for the anion with increase in concentration. Upon investigating salts which were capable of forming complex ions or undergoing hydrolysis, the values obtained for the transport numbers did not agree with those obtained by Hittorf, even after this correction had been applied, but there is a parallelism between the two series of results. In a water solution where the electrolytes were separated by gelatin, he also observed that crevices occurred in the gela- tin which began by the appearance of a bubble of gas, and that this grew rapidly and became a large space. This, as was referred to above, was a serious difficulty which Lodge and Masson had encountered ; but he succeeded in showing that this did not change the potential fall in the middle electrolyte but did make small differences in the endosmose, which had to be taken into account. In this investigation he also studied the effect of gelatin on the transport numbers. He observed that the transport numbers measured in gelatin solution are the same as those obtained in aqueous solution; so long as the gelatin is liquid, the concentration of the gelatin exerts no influence. In solidified gelatin the transport numbers are quite differ- ent, and it appears that under these conditions the velocity of the cation is retarded relatively to that of the anion, the absolute velocity in gelatin being slower than in water. Thus, the transport number for the anion in gelatin always appeared too large. A similar phenomenon is observed in very con- centrated aqueous solutions, and it is very probable that in both cases the specific frictional coefficient of the ions, as well as the formation of complex ions, play an important part. He also considers it probable that the gelatin enters into combination with certain salts, forming complex cations. He also states, in support of this view, that it may be pointed out that various proteids have the power of combining with acids and alkalies, forming compounds of a Salt-like character, and 27 therefore there are good reasons for regarding the proteids as weak acids and bases. They, themselves, have practically no ionizing tendency, but the salts which they form with strong acids and bases have a strong ionizing power. It is thus very probable that gelatin or some product formed by hydrolysis would act in this way, and what is supposed to be a solution of an acid or base in gelatin, would contain no free acid or base until an excess was added. This would ex- plain the above difference in the transport numbers in liquid and solid gelatin. Very little work has been done in any other solvent than water. A few determinations were made ten or twelve years ago by Lenz and some by Mather in his dissertation at this University, but still the field is practically unworked. Carrara" undertook an investigation in this field quite re- cently and has determined the transport numbers in methyl alcohol solutions for different dilutions of the following salts: silver, copper, cadmium, lithium nitrates, silver, copper, cad- mium and lithium chlorates, copper and cadmium chlorides, cadmium, lithium, tetra ethyl ammonium and trimethyl am- monium iodides, copper sulphate, cadmium and copper ace- tates. He used three different forms of measuring apparatus. One was an apparatus with a membrane similar to one of the forms used by Hittorf. Another was that used by Loeb and Nernst, while the third he describes as a new form of appara- tus. This third form is in fact a slight modification of that used by Mather in this University, but he does not even men- tion the work carried out by Mather, nor does he even give him any credit for devising this form of apparatus. In his investigation he comes to some general conclusions which have been brought out before by a number of investi- gators; for instance, he states that the transport numbers vary considerably with the concentration, the values sometimes indicating the existence of complexions in solution, especially with such salts as cadmium iodide. He, however, brings out an interesting point in the investigation of lithium chloride. * Gazz, chim. ital., 33, I., 24I (1903). 28 In this case his results indicate the existence of complex ions even in a binary electrolyte. This he assumes can only be explained by considering lithium chloride in solution to have the formula Li,Cl, and that when this dissociates it may dis- sociate into the ions LiCl, and Li. The power of forming these complex ions was found to vary considerably for differ- ent salts. On comparing the transport numbers found by him for the same salt in aqueous and methyl alcohol solutions, it is seen that the difference between them is in general very small, and of the same order of magnitude as the difference obtained by a change of concentration. In general, the transport num- bers for the anion in methyl alcohol are higher than in water solution, only three exceptions having been found. These were the following salts: lithium chlorate, cadmium chloride, and cadmium iodide. From these considerations he draws the conclusions that the transport numbers of the ions of an electrolyte tend toward the same value independent of the solvent in which it is dis- solved. In other words, if the dilution is sufficiently great and no secondary reactions take place, the transport numbers of an electrolyte are the same in all solvents. The transport numbers found for solutions of salts in methyl alcohol are the same as in aqueous solutions at greater con- centrations. The most recent investigations upon this subject were made by Huybrechts' and Wolff.” Nothing new, however, is brought out by their work on this subject. They used an apparatus which was a very slight modification of that used by Jahn and his pupils. Huybrechts’ investigation was to determine the transport numbers for sulphuric acid and mag- nesium sulphate in very dilute solutions. Wolff's investigation had to do with barium chloride and hydrochloric acid. EXPERIMENTAL WORK. This investigation was undertaken for the purpose of de- 1 Dissertation, University of Berlin, 1902. * Ibid., 1903. 29 termining what effect mixtures of methyl alcohol and water would have on the relative velocities of the ions of such a salt as silver nitrate. The work of Jones and Lindsay' on the conductivity of cer- tain salts in water, methyl, ethyl, and propyl alcohols, and mixtures of these solvents suggested this work. In their work, Jones and Lindsay found that the conduc- tivities of such salts as potassium iodide, ammonium bromide, strontium iodide, etc., were less in mixtures of the solvents than in either of the solvents alone. Especially was this the case in mixtures of methyl alcohol and water. Considering these facts, the first thing to determine was whether silver nitrate would give similar conductivity results, and if so, whether there was any relation between this phenomenon and the relative velocities. The conductivities of silver ni- trate in these solvents and varying mixtures of them were de- termined. The water, methyl and ethyl alcohol, were puri- fied by the methods described by Jones and Lindsay. In each case a mother solution was made in the solvent in ques- tion, and the remaining solutions were obtained by successive dilutions with some of the solvent of the same composition. In this way an error was avoided which would result from the contraction when alcohol and water were mixed, and also prevent the accompanying heat effect. In some cases, as in very dilute solutions, where such small quantities of the mother solution were required, a second mother solution was made from the first, and the more dilute solutions made from it in the way described. The strength of these mother solu- tions was determined by titrating with a standard solution of ammonium sulphocyanate, - Conductivity Apparatus Employed. The apparatus described and used was similar to that em- ployed by Jones and Lindsay. The cells differed from the ordi- nary Arrhenius cell, being provided with a ground-glass top to, prevent evaporation of the more volatile solvents, and also protect the anhydrous alcoholic solutions from the moisture 1 Amer. Chem. Journ., 28, 329 (1902). 3O of the baths and air. The glass tubes carrying the electrodes were passed through thin rubber tubes in the cap. Sealing- wax was then run over the outside of the joint. The zero-bath was prepared as follows: A 1arge glass battery-jar was filled with finely crushed ice and distilled water. It was then placed in a water-bath and the space between filled with finely crushed ice and water. This proved very efficient, as it was possible to keep within O’.05 of zero for hours. The bath at 25° was of the ordinary form, and was kept in constant motion by a stirrer driven by means of a hot- air engine. The thermometers used could be accurately read to O’.O2. The burettes and flasks were carefully calibrated. Conductivity Measurements. All the conductivity measurements were made at the two temperatures, o' and 25°. In the following tables v = num- ber of liters of solution containing a gram-molecular weight of the salt; pu, o” = molecular conductivity at O’; July 25° = molecular conductivity at 25°: Table Z.--Molecular Conductivity of Silver Nitrate in Water. º). ſu, O’. Juv 25°. IO 55.72 99.46 2O 58.63 IO5.72 4O 63. IO I IO. 22 8O 63. I6 II 5.81 I6O 65.38 II9.86 32O 69.9 I I25.08 64O 7.I.O5 125.86 I 28O 70.59 I25.35 Table II.—Molecular Conductivity of Silver Nitrate in Ethyl Alcohol. Z). ſu, O’. 14, 25°. 9.7 I 7. II . . . . . I9.43 8.90 I4.26 38.86 II. 35 16.96 77.73 I3. IO 2O. II I55.47 I5. I3 23.87 3IO.95 I7.O4 26.46 621.89 I9.43 30.62 3 I Table III.--Molecular Conductivity of Silver Witrate in Methyl Z). IO 2O 4O 8O I6O 32O 64O Table / V.—Molecular Conductivity of Silver Witrate in 25 Per Cent Ethyl Alcohol and Water. Z). 38.86 77.73 I55.47 3IO.95 621.89 Table V.--Molecular Conductivity of Silver Nitrate in 5o Per Cent Ethyl Alcohol and Water. 7). I9.43 38.86 77.73 I55.47 3IO.95 621.89 I243.78 Table VI.-Molecular Conductivity of Silver Nitrate in 75 Per Cent Ethyl Alcohol and Water. I9.43 38.86 77.73 I55.47 3IO.95 621.89 Alcohol. Juvoº. 25.96 32.63 39.7 I 45.28 5.I.O.9 56.7 I 6I.42 ſu, O’. 25.95 26.65 26.45 28.72 28.84 My O’. I5.25 I5.8 I I7.O4 I 7.92 I9. IO I9.90 2O.79 Juvoº. I3. I2 I4.3O I6.79 I9.48 I8.OO I9.4. I Mw 25°. 35.77 44.67 53.42 62.95 70.36 8o. 17 88, 22 Juv 25°. 59.70 62.75 63.82 64.87 68.28 Juv 25°. 37.87 39.5C) 42.42 45. I5 47. I3 49.39 52.8o Juv 25°. 27.OI 3O.43 33.65 35.94 39. OI 4O. I4 32 Table VII.-Molecular Conductivity of Silver Nitrate in 25 Per Cent Methyl Alcohol and Water. Z}. 4O 8O I6o 32O 64O 11, O’. 35.63 36.95 39. O3 4 I.O3 4 I. 23 ſaw 25°. 72.68 75.56 79.34 82.93 83.9 I Table VIII.-Molecular Conductivity of Silver Witrate Per Cent Methyl Alcohol and Water. 7). 2O 4O 8O I6O 32O 64o Juv O’. 27.27 28.63 29.93 3I.47 32.29 34.67 Juv 25°. 53.33 56.8o 59.75 63.22 65.85 68.67 £n 5o Table IX. —Molecular Conductivity of Silver Witrate in 75 Per Cent Methy/ Alcohol and Water. 7). 2O 4O 8O I6O 32O 640 JAw o°. 27.98 3O.O3 32.81 35.22 35.7 I 4O. 27 O //w 25 . 48.2O 52.33 57. I7 61.3.I 63.23 69.42 Table X. — Temperature Coefficients of Conductivity of Silver Nitrate in Water (o’ to 25°). 7). IO 2O 4O 8O I6O 32O 64o I28O I.75 I.88 I.88 2. IO 2. I4. 2.2 I 2.2C) 2. I9 Temperature coefficient. 33 Zable XI.- Temperature Coefficient of Conductivity of Silver Mitrate in Ethyl Alcohol (o" to 25°). 7/. Temperature coefficient. I9.43 O.2I4. 38.86 O. 224 77.73 O.28O I55.47 O.35O 3IO.95 O.377 621.89 o.488 Table XII.-Temperature Coefficient of Conductivity of Silver Mitrate in Methyl Alcohol (o" to 25°). 7). Temperature coefficient. IO O.392 2O O.482 4O O. 548 8O O.707 I6O O.771 32O O.938 640 I.7O2 Table XIII.-Temperature Coefficients of Conductivity of Silver AWitrate in Mixtures of Ethyl Alcohol and Water of Various Compositions. Temperature coefficients. Twenty-five per Fifty per cent Seventy-five per 7/. cent alcohol. alcohol. cent alcohol. I9.43 e e º 6 O.905 O.556 38.86 I.35 O.962 O.645 77.73 I.44 I.O.I.5 O.674 I 55.47 I.49 I.O.89 o.658 3IO.95 I .45 I. I 2 I O.84O 621.89 I.58 I. I80 O.829 I243.78 tº tº ſº & I. 28O tº Q 6 tº Table XIV.- Temperature Coefficients of Conductivity of Silver Mitrate in Mixtures of Methyl Alcohol and Water of Various Compositions. Temperature coefficients. Twenty-five per Fifty per cent Seventy-five per 7/. cent alcohol. alcohol. cent alcohol. 2O e e o º I.O4. O.8 IO 4O I.48 I. I.3 O.892 8O I. 54. I. IQ O.974 I6O I.6I I. 27 I.O24 32O I.68 I. 34 I. IOO 64O I.7I I.36 I. I66 34 In order to see the connection existing between the con- ductivities in each solvent, the following tables are given for comparison : Table XV –Comparison of the Molecular Conductivities of Sil- wer Witrate in Ethyl Alcohol and Mixtures of It with Water at 25° C. Twenty-five Seventy-five One hundred per cent Fifty per per cent per cent 7/. alcohol. cent alcohol. alcohol. alcohol. I9.43 e e o & 37.87 27.OI I4.26 38.86 59.7O 39.5O 3O.43 I6.96 77.73 62.75 42.42 33.65 2O. II I55.47 63.82 45. I5 35.94 23.87 3IO.95 64.87 47. I3 39. OI 26.46 621.89 68.28 49.39 4O. I4. 30.62 It is seen from these values that the molecular conductivity in ethyl alcohol and mixtures with water does not show a minimum in the ordinary range of dilution, but still does not obey the law of mixtures. This is in accordance with Jones and Lindsay’s work on potassium iodide. In that case they did not find a trace of a minimum at 25°. The values in Table XV. are plotted as curves in Fig. I., the abscissae representing the different per cents of alcohol, and the ordinates the molecular conductivities. Table XVI.—Comparison of the Molecular Conductivities of Sil- wer Witrate in Ethyl Alcohol and Mixtures of It with Water at o' C. Twenty-five Seventy-five One hundred per cent Fifty per per cent per cent 2/. alcohol. cent alcohol. alcohol. alcohol. 9.7I O tº º º tº ſº tº Q tº Q & © 7. II I9.43 I5.25 I 3. I2 8.90 38.86 25.95 I5.8I I4.3O II. 35 77.72 26.65 I 7.O4 I6.79 I3. IO I55.47 26.45 I7.92 IQ.48 I5. I3 3IO.95 28.72 I9. IO I8.OO I7.O4 621.89 28.84 I9.90 I9.4 I I9.43 I243.78 o º º q 2O.79 tº C C tº Q & © º These values are plotted in Fig. II. same general form as in Fig. I. /S 0 tº 2.04. I ur: 3 8.3% The curves are of the No distinct minimum is II v = 77.73 III v : /53, #7 I /0 Ilſ v = 3 / 0.93 V U-- 6 2.1.8% IF7 +07% % /90% Fig. I. shown, but the form of the curve indicates that a minimum value is approached. Table XVII.-Comparison of the Molecular Conductivities of Silver Witrate in Water, Methyl Alcohol, and Mixtures of These Solvents at 25° C. IO 2O 4O 8O I6O 32O 64O I 28O Water. 99.46 IO5.72 II O. 22 II.5.8 I II9.86 I 25.O8 I25.86 I25.35 Twenty-five per cent alcohol. 72.68 75.56 79.34 82.93 83.9 I 9 @ e > Fifty per cent alcohol. 53.3 56.80 59.75 63.22 65.85 68.67 alcohol. 48.2O 52. 33 57. I 7 61.3.I 63.23 69.42 © e o a Seventy-five One hundred per cent per cent alcohol. 35.77 44.67 53.42 62.95 70.36 8o. 17 88.22 & e s e. 36 These values are plotted in Fig. III. In nearly every case the minimum, as shown by the curve, lies between mixtures '80 y rº-º-º- — `ſ IV III II I 2.5 %