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/cu31924004429050 Cornell University Library QD 571.C33 Single differences of potential 3 1924 004 429 050 SINGLE DIFFERENCES OF POTENTIAL SINGLE DIFFERENCES OF POTENTIAL DISSERTATION Submitted to the University Faculty of Cornell University for the degree of Doctor of Philosophy by HECTOR RUSSELL CARVETH SINGLE DIFFERENCES OF POTENTIAL BY HECTOR R. CARVETH The progress of scientific electrochemistry has been so rapid in the past decade that it is not surprising to learn that a school of physical chemists regards the problem of the voltaic cell as already solved, and thinks that future work along this line will be merely corroborative in its nature. Recent literature has shown, however, that the adherents of this school may not be thoroughly consistent in their doctrine, and that whatever may be (and certainly are) the triumphs of the modern electrochem- ical view, it is necessary that there be eliminated from it any in- consistency which impairs its general usefulness. The adherents of this successful theory claim that the electromotive force of any ordinary chemical combination may be predicted with a fair degree of accuracy. This is done by adding up the single differ- ences of potential in a cell, all of which, the theory claims, are capable of formulation, and one of calculation. It thus appears that in the first place it must be known where differences of potential are to be observed in a cell, and secondly, what are their intensities. The total electromotive forces of a cell may be considered as composed of four single differences of potential which are located at the boundary sur- faces of meta^ | metal 2 , metal 2 ! electrolyte^, electrolyte 2 1 electrolyte j and electrolyte i ! metal. The intensity at the first-mentioned contact surface is so small as to be ignored. 1 With regard to the other three potential differences, it may be said that no simple mathematical formula was given for their calculation until the appearance of the Nernst classic 2 in 1889. Since the Nernst 1 Ostwald. Lehrbuch II, 919. 2 Zeit. phys. Chem. 4, 129 (1889). 6 Hector R. Carveth theory has as its basis the theory of osmosis, it is evident that its application holds rigidly only in so far as the so-called 'law of osmotic pressure ' holds, namely for dilute solutions. When re- stricted to these, experiments show that the theory is able to predict and to explain results very satisfactorily. By use of it alone, however, the difference of potential at the contact surface metal j electrolyte while capable of formulation, cannot be calcu- lated. It is here that another theory has been introduced in order to supply the missing link. That the two theories should be merged together is not un- expected. But by this procedure many abnormalities have been produced, for which no satisfactory explanation can be given. In a recent article 1 Nernst has called attention to the fact that the two theories cannot both be correct, while Taylor 2 in a dis- sertation presented in June, 1896, had arrived at similar conclu- sions. The object of this research is to examine the theories of today with respect to single differences of potential, directing attention more particularly to the several methods which claim to determine the actual value at the surface, electrode ! electrolyte, and from theoretical considerations and results obtained by use of one of these methods, to attempt to answer the question, " Do these methods give the true potential difference?" The history of single potential differences is most intimately connected with the change of surface-tension of mercury. The relation existing between the two was not discovered, however, until many years after the announcement of the fact that the electrical condition of a mercury surface exercises a determining influence on its surface-tension. To the investigation of the phenomenon many scientists applied themselves with little or no success, until, by a very careful research, Lippmann showed that the surface-tension at the surface, mercury | sulfuric acid, is a constant function of the electromotive force of polarization at that surface, that when the surface of mercury is polarized by 1 Wied. Ann. 58, Beilage, (1896). 2 Jour. Phys. Chem. i, i (1896). Single Differences of Poieittial 7 hydrogen it contracts until a certain electromotive force is reached, and that when this is further increased, expansion takes place. He plotted his results using as abscissas the different electromotive forces applied, as ordinates the surface-tension expressed in arbitrary units, and thus obtained a curve which con- sisted of a rising and a falling branch, and which approached the symmetry of a parabola. The practical application of Lipp- mann's discoveries appears in the electrometer that bears his name and is so extensively used in the measurement of electromotive forces. Lippmann had thus shown that the intensity of the polar- izing current had a decided effect on the surface-tension of mer- cury; other experiments performed by him showed that the re- verse phenomenon could take place, viz., that by changing the surface-tension it was possible to produce changes in the electro- motive forces. It is to these experiments that is clue the mathe- matical treatment which was given the subject by Helmholtz 1 and of which the introduction only is here translated. " Now in dealing with polarized mercury surfaces we have to do with a much more complicated process, since the electricity present in electrolytes has, according to Faraday's law, taken with it ponderable ions of the electrolyte. But the treatment of the subject just given may be generalized in a way which has already been used by Iyippmann, in which it is necessary merely to make the supposition that the forces under whose influence the doiible layers are formed may be conservative forces, and that the variations produced are thus perfectly reversible. The actual occurrence of the reversibility of this process has been to a great extent proved at the same time by the researches of Lippmann." Making use of the supposition above given, Helmholtz de- rived the formula ST where dT is the differential of the surface-tension of the mer- Wied. Ann. 16, 30 (1882) 8 Hector R. Carveth cury, dP is the differential of the potential and e is the amount of electricity per surface unit, forming the charge of the ions of the electrolyte. Consideration of this formula shows that when the mercury is at its greatest surface-tension, it should show no difference of potential against the electrolyte, and Helmholtz concluded that such a result would be reached if one allowed mercury to fall in a fine stream into an electrolyte. Under his direction, Konig 1 examined the surface-tension of mercury in a few solutions ; he found that while the absolute value of the surface-tension of mercury was not the same for all solutions, the surface-tension of mercury dropping into a solution was actually of the same value as the maximum obtained when it was polarized in the same solution. The theory was thus able to explain all the phenomena known at that time ; and, although Helmholtz himself did not draw attention to the fact, there was a deduction to be drawn from his conclusion which has since influenced electrochemical views to a great extent. It was Ostwald 2 who showed that the conclusions of Helmholtz should lead to a knowledge of the sin- gle difference of potential between metal and electrolyte, since by the Helmholtz theory the dropping mercury could have no dif- ference of potential against the electrolyte into which it fell, and that hence any electromotive force observed with such a combi- nation as dropping mercury | electrolyte j metal should give the single difference of potential, electrolyte ! metal. Important as this work appears, and so simple its execution, the results obtained by its use have not been so uniform as to be considered satisfactory. Such at least must be said of the work of Ostwald, Exner and Tuma, Pellat, Moser and Miesler. It was Paschen who, in 1890, after studying carefully the phe- nomena of polarized mercury surfaces, directed his attention to dropping mercury electrodes, coming finally to the conclusion that the lack of uniformity in the results of other observers was 1 Wied. Ann. 16, 1 (1882). - Zeit. phys. Chem. i, 583 (1S87). Single Differences of Potential 9 caused by their not having the flowing mercury assume its greatest tension. This error 1 he claimed to have eliminated by having the flowing mercury ' break ' just as it entered the sur- face of the electrolyte. The results he obtained by this method of dropping mer- cury he compared, and found to agree remarkably well with results obtained by the polarization method as first used by Lippmann (see Table II on page 306). This method is regarded as the exact converse of the dropping mercury method. The mercury and electrolyte are put into a capillary electrometer and then the mercury is polarized by known electromotive forces until it attains its maximum of surface-tension. According to the Helmholtz theory, the electromotive force which must be applied at this point is equal, with reversed sign, to the potential difference of mercury ! electrolyte. In practice, the usefulness of this polarization method is impaired by the following disadvantages : — (a) It is exceedingly difficult to ascertain when the maxi- mum of surface-tension has been attained, more especially with dilute solutions. To find the maximum, it is hence necessary to resort to interpolation curves. (6) With some electrolytes, mercury either does not move at all, or moves so very little as to render the method useless. This is the case when mercury is in contact with a solution of a soluble mercury salt where the current in passing through causes decomposition at the electrodes. (c) The method is obviously inapplicable when mercury comes into contact with salts of silver, platinum or palladium. The dropping mercury method should obviate the objection (a) ; while the proper variation of the method should allow the other two disadvantages to be overcome. If then it were found that this method actually fulfilled the conditions imposed in order that the Helmholtz theory might be strictly applicable, we should have here what Paschen thought he had — a beautiful experimental method of finding single differences of potential 1 Wied. Ann. 41, 42 (1890). io Hector R. Carve th between metal and electrolyte or electrolyte and electrolyte. Values have been obtained, however, which can be explained only by the assumption that the mercury on entering the solu- tion is not completely deprived of its charge. Instances of this are to be found in Paschen's 1 measurements with zinc and cadmium amalgams, when the flowing amalgam played into solutions of zinc sulfate, magnesium sulfate, magnesium chlorid and cadmium bromid. In these cases the investigator drew at- tention to the fact that the amalgams could no longer be con- sidered as entering the electrolyte without a difference of poten- tial. If then, in some cases, the failure of the method is only too obvious, while in the remaining cases no proof is adduced to show that the flowing mercury does actually attain the maximum of tension, 2 it is not surprising that the significance of the meas- urements made by both of these methods (since they agree fairly well with each other) should be doubted, and another theory given to explain the presence of these electromotive forces. This theory, which was first advanced by Warburg 3 and afterwards 4 strongly supported on theoretical grounds, was based on his discovery that when mercury was in contact with solu- tions of electrolytes, such as H 2 S0 + , MgS0 4 , NaCl, KC1, etc., containing oxygen from the air, compounds of mercury were produced. Ostwald, 5 Paschen 6 and others have also observed the solubility of mercury in H 2 S0 containing oxygen, and it is not improbable that such solubilities may be observed with almost every electrolyte. Accordingly in an electrometer hold- ing mercury and sulfuric acid, the latter containing oxygen, there will always be present some mercurous sulfate. The pas- sage of a current through the electrometer will cause decompo- sition of the latter electrolyte. The mercury precipitating at the cathode will render the mercurous sulfate solution there more 1 Wied. Ann. 43, 568 (1891). 2 Paschen. Wied. Ann. 41, 205 (1890). a Wied. Ann. 38, 321 (1889). 4 Ibid. 41, 1 (1890). " Zeit. phys. Chem. 3, 354 (1889). 6 Wied. Ann. 43, 568 (1891). Single Differences of Potential 1 1 dilute, while at the anode the concentration of the salt is increased. Now, if at any moment before the maximum tension is reached, the current is suddenly disconnected, and the elec- trometer is not short-circuited on itself, the latter will, on being connected with a sensitive galvanometer, indicate a current run- ning in a direction exactly opposite to the polarizing current previously applied. From the standpoint of the Helmholtz theory, this is the charge from a condenser ; but the Warburg theory regards it as a concentration element produced by Hg j dil Hg,S0 4 ! cone Hg 2 S0 4 1 Hg. To establish the Warburg theory, it was absolutely necessary to show that the surface-tension of mercury or of amalgams could be affected by other means than a polarizing current — viz : by the nature of the solution with which it was in contact. G. Meyer 1 has performed experimental work in this direction. He determined, by Lord Rayleigh's method, the surface-tension of mercury or amalgam, when there was added to the electrolyte with which it was in contact a salt of mercury or of the metal contained in the amalgam. In most cases this had the effect of decreasing the surface-tension of the mercury or the amalgam. With some, however, such as HgCu in caustic soda or potassium cyanid, HgZn in sulfuric acid, magnesium sulphate, sodium hydroxid and chlorid, and HgCd in sulfuric or hydrochloric acids, the addition of the salt of the metal contained in the amalgam did not effect the surface-tension and in all these cases the ascending part of the surface-tension polarization curve was lacking. The absence of this part of the curve in these cases is not explained by the Helmholtz theory since it deals with polarizable electrodes only ; the Warburg theory ascribes the decrease of surface-tension to the formation of amalgam. Since mercury in the presence of a salt of mercury cannot attain its maximum surface-tension, we have according to the Warburg theory when we polarize mercury in an electrometer until the mercury reaches its maximum tension, a combination, Hg ! electrolyte ! solution of mercurous salt I Hg, whose electromo- 1 Wied. Ann. 53, 845 (1894). 12 Hector R. Carveth tive force gives the intensity opposing polarization. Thus, in addition to the single potential difference Hg I electrolyte which the upholders of the Helmholtz theory regard as the only one present, there should also be present the two — electrolyte I solution of mercurous salt, and solution of mercurous salt i mercury — the latter of which will be regarded by very few scientists as negli- gible. With an ideal dropping mercury electrode, one should have an element similar to the one in the electrometer, since the mercury in falling thus assumes its greatest tension ; hence the experimental result that both methods give (at times) the same values may be explained just as well by one as by the other theory. But does such- an ideal electrode exist ? Consider from the Warburg point of view the case of mercury flowing into potassium chlorid. There is formed here caustic potash (shown by alkaline reaction) and mercurous chlorid. The presence of the latter prevents the mercury from assuming its maximum tension. If we measure this at any time after it has been run- ning an indefinitely short time, we are actually measuring Hg | dil Hg salt | cone Hg salt | Hg and not Hg j KClHg 2 Cl 2 j Hg. The formation of the mercurous chlorid and its effect on the flowing mercury can certainly not be ignored in this case. Considering the case from the stand- point of the double-layer theory, one notes, bearing in mind that Hg in KC1 was found by Gouy 1 to have a lower surface-tension than Hg in KOH, and that the mercury in dropping into KC1 is continually changing its maximum of surface-tension as the composition of the solution into which it falls changes, that it is not connected with the electrolyte without a difference of potential. In the face of facts such as the above, it appears unreasonable to introduce as the value of the normal potassium chlorid electrode (Hgl Hg 2 Cl 2 KCl in normal solution) 0.560 volt, when according to either of the theories, this is not the value of the single poten- tial difference of Hg i KC1. It would be just as reasonable to in- troduce the value of Hg| KBr = 0.49 since this value has been ' Comptes rendus, 114, 211 (1892). Single Differences of Potential 13 found by several observers. But if then we make such a combi- nation as 1 Hgi Hg,Cl,KCl(i) ! KBr(i)Hg a Br 2 1 Hg we should expect an electromotive force not much more than 0.07 volt, since the Nernst-Planck theory would allow us to neglect the potential difference at the surface of the two electrolytes. But the electromotive force actually found is (roughly) 0.14 volt. By making use of the double-layer idea, it should be found that the dropping electrode measurements always err (if at all) by giving too low values, because the mercury can hardly be considered as passing beyond its maximum of surface-tension. If then Hg j KBr = 0.49, and the potential difference between the solutions be equal to zero, the value found for Hg ] KC1 must be too low. A consideration of other similar cases serves to con- firm the conclusion that there is at present no justification for re- garding even one potential difference, metal | electrolyte, as known. If only one of these were known, and the Nernst-Planck theory were accepted as true, all other values could be calculated readily therefrom. That a knowledge of the values of true single differences of potential will be of great importance, especially theoretically, may readily be granted. From them may be deduced clearer ideas as to the solution-pressures of metals, temperature coeffi- cients of certain types of cells, heats of ionization of the elements, etc. In this as in so many other branches, Ostwald has been the pioneer ; but whether the values which he and many others assume as known definitely are true values, is the subject con- sidered in this paper. Unsatisfactory as the condition of the theoretical side of the subject appears, it seemed advisable to attempt further measure- ments by means of the dropping mercury method, comparing where possible the results obtained with those of other investi- gators. Attention has been directed more especially to the measurement of metals in solutions of their salts, since a con- 1 The figures after the chemical formula are used throughout this paper to denote the number of liters in which 1 grm mol weight is dissolved. 14 Hector R. Carve th sideration of the combinations of this type will probably lead to more definite conclusions than a discussion of cells with irrever- sible electrodes. Apparatus and material used. — In the description of his apparatus, Paschen drew attention to the necessity of performing the work of measurement by means of dropping mercury elec- trodes in a place free from jarring or other disturbance. In the work here described, no such effect was noticed at all, all due precautions having been taken at the beginning to obviate such. In the room placed at my disposal by Professor Bancroft, the" (unused) fume cupboard had a stone floor which had been built into the wall, and hence was not disturbed by any motion or jarring in the room. On this floor was built a wooden platform which had an area outside of fume cupboard of about 0.6 sq. m. (100 cm by 60 cm). This was sufficiently large to hold all the apparatus required in the measurements. The electrode from which the mercury flowed .was supported by clamps attached to an iron bar about 130 cm in length, which in its turn was at- tached to the side of the fume cupboard. The electrodes for the dropping mercury varied in length from 80 cm to 200 cm. The one finally adopted consisted of 1 50 cm of glass tube of about 1 2 mm diameter, to the lower end of which was fused 10 cm of capillary tube (1 mm bore). This was connected to the tip by double rubber tube, the latter being securely wired to the glass tube. The tip was made by drawing out capillary tubes; diameters of different tips ranged from 0.2 to 0.05 mm. The greater number of the measurements were made with a tip of diameter 0.12 mm (calculated) which, with a pressure of 150 cm of mercury, gave a stream breaking about 8 mm below the tip. A wire pinch-cock over this rubber served to stop the flow of mercury when the electrode was not in use. This has several advantages over a stop-cock, which was discarded entirely after the former method had been tried. They are : (1) It allows rapid change of tips. (2) There is less danger of spilling mercury. Single Differences of Potential 15 (3) Electrical connection between the flowing mercury and the platinum connection of the drop electrode is assured. This platinum wire was fused into the wider part of the tube, and thus formed the terminal connection on the sides of the dropping mercury. For a number of the measurements first taken, a platinum wire fused into the vessel receiving the falling mercury served as the other terminal, and thus formed electrical connection with the mercury there. As this method was somewhat inconvenient, it was soon given up. Accordingly in all the measurements given in this paper, the fallen mercury plays no part. The diagram shows the method used. The mercury falls from the drop electrode into a funnel, which is so made that it discharges mercury as rapidly as it flows in. This stream of mercury breaks just as it enters the surface of the electrolyte in the fun- nel, and thus when once the adjustment is made, the apparatus is self-regulating. The electrolyte in the funnel is connected by a siphon with a half-cell. The latter consists of a metal which forms the other terminal, and the solution of an electrolyte. Since these half-cells may be readily connected or disconnected without disturbing to any extent any other part of the apparatus, it is possible to make a considerable variety of measurements ' quite rapidly. There is, moreover, the advantage that they may- be used repeatedly so that one knows he is always measuring the same half-cell, whereas if it is made up and then used im- mediately, it does not usually have the same value it finally attains. In all cases examined, the metals stood in the electro- lytes some time before a measurement was taken. In obtaining pure mercury, great trouble was taken. Two methods were used, both of which gave excellent results. The first was the ordinary method of shaking the mercury with dilute sulphuric acid and a few drops of potassium dichromate, and then washing it thoroughly with dilute nitric acid and water. The other method was the one in use in the gas laboratories here. The mercury is allowed to remain under sulfuric acid and mercurous sulfate in the separating funnel for some time. In this way a very pure mercury is obtained, which when washed 1 6 Hector R. Carve th thoroughly was ready for use. In all cases, the mercury after passing through the funnel was again cleaned if the surface appeared the least tarnished. The copper, nickel, zinc, cadmium and lead electrodes used in the half-cells were in round sticks about 4 mm diameter and 5 cm long. The first two metals had been prepared electrolyt- ically, and were quite pure. The zincs were carefully amal- gamated before using. The cadmium electrodes (from Eimer & Amend) were always, like the other electrodes, given a bright surface before being put into the solution. The lead electrodes were made by reduction of pure lead oxid. The platinum elec- trodes had been previously platinized. Especial care was taken with regard to the purity of the alkali halid salts. The sodium and potassium chlorids, and the potassium bromid were precipitated by hydrochloric or hydro- bromic acids, the former two salts three times, the latter once. They were then fused. Tests showed no trace of impurities. The barium and magnesium chlorids, potassium iodid and potas- sium sulfate were each recrystallized twice, as were also copper sulfate and nitrate. All the nickel, cadmium, and zinc salts used, zinc sulfate excluded, were taken from the museum and subjected to no further treatment. The zinc sulfate was ex- ceptionally pure, being the same as was used in making my Clark cells. The mercurous chlorid, 1 bromid, iodid, sulfate and oxid which were used as depolarizers were made by precipitating from mercurous nitrate, washing rapidly and carefully, and, when possible, drying. When drying was not resorted to, the precipitates were carefully washed by a solution of same mate- rial as that in which the measurement was to be made. The hydrochloric and sulfuric acids and the ammonia were quite pure. In none of the solutions (with the exception of potassium chlorid) was especial care taken to make weighing or titrations 1 The statement is frequently made that mercurous chlorid darkens on exposure to the light ; but the product of the writer is now unaltered in color, although it was made over fifteen months ago and has since been standing on an open shelf of the laboratory, but not in the sunlight. Single Differences of Potential 17 closer than one percent, since the method of measurement could in no case detect an error so small. Measuring apparatus. — Two Clark cells were made up ; they were carefully compared with a Reichsanstalt, and found to differ from it by less than a millivolt. One was used as a working standard, the other reserved for comparison. At no time while measurements have been taken, has a variation from each other of 0.002 volt (referred to the temperature of 15 ) been observed. The Eeclanche" working cells were very constant. The electromotive force of individual cells varied from 1.46 to 1.53 volts. The fluctuations in the daily measurements for a month did not exceed 0.01 volt, and for a day 0.002 volt. As it was frequently necessary during a measurement to have the cell closed for five minutes on a resistance of 1000 ohms, or a little more, preliminary measurements were made by means of a Weston voltmeter of 200 ohms internal resistance, in order to examine the effect on the electromotive force of the cell. The following are the readings : — p. m. volts At start : 3-53 1.460 Cell now put on 1100 3-56 ] .461 ohms external resist- 3-59 1. 461 ance. 4.05 1. 461 4.10 1.460 4.20 i-459 This showed that the electromotive force of the cell remained quite constant, even with so low a resistance, for a time very much longer than was ever required in making a measurement. The general arrangement of the apparatus is indicated by the diagrams, Figs. 1 and 2. Here DE is the dropping mercury elec- trode; HC the half-cell; 1, 2, and 3 are switches that are always thrown in for each measurement with the dropping electrodes ; 4 is a switch used only in throwing in C, the standard Clark element, for purposes of comparison. E is an ordinary Lipp- Hector R. Carveth Fig. i mann electrometer, L the Leclanche working element, while R z and R are the resistance boxes. 2 In using the Lippmann electrometer by this method diffi- culties are frequently to be met. They are not of such a nature however as to preclude its use, although Palmaer 1 seems to have been unable to use it in his measurements because its polariza- tion capacity was greater than that of the cell being measured. The objection is overcome by the use of the half-cells, with de- polarizer always present. Two resistance boxes each of mo ohms were used in mak- ing the measurements. The readings on the electrometer were made by the zero method, and in the concentrated solutions (e. g. normal) could be taken as accurately as o.ooi volt. With the more dilute solutions such a degree of accuracy seems im- possible, and notwithstanding the greatest care taken, the read- ings may possibly be incorrect to the extent of 0.008 volt in the case of hundredth-normal solutions. In making the measure- ments, the electrode tip was first adjusted so that the mercury might break just at the surface of the electrolyte. By using different switches (1 and 2) the terminals were connected directly to the electrometer, and the tip adjusted so that the mercury in the electrometer just moved slightly. Then switch (3) was thrown in, and the measurement made in the usual manner. 1 Zeit. phys. Chem. 25, 265 (1 Single Differences of Potential 19 This method of using the electrometer as an indicating instru- ment requires that it should always be short-circuited on itself when not in use. In this respect at least, too great care in its use cannot be taken. Prelnmnary measurements. — The results of Paschen's ex- periments with electrodes of va- rying lengths, and tips of vary- ing rates of discharge appeared at first sight somewhat strange, but a repetition of them leads to their confirmation. There was found for every electrode height a minimum diameter of the capillary tip, and hence a minimum flow below which the measurements did not agree when the other conditions were kept alike as far as possible. But when these so-called "crit- ical" heights had been deter- mined, it was found that the same values were obtained whether one used an electrode 80 cm long, which gave a stream of mercury 2 mm long before breaking, or one of 175 cm giving a 35 mm stream, or of any intermediate values of heights of electrodes or lengths of streams. The 8 mm stream with which many of the measurements were taken was so chosen merely be- cause it served better to keep the electrolyte in the funnel at the constant level. The values obtained by having the mercury break below the surface of the electrolyte, and by having the tip itself dip below the surface, were also of interest. In the latter case one could, by making the mercury flow in a stream of large cross- section and from low pressures, obtain, e. g. with Hg | HC1 1 S 1 or 1 S is used throughout the paper to denote the dropping mercury — in con- formity with the nomenclature used by the first German investigators ( Strahl- electrode). 20 Hector R. Carveth Hg i H 2 S0 ! S, values approaching zero. By decreasing the cross-section, and increasing the pressure, the value was raised. A brief statement of the facts observed would be that almost any value may be observed which ranges from zero up to that maxi- mum which is obtained by having the mercury break just at the surface. (We are here dealing with the case of Hg| electro- lyte I S.) Similar results seem to have been obtained by Paschen, 1 although he does not draw especial attention to them. It was found by the writer that it was possible to obtain fairly constant readings when the mercury broke below the sur- face of the electrolyte. Two illustrations are given to show this. The mean value for S I KCl(i) I KCl(i)Hg 2 Cl 2 i Hg was found to be 0.560 volt. This is the average of a great number of observa- tions of which the extreme variation from the mean was 0.003 volt. The electrode tip was then adjusted to break below the surface of the solution so that on three different occasions it gave the values 0.514, 0.519, 0.523 volt respectively. The normal electrode was then replaced by different metals in solutions of their salts, and the combination S KCl(i) i metallic salt (2) ! metal, measured. Knowing the electromotive force of the whole cell, Hg ! Hg 2 Cl 2 KCl(i) i metallic salt(a) i metal, we should be able by subtracting the two numbers obtained in the measurements to obtain a constant number for the value SKCl(i)!KCl(i)Hg 2 Cl 2 jHg. This is shown in the following table : — Table I A. E.M.F.of whole cell I la II Ha III Ilia ZnCl,Zn ZnSO„Zn Zn(Ac),Zn CuSO.Cu Cu(NO,),Cu 1-057 1.079 1.083 0.019 0.047 0.546 0-575 0-574 0.540 0.566 Mean 0.511 0.504 0.507 0.521 0.519 0-539 o.559 0.558 0-535 0.561 Mean 0.518 0.520 0.525 0.516 0.514 0.521 0-535 o.557 0-555 o.539 0.564 Mean 0.522 0.522 0.528 0.520 0.517 0.512 0.522 1 Wied. Ann. 41, 50 (1890). Single Differences of Potential 2 1 In column A are given the electromotive forces of the whole cell, Hg J Hg 2 Cl 2 KCl(i) J metallic salt(2) I metal, copper being cathode when it was used, and zinc anode when it was used. In columns I, II and III are found the values of S KCl(i) | metallic salt(2) I metal, the electrode tips being adjusted to different positions in the three cases, but always having the same adjust- ment for one series. la, Ha and Ilia give the values for S KCl(i)Hg 2 Cl 2 Hg which should be found, in case the sum of the values S KCl(i)i metallic salt(2)metal and S KCl(i)iKCl- (i)Hg 2 Ch I Hg were equal to the value of the whole cell as given in column A. These three columns are therefore obtained by subtraction of columns I, II and III, respectively from A. For the same adjustment of the electrodes was actually found for S KCl(i)| KCl(i)Hg 2 ClHg in la 0.514 in place of 0.512 Ila 0.519 in place of 0.521 Ilia 0.523 in place of 0.522 The variations are easily explained by the slight jarring of the electrode clamps when changing one half-cell for another. This is clearly proved by noting the way in which the variations from the mean value occur. In the case of measurements where the mercury broke just as it met the surface of the liquid it was found possible to make adjustments better than in the experi- ments here indicated. The table given above is the shortest one of a number made with potassium and hydrogen chlorid, in dilutions of 1, 10 and 100 liters; but it shows clearly the points to be illustrated — that by preserving like conditions in the ad- justment of the breaking point of the mercury one may repeatedly obtain the same value for S I electrolyte | metal, and also that, as would be expected, the sum of S I electrolyte i | electrolyte i | metal r and S I electrolyte i | electrolyte^ | metal 2 is equal to the electromo- tive force of the whole cell metal, | electrolyte, | electrolvte 2 1 metal,. Other experiments were made to ascertain if the absolute value of S i KC1 Hg were the same as when a depolarizer was present. ■ Other electrolytes were also used in place of potassium 22 Hecter R. Carveth chlorid. The results proved that if the measurement were taken after the mercury had remained for some time in the electrolyte, and when it was perfectly quiet, the same electromotive force might be observed as when the depolarizer was present. The results were, however, very variable, and so it was thought ad- visable not merely to use a depolarizer, but always to allow the half-cell when made up to remain some time before being meas- ured. The following table allows of a comparison being made between the results obtained by Paschen in two ways — B by the drop electrode, C by polarization method, while under A stand my own measurements obtained as absolute values. Table II A B C A B C HCl(i) o.557 0.560 0.561 HBr(o. 9 8 33 ) .... 0. 459)0. 501 HCl(io) 0.605 o-55i o.553 HBr(io) .... 0.470 ,.494 HCl(ioo) 0.659 0.584 0.622 HBr(ioo) .... 0.488 ! 5.528 KCl(i) 0.560 o.539 .... KI(i) 0.412 0.400I .... KCl(io) o.593 0-553 KI(io) o.455 0.41210.426 KCl(ioo) 0.6200.584 KI(ioo) 0.497 0.412! .... NaCl(i) o.557 0.556 K 2 S0 4 (2) 0.922 jo. 670-0. 734 NaCl(io) o.593 o.557 0.560 K,S0 4 (2o) 0.89710.700-0.745 NaCl(ioo) 0.626 0.590 .... K 2 S0 4 (200) o.8i2;o. 720-0. 743 BaCl 2 (2) 0.584 0-555 .... H,SO,(i-6) o.975 0.934 .... BaCl 2 (2o) 0.615 0-553 .... H 2 S0 4 (i) 0.931 BaCl„(20o) 0.639 0.586 H 2 S0 4 (2) 0.921 0.818-0.853 MgCl s (2) 0.582 o.547 .... H,SO,(io) 0.875 MgCl 2 (2o) 0.600 0.548 .... H,S0 4 (20) 0.868 0.797-0.824 MgCl 2 (20o) 0.624 0.580 .... H 2 SO,(ioo) 0.818 KBr(i) 0.490 0.483 0.488 H a S0 4 (2oo) 0.818-0.834 KBr(io) 0.542 0-493 0.494 KBr(ioo) 0.584 0.505 0.509 Discussion. — The first glance shows that the values given in A and B do not agree any too well. It would indeed be a matter of surprise if two investigators working on this subject should obtain values agreeing at all well, for probably in few other fields of physico-chemical measurement is there present, at least with our present imperfect apparatus, such scope for per- sonal error. An attempt was made to eliminate this by repeat- Single Differences of Potential 23 ing the observations from three to ten times. At dilutions of one liter, the variations from the average were 0.002 volt. At dilutions of 100 liters, variations were 0.008 volt. But where the chance of the variation comes in is in the adjustment of the ' breaking ' point of the mercury. From the measurements in A it might seem as if the adjustments regulated by the use of the electrometer to detect the passage of a current were more sensitive than the method employed by Paschen. This, how- ever, is not claimed, although it is by no means impossible. Other conditions at present unknown, may have caused the vari- ations. The latter are most apparent in dilute solutions, where the difficulties of measurement are greater than in the more con- centrated. The fact that the values found by me for dilutions of 100 liters vary from those obtained by the polarization (capillary electrometer) method, counts for little, since in these solutions it is extremely difficult to ascertain where the maximum of sur- face-tension actually is. If the very careful measurements of Paschen on this subject 1 are right, it would indicate either that some conditions under which he worked were different from mine, or else that the values obtained by me were those corre- sponding to different parts of the descending branch of the polari- zation curve after it had passed through its maximum of surface- tension. From the standpoint of either the Helmholtz or the Warburg theory, this latter conjecture must be discarded as im- possible. A test of the former by repetition of the polarization measurement could not be attempted, the apparatus at my dis- posal not being sufficiently sensitive to read with the accuracy obtained by Paschen, viz., 0.1 mm. It is probable that the presence of the depolarizer in the combinations measured by me had a very considerable influence, and that a repetition of the measurements by the polarization method, with depolarizer present, would give values different from those obtained by Paschen. This, however, must remain an open question at present. In opposition to the results of Paschen it would appear that both anion and cation have an effect. The effect of the anion 1 Wied. Ann. 43, 579 (1891). 24 Hector R. Carveth may be observed especially between potassium chlorid, bromid, iodid and sulfate. KCl(i)= 0.560, KBr(i)= 0.490, KI(i)=o.4i2, K ? SO (2)= 0.922. The effect of the cation is not so apparent from the previous table, but is shown well by the following : — CuSO,(2) |Hg = 0.200 K a S0 4 (2) |Hg=0. 9 22. The effect of concentration appears from column A to be more regular than is apparent in column B. In all cases (with one exception, HC1) where attention was paid to this subject, regularity was found — either with increasing concentration the electromotive force increased else it decreased. Thus with sul- furic acid a case of the former may be observed and with sodium chlorid, a case of the latter. Hydrochloric acid, according to Paschen's 1 measurements, seems to give a decreasing value as the solution becomes more dilute, passes through a minimum and then again increases. The following results obtained by myself confirm this : — S|HCl(o.i) Hg,Cl,|Hg 0.645 S|HCl(i) Hg.Cl.IHg 0-557 S|HCl(o.i25) Hg 2 Cl 2 |Hg 0.631 S|HCl(io) Hg.CI,|Hg 0.605 S|HCl(o.2) Hg,Cl,|Hg 0.609 S|HCl(ioo) Hg,Cl,|Hg 0.659 S|HCl(o. 5 ) Hg,Cl,|Hg 0.590 It is thus very apparent that the effect of varying the concentra- tions of different electrolytes is not always regular. In the light of our present knowledge, it is not possible to say which are ' normal ' or which are ' abnormal' cases. A number of measurements were also taken for combina- tions of this type : — S metallic salt | metallic salt | metal. In the following table, the figures at the head of the column denote the number of liters in which one gram-molecular weight of the metallic salt is dissolved, while the results obtained are given in the columns. The arrow points toward the cathode. 1 Wied. Ann. 41, 54 (1890). Single Differences of Potential Table III 25 (2) (20) (200) Cd|CdCl 2 S • • ■ • 0.170 0.258 0.309 Cd|CdBr 2 S .... 0.136 0.165 0.218 Cd|CdI, S .... 0.113 0.128 0.157 Cd|CdS0 4 S .... 0.248 0.335 0.362 Cd|Cd(N0 3 ) 2 S .... 0.132 0.249 0.283 Ni|NiCl 2 S 0.125 0.250 0.239 Ni|NT(N0 3 ), S 0.156 0.249 0.274 - (1) (2) (20) (200) Zn|ZnCl, S 0.514 0.526 0.585 0.639 Zn|ZnBr 3 S 0.460 0.468 0.513 0.582 Zn|ZnS0 4 S 0.645 0.653 0.685 0.734 Zn|Zn(Ac) 2 S 0.630 0.634 0.649 0.695 Cu|CuS0 4 S O.OIO 0.019 .... — Cu|Cu(N0 3 ) 2 S 0.056 0.024 .... .... Pb|PMNO,), S O.I2I O.IOI 0.105 — PbTPb('Ac) Q S 0.170 0.125 0.159 — In this table also may be noticed the change of the elec- tromotive force produced by changing the concentrations, as well as that produced by the variation of the anion. The effect of increasing the concentration of the zinc and cadmium salts is to cause the electromotive force to fall quite regularly ; similarly for copper sulfate and nickel nitrate. The lead salts apparently- pass through a minimum in the same manner as hydrochloric acid, while nickel chlorid seems to pass through a maximum. The effect of variation of the concentration may also be shown by figures gathered from Paschen's measurements 1 with ZnSO and Zn. In column A are given the specific gravities of the solutions at the (conjectured) temperature of 18 . In column B are given the values found for Hg |Zn'S0 4 IZn. (All the elec- tromotive forces in this table are expressed in terms of Daniell cell.) In column C are given the values which he obtained for S ZnSO IHg. In column D may be found the values of Wied. Ann. 41, 63, 66, 179 (1890); 43, 570, 57i (1891). 26 Hector R. Carveth S ZnSO | Zn, either given directly by Paschen's measurements (observed) or calculated from the two previous columns by subtraction of the value given under C from that in B (cal- culated). Table IV A B c D Spec, gr Hg | ZnS0 4 1 Zn S ZnS0 4 1 Hg S ZnS0 4 1 Zn i-°54 ■ ■ . • .... O.5876 Observed i 163 .... .... O.5699 1 ' i 305 I- 157 0.598 0.559 Calculated i 316 I.224 0.681 0-543 1 1 i 40 1. 150 0.607 o.53I ' ' i 403 I.240 0.709 Q-53 1 " i 406 .... .... 0.5358 Observed i 409 1. 1 70 0.639 0.53I Calculated i 433 1. 167 0.640 O.527 1 ' i 456 0.5I9 Observed It is to be observed from this method of arranging the results of Paschen that the concentration effect is, with zinc sulfate at least, a very regular one, and shows that in this case the low electromotive force is to be observed in the most concentrated solutions. If the values found above in Table III give the actual potential difference between a metal and a salt of the metal, a comparison with those predicted by the Nernst theory should allow us to see whether there were agreement between the • ob- served and predicted values. According to this theory the potential difference between a metal and a solution of its salt may be thus formulated o 0002T logr- A (1) where P is a pressure function depending on the nature of the electrode, and p z denotes the osmotic pressure of the metallic ions in the solution. Accordingly, if there are chosen two iso- hydric solutions of different salts of a metal, the term p and hence also the potential difference between metal and the solu- Single Differences of Potential 27 tion of the salt of the metal will be the same for each solution. Now equimolecular solutions of zinc chlorid and zinc bromid are practically isohydric in respect to the zinc ions ; but it will be observed (Table III) that the values given by the dropping mercury method for the potential differences Zn | ZnCl ? and Zn|ZnBr 2 differ very considerably — the difference varying from 0.054-0.072 volt with changing concentration. Similar results are obtained when any of the other values given in Table III are examined in this way. If in place of choosing isohydric solutions, one chooses differently concentrated solutions of the same salt, the pressure p will vary in a way which may be determined by conductivity measurements, and for a solution of different concentration from the one used in equation (1) may be called p n . The difference of potential between the electrode and this solution will be 0.0002 T. P v 2 — lo g->r- ( 2 ) The difference between the two single potentials at the electrodes will be 0.0002T, p. , . n L a p^ Inserting for p and p^ values corresponding to normal and tenth-normal solutions, and for //, the valency of the metals used (in this case two) it is found that at ordinary temperatures 0.0002 X (273 + 17) H / \ „-— „- = '-^— ■ — — =0.029 volt. (4) 1 1 2 The table which is now to be given contains values which may determine whether this formula holds. In the first column are denoted the metal and its salt ; in the column (2) — (20) are o-iven values obtained by subtraction of the values given in column (20) from those in column (2) of the same table ; in the column (20) — (200) are given values obtained by subtraction of the values given in column (200) from those in column (20). 28 Hector R. Carveth Table V (2)— (20) (20) — (200) (2)-(20) (20) — (200) Cd|CdCl 2 0.088 0.051 Zn|ZnCl 2 O.O59 O.O54 Cd|CdBr 2 0.029 0.053 ZnlZnBr, O.O45 O.069 Cd|CdI 2 0.015 0.029 ZnlZnSO, O.O33 O.O49 Cd|CdS0 4 0.087 0.027 Zn|Zn(Ac) 2 O.OI5 O.O48 Cd|Cd(N0 3 ) 2 0.117 0.034 Pb|Pb(N0 3 ) Q 0.020* O.OO4 Ni|NiCl, 0.125 0.01 1* Pb|Pb(Ac), 0.055* O.O34 Ni|Ni(N0 3 ), 0.093 0.025 It is to be observed from the table that in all cases except the ones marked with the asterisk, the difference of potential is in the same direction as the theory requires. Where, however in one column the numerical value seems to agree with the theoretical one (equation 4) as closely as the experimental error would allow, the value in the other column diverges considerably from what it should be. Speaking generally, we must there- fore conclude that the dropping electrode does not give the values which the Nernst solution-pressure theory would require. If from Table II a table is prepared in a similar manner, irregular results such as appear in the last table would be found present ; but it must be pointed out that the values obtained for HC1, KBr and KI in dilutions of 1, 10 and 100 liters, approxi- mate values required by the Nernst theory. Thus arranging the table in exactly the same way as Table V. Table VI (i)-(io) (10) — (200) Hg|Hg 2 Cl 2 HCl Hg|Hg,Br 2 KBr Hg|Hg,I,KI 0.052 0.052 0.043 0.054 0.042 0.042 The value as predicted by the Nernst theory is ■k =0.058 volt. * Values marked with asterisk denote currents running in other directions. Single Differences of Potential 2 9 Hydrochloric acid shows the best agreement with the theoretical value, but this and the other values given above are in my opinion to be regarded as accidental so far as the Nernst theory is con- cerned. Reference need only be made to the table (III) where it is to be noted that if drop electrode values be regarded as true single differences of potential, a solution containing 5 gram-mols of HC1 per liter will have approximately the same potential against the electrode as a solution containing 0.1 gram-mol of HC1 ; which can hardly be accepted as a fact. Whoever upholds the correctness of the view that single differences of potential may be determined by means of dropping mercury electrodes, must necessarily assume that the contact surface of two electrolytes is the seat of a potential difference, whose value may by no means be neglected. This follows directly from the consideration of any combination such as, Zn|ZnS0 4 (2) |CuS0 4 (2) |Cu, whose value was found on measurement to be 1.098 volts. By dropping electrodes we found Zn |ZnSO (2) = 0.653, an d the same method gave for CuSO (2) |Cu = 0.019. Whence it follows that at the contact surface of ZnSO (2)1 CuSO (2) there must exist a potential difference of (1.098 — 0.653 + 0.019) volts, i. e. 0.464 volt. Selection of any other values from Table III will illustrate the same point. Further emphasis is given this fact by the following table of values, where the normal electrode side of the cell has been retained throughout, but the electrolyte into which the mercury fell was varied. In the table, N. E. is used to represent the normal electrode half-cell. In all cases, except with the solution of copper sul- fate and nitrate, the mercury of the normal electrode was cathode. Table VII SKCl(i)|N.K. SCdCl a (2)|N.E. SCdBr(2) |N.E. o.559 o.555 o.595 SZnCAc) 2 (2)|N.E. SCuS0 4 (2) |N.E. SCu(N0 3 ) 2 (2)|N.E. SCd(NO s ) s (2)|N.E. SZnCl 2 (2)|N.E. SZnS0 4 (2) [N.E. o.449 0.036 0.068 o.549 0.530 0.426 3<3 Hector R. Carveth Here instead of all the values coming out 0.559 as would be expected if there were no potential differences between the solutions, they fluctuate very much, and in the case of copper sulfate, actually change sign. One is then forced to ask the question : Is it probable that between solutions of approximately the same concentration such enormous potential differences may be considered present? Since, for obvious reasons, no direct ex- perimental test of this can be given at present, it is necessary to obtain an opinion on this subject from a consideration of the phenomena at the surface of the two liquids. This is exactly what Nernst had to do before it was possible for him to reach his con- clusions in respect to the electromotive force present at the con- tact surface of liquids. In support of his views, we have much evidence, both experimental and theoretical ; in support of the idea that there exist large potentials at the boundary surface of electrolytes, there is no evidence at all, save such as is based on this method of determining single differences of potential. So-called irreversible electrodes. — The question has often been raised as to whether a cell containing one electrolyte and two electrodes of different chemical nature has a perfectly definite value. Measurements with cells of this type have been made by Ostwald, Bancroft, Braun, Oberbeck and Edler, Paschen, Taylor and others. A summary of some of the measurements (this Journal 1, 9, 1896) shows that the results agree with each other none too well. An attempt was made by the writer to repeat these measurements, but as it was found too tedious and un- profitable to sit down and wait varying periods of time to allow such combinations to come, to a maximum, 1 the following plan suggested itself. In the measurement of a combination of such a type as ZnlKCl |Cd, if there were any variation in the elec- tromotive force caused 'by the lapse of time, this would probably be caused by the variations at both electrodes. Measurements at different times would thus always show the sum of the effects, whereas it is always desirable to examine the single variations when this is possible. Accordingly use was made of the potas- 1 Taylor. Jour. Phys. Chem. 1,3(1 Single Differences of Potential 3 1 sium chlorid, mercurous chlorid, mercury electrode, which had been found by Coggeshall 1 to give very constant results. The cell was then made up, e.g. Hg|Hg 2 ClKCl(i) |KCl(i) |Zn, the two vessels, each of which held one electrode, being connected by a siphon as in previous experiments. Then another metal was measured against the normal electrode, e.g. Cd|KCl(i)| KCl(i)Hg 2 ClJHg. The difference in the two measurements gives the value Zn ,KCl(i) |KCl(i) |Cd (calculated). The cells were measured immediately after setting up. The correspond- ing results are given under I. They were then measured 24 hours (II) and 48 hours (III) later. Under ' found ' values are given those actually observed ; under ' calculated ' those obtained by subtraction of the potentials in question. These should agree ; any disagreement rises from errors of measurement. Table VIII I Hg|Hg,Cl,KCl(i) Hg|Hg 2 Cl 2 KCl(io) Hg|Hg a Cl 2 KCl(ioo) Cd Cu Zn o. 8190. 284I1. 085 o. 83210.255 1. 170 0.845I0.230II.264 Cd — Zn found calc. O.2760.276 O..3380.33 8 O.419S0.419 Cd — Cu found calc. Zn — Cu found calc. o.534|o.535:,°-799|°.8oi o.577jo.577 ! °.9i5iO-9i5 0.614,0.615110.0374.034 II Hg|Hg,Cl,KCl(i) Hg|Hg 2 Cl 2 KCl(io) Hg|Hg 2 Cl 2 KCl(ioo) 0.810 0.8591 0.890I 1. 119 1.208 1.247 0.310 0.350 o.358 0.309 o.349 o.357 III Hg|Hg,Cl Q KCl(i) Hg|Hg,Cl,KCl(io) Hg|Hg 2 CLKCl(ioo) 0.817 0.855 0-935 0.285 0.205 0.245 1. 127 I.I35J 1. 1 50. 0.309 0.279 0.215 0.310 0.280 0.215 0-531J0.532l0.8400.S42 0.6500.6501 0.690)0. 690) 0.928(0.930 0.906)0.905 ' Zeit. phys. Chem. 17, 62 (1895). 32 Hector R. Carveth Discussion. — The extreme irregularity of the results at once attracts attention. While other observers have found a maximum value for the combinations, it is found by this method (which should assuredly be a more accurate one) that even after two days have passed, the values are not yet definite and con- stant. That chemical action had taken place at the contact sur- face of metal I electrolyte was certain. If then such an action were so apparent as to be observable after a few hours, it is cer- tain that it would be impossible to leave it out of a theoretical consideration of the subject, even if the metal had been in con- tact with the electrolyte only so long as would be required for the measurement. The conclusion then presents itself that in all measurements which have been made by this method, since they were made in an atmosphere containing oxygen, and in electrolytes containing oxygen, this oxidizing action must be present. The effect of the presence of oxygen on the electromo- tive force of cells was examined very carefully by Warburg, 1 whose results have been confirmed by Paschen. 2 Their results, however, seem to have been overlooked by later writers on the subject. In giving the few and necessarily incomplete results above, the author wishes merely to insist that the claims of Warburg and Paschen are correct, i. e. that the oxygen of the air has an effect in causing a change in the electromotive force of a cell where irreversible electrodes are used. Before the cells given in the last table had been measured, the writer had made a large number of measurements with combinations such as S KC1 |Cd; the table shows that the measurements should all vary with the time the electrolyte had been in contact with the electrode. Such of course was found, the measurements not agreeing from day to day. They were of importance only in the consideration of the question whether it was advisable to use reversible or the so-called irreversible electrodes in the half-cells when making measurements with the drop-electrodes. 1 Wied. Ann. 38, 321 (1889). 2 WieJ. Ann. 43, 568 (1891). Single Differences of Potential 33 Comparison with Rothmund. — Among the many interest- ing measurements bearing on the question as to the relations be- tween surface-tension and polarizing currents are those of Roth- mund, 1 who determined the electromotive force necessary to polarize amalgams to their maximum. The electrolytes used were sulfuric and hydrochloric acids, containing dissolved in them an arbitrary amount of the salt of the metal contained in the amalgam. Having determined these maximum values by use of interpolation curves, he compared them with the values calculated from the whole cell, assuming Hg |H 2 S0 (2) = 0.926 and Hg|HCl(i) = 0.560. In the following table are collected under column "Polarization method" the results obtained when he made use of this interpolation-curve method ; under column " Calculated " are to be found the results obtained, when he sub- tracted from the electromotive force of the whole cell the value he obtained by the polarization method for his normal electrode. Under the column " Drop-electrode " are to be found the values obtained by the writer when he made use of combinations such as S H S0 4 (2) saturated with Hg 2 S0 4 |H 2 S0 4 (2)Hg 2 S0 4 |Hg. Table IX Polarization Drop method Cale electrode Hg|Hg 2 S0 4 H 2 S0 4 (2) 0.926 .... 0.921 Hg|Hg,Cl.HCl(i) 0.560 .... 0.560 Pb|PbS0 4 H 2 S0 4 (2) 0.008 0.003 0.004 Cu|CuS0 4 (ioo)H,S0 4 (2) 0-445 0.481 0.221 Zn|ZnS0 4 (ioo)H 2 S0 4 (2) —0.587 —0.546 — 0.629 Cd|CdS0 4 (ioo)H„S0 4 (2) — 0.079 — o.i6a — 0.280 Hg|HgI,(ioo)KI(i) 0-437 O.I57 0.120 In this table numbers after the chemical name represent the number of liters in which one gram-equivalent was con- tained. When no figures are given, a solution of the substance, saturated at 20 C, is denoted. Of the seven cases here compared, it is to be seen that only in the first three do the values obtained by both methods agree Zeit. phys. Chem. 15, 1 (1894). 34 Hector R. Carve th at all. As to the other four cases, one method gives values about as near to the calculated as the other, and with neither method is there good agreement with that value. That the values given in Table IX represent single differences of potential can cer- tainly not be maintained by the adherents either of the Helm- holtz or of the Warburg theory. The former requires that the electrode shall be polarizable, and certainly a zinc amalgam in a solution of a zinc salt is not to be regarded as a polarizable electrode.' As previously stated, the Warburg theory does not regard these values as single potentials at all, but rather as a sum of several potential differences. To these measurements, there- fore, regarded as determinations of single differences of poten- tial, no importance can be attached. This conclusion is strengthened by a closer consideration of the values which Rothmund considered as fully determined, e.g. Hg|H 2 S0 4 (2) =0.926 Hg|HCl(i) =0.560. When he formed the cell Hg|H gl S0 4 H,S0 4 (2)|HCl(i)Hg,Cl,|Hg he 2 found for its value 0.369 volt, whereas its value calculated from polarization was 0.366 volt. But if now in the place of using normal solutions of the acids, he had made use of tenth- normal solutions and applied values obtained from either the drop electrode or the polarization method, he would have calcu- lated values (using the writer's values) of 0.868 — 0.605 = 0.261 volt, or for hundredth-normal solutions, 0.818 — 0.656 = o. 159 volt, whereas the values actually obtained will in each case be very much higher than these. The differences here observable can- not, if the Planck theory be accepted, be due to the potential 1 Compare with Le Blanc who disagrees ( English edition Le Blanc's Elec- trochemistry, 214) and with Nernst (Jahrbuch der Electrochemie, 1, 38 (1894)), who thinks it probable that on polarizing zinc amalgam the zinc is dissolved until there is left a surface of pure mercury. 2 Meyer found for this combination 0.407 volt. Single Differences of Potential 35 difference at the boundary surfaces of the two acids. From the consideration of this case, we must therefore draw one of two con- clusions : (a) The Hehnholtz theory is applicable here in the case of normal sulfuric and hydrochloric acids, the amount of mercurous salt being so small as to be left out of consideration entirely. (6) By some coincidence not explained by the Helmholtz theory, the values obtained for Hg| H 2 S0 4 (2) and Hg|HCl(i) by both the polarization and the dropping mercury method add up to give the electromotive force of the cell, whereas if other dilu- tions of these acids be used, the values agree no longer. Conclusion (a) cannot be correct since the presence of anv mercurous salt is sufficient to exclude the mercury in this case from being classed as a polarizable electrode to which alone the Helmholtz theory applies. That it may under certain experi- mental conditions be polarized is also true, but the fact that the disturbing influence exerted by the presence of the salt is not definitely known certainly prevents a rigid application of this theory. The second conclusions seem the more probable. Since therefore the results of Rothmund may not be ex- plained by the theory which they are given to support, and do not agree with the results predicted by this theory when one employs for the determination of these values the other method which is supported by this theory, grave doubts must be cast upon their being true single potential differences. The work of Luggin 1 has been directed toward an exami- nation of the two theories which attempt to explain the relation existing between electromotive force and surface-tension. His method consisted in polarizing mercury in an electrolyte until it had reached its maximum surface-tension, and in then measur- ing it against a normal electrode. The Helmholtz theory would require that in these cases almost the same potential should be observed, no matter what the electrolyte was. Experimentally Luggin found values which could not fulfil this requirement in its strictness, but so many regularities were found that it is cer- 1 Zeit. phys. Chem. 16, 677 (1895). 36 Hector R. Carveth tain the chemical theory alone cannot account satisfactorily for the alteration of the surface-tension. It is an easy step to pass from the conclusions of Luggin to the explanation that the Helmholtz theory does hold, but that exceptions are found where other and secondary influences may also affect the surface-tension. Under such a category must be placed the influence exerted by the salts of the metal or amalgam polarized. It may be found possible to discover the experimental conditions which must prevail in order that the Helmholtz formula may apply. One of these will of course be that the change of surface-tension energy into electrical energy shall be completely reversible. Another has been recently in- dicated by Wiedeburg, 1 who has shown that the formula holds only when a current does not pass when the mercury is polar- ized to its maximum. According to his view the values ob- tained are always higher than the true single differences of potential. Wiedeburg has also drawn attention to the fact that the measurements made with a view of testing the theories of today should be made under as simple conditions as possible. The principal conclusion to be drawn from this paper is that neither on the ground of the Helmholtz theory, the War- burg theory nor that of Nernst 2 is there reason for regarding one single potential difference as known. Some of the conditions which must be observed before applying the Helmholtz theory have been noted. Cases where the dropping electrode gives values corresponding to the polarization method have been ob- served, as well as cases where a difference in the values occur. It has been found that the values obtained by the dropping electrode with different concentrations of the same electrolyte apparently follow in regular order ; also that both the anion and the cation affects the values obtained. The solution-pressure formula of Nernst has been tested by use of the drop-electrode and found to hold approximately in a few cases, while in the great majority of cases it failed. The action of oxygen on the 1 Wied. Ann. 59, 744 (1896). 2 Palmaer. Zeit. pliys. Cliem. 25,265 (3898). Single Differences of Potential 37 electrodes of irreversible cells has also been briefly examined, and the views of Warburg and Paschen thus substantiated. The main query of the paper, however — "Are the values given by the drop electrodes true single differences of potential " must be answered in the negative. The writer wishes to express his warmest thanks to Profes- sor Bancroft, both for the suggestion of the subject of investiga- tion and for the assistance and encouragement he has given in carrying it to completion. Cornell University S^W-aBtS