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A Study of the Transference Numbers of 
 Sulfuric Acid and the Influence of 
 Gelatin on the Transference 
 Numbers by the Concen- 
 tration Cell Method 
 
 A THESIS 
 
 SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE 
 UNIVERSITY OF MICHIGAN IN PARTIAL FULFILLMENT OF 
 THE REQUIREMENTS FOR THE DEGREE OF DOCTOR 
 OF PHILOSOPHY 
 
 June 1921 
 
 By 
 Wesley George I France 
 
 EASTON, PA. 
 ESCHENBACH PRINTING COMPANY 
 
 JUNE 1921 
 
A Study of the Transference Numbers of 
 Sulfuric Acid and the Influence of 
 Gelatin on the Transference 
 Numbers by the Concen- 
 tration Cell Method 
 
 A THESIS 
 
 SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE 
 
 UNIVERSITY OF MICHIGAN IN PARTIAL FULFILLMENT OF 
 
 THE REQUIREMENTS FOR THE DEGREE OF DOCTOR 
 
 OF PHILOSOPHY 
 
 June 1921 
 
 By 
 
 Wesley George France 
 tf 
 
 EASTON, PA. 
 
 ESCHENBACH PRINTING COMPANY 
 JUNE 1921 
 
F/ 
 
 *CHANGfc 
 
TABLE OF CONTENTS. 
 
 I. Introduction 5 
 
 II. Historical ' 5 
 
 III. Theoretical 7 
 
 IV. Apparatus and Materials 9 
 
 V. Arrangement of Cells and Method of Procedure 10 
 
 VI. Experimental Results with Sulfuric Acid 11 
 
 VII. Experimental Results with Sulfuric Acid Containing Gelatin 17 
 
 VIII. Summary 27 
 
ACKNOWLEDGMENT. 
 
 The author wishes to express his appreciation for the most valuable 
 aid and advice given during the progress of this work by Doctor Alfred L. 
 Ferguson, at whose suggestion and under whose direction it was carried out. 
 
 It is with much pleasure that acknowledgment is made to Professor 
 S. Lawrence Bigelow, for his many valuable criticisms. 
 
A STUDY OF THE TRANSFERENCE NUMBERS OF SULFURIC 
 ACID AND THE INFLUENCE OF GELATIN ON THE 
 TRANSFERENCE NUMBERS BY THE CON- 
 CENTRATION CELL METHOD 
 
 INTRODUCTION. 
 
 Three methods have been used for the determination of transference 
 numbers ; the analytical, the moving boundary, and the concentration cell. 
 The oldest and most generally used is the analytical discovered by W. 
 Hittorf. The moving boundary method was first described by O. Lodge 
 and has been developed and used by R. B. Dension and B. D. Steele. 
 The concentration cell method has been used in only a few cases and with 
 varying success; its reliability for uni-univalent electrolytes, however, 
 has been demonstrated in this laboratory. 
 
 The present investigation is an application of the concentration cell 
 method to the determination of the transference numbers of a uni-bivalent 
 electrolyte. In the first part of the work the electrolyte used was sulfuric 
 acid, and in the second part sulfuric acid plus definite quantities of gelatin. 
 
 Historical. 1 
 
 The first investigator to develop a successful method for the determina- 
 tion of transference numbers was W. Hittorf. (Pogg. Ann., 89, 177 (1853)). 
 In this work an electrolytic cell was used in which a strip of silver always 
 served as cathode and a metal which corresponded to the metal ion of the 
 electrolyte as anode. The transference numbers were calculated from the 
 change in concentration around the anode which resulted from the passage 
 of a measured quantity of electricity. This method was improved in 
 many respects by him during the next few years and, as finally used, was 
 the same in all essentials as the present Hittorf method. 
 
 Hittorf is given credit for the origination of this method for the determi- 
 nation of transference numbers, although there were several earlier in- 
 vestigations on the changes which take place about the electrodes during 
 electrolysis. As early as 1814 R. Porrett (Abst. Phil. Trans., 1, 510) 
 investigated the movement of iron and potassium ions when a solution of 
 ferrocyanic acid was electrolyzed. M. Faraday (Phil., Trans. 123, 682, 
 525, (1833)) studied the relative changes in acidity produced by electroly- 
 sis in equivalent solutions of NaOH and H 2 SO 4 . J. F. Daniell (Phil. Trans., 
 129, 97 (1839) ; 130, 209 (1840)) ; J. F. Daniell and W. A. Miller (ibid., 134, 
 1 (1844)); and M. Pouillet (Comptes rendus, 20, 1 sem. 1544 (1845)) 
 conducted similar investigations and were able to calculate from their 
 1 For a complete abstract and bibliography of Transference Numbers up to and 
 including the work of 1905, see J. W. MacBain. (/. Wash. Acad. Sci., 9, 1.) 
 
6 
 
 results migration ratios. The values so obtained are approximations 
 only, since strict quantitative procedures were not employed. 
 
 The moving boundary or direct method for the measurement of the 
 migration velocity of ions was first described by O. Lodge (Brit. Assoc. 
 Rep., 389 (1886)). Two cups with suitable electrodes and electrolytes 
 were connected by means of a horizontal siphon filled with gelatin which 
 contained phenolphthalein or some salt. When a current was passed 
 through the apparatus the diffusion of the ions caused either a color 
 change or a precipitation in the gelatin. As the diffusion progressed the 
 color change or precipitation produced a sharp boundary. From the 
 velocity of movement of this boundary the transference numbers were 
 calculated. 
 
 The concentration cell method was first suggested by von Helmholtz 
 (Ges. Abh., I 840, II 979) . By the use of thermodynamic principles together 
 with the phenomenon of vapor pressure, he showed that transference 
 numbers can be expressed by the ratio of the potential of a concentration 
 cell with diffusion to that of a concentration cell without diffusion. This 
 method appears open to fewer objections than either the analytical or 
 moving boundary methods. It has, however, been used less extensively 
 than the others. This is undoubtedly due to the difficulties encountered 
 in the construction of suitable electrodes. 
 
 The method was first experimentally tested by J. Moser (Wien. Sit- 
 zungsber., 92, Abth. II, 652 (1885). He obtained for the transference 
 numbers of the anions of ZnSC>4 and ZnCl 2 .64 and .71 which agreed well 
 with the values, .636 and .700, obtained by Hittorf . 
 
 No further use of the method was made until 1898. At this time G. 
 Kummell (Wied. Ann., 64, 655) determined the transference numbers of 
 ZnCl 2 , ZnSO 4 , CdCl 2 , and CdSO 4 . These results did not agree well with 
 those obtained by Hittorf. 
 
 The same year D. Mclntosh (J. Phys. Chem., 2, 273) made an investi- 
 gation of the method. The transference number of the hydrogen ion in 
 H 2 SO 4 , HC1, HBr, HI, and H 2 C 2 O 4 was determined. In most of the work 
 cells of the types 
 
 Pt H HC1 ci HC1 c 2 Pt H 
 and 
 
 Pt H HC1 cr- HgCl Hg HgCl HC1 C 2 Pt H 
 were used. However some work was done with cells of the types 
 
 Ptci HC1 ci HC1 CT- Pt a 
 and 
 
 Pt C i HC1 ci PtH HC1 c 2 Pt a . 
 
 As a result of his investigation, Mclntosh was led to conclude that the 
 method was not suitable for use with gas cells. This conclusion appears 
 to be founded on two facts ; the failure of the cells of the first type to give 
 
values in agreement with those of the second, and the lack of agreement 
 between the velocity which he obtained for the hydrogen ion and that 
 calculated from the conductivity data of Kohlrausch. That this con- 
 clusion was not entirely justified is evident from a consideration of the 
 rather wide variation between the cells intended to be duplicates. The 
 variation in some cases is .0015 volt. There also appears to have been 
 no effort made to maintain the cells at a constant temperature. From 
 the results obtained later, by other investigators, it appears that his diffi- 
 culty was not inherent in the method, but in the construction of the 
 electrodes. 
 
 The same method was employed by D. A. Maclnness and K. Parker 
 in their determination of the transference numbers of KC1 (/. A. C. S., 
 37, 1445 (1915)). They used potassium amalgam and silver chloride 
 electrodes and obtained satisfactory results. 
 
 The most recent application of the method was in the investigation of 
 the transference numbers of HC1 by A. I,. Ferguson (J. Phys. Chem., 20, 
 326 (1916)). Hydrogen and calomel electrodes w r ere used the tempera- 
 ture was maintained at 25 C. The potentials were measured to .00001 volt 
 and the maximum variation of the cells was about .0001 volt. The trans- 
 ference numbers obtained agreed very well among themselves and also 
 with the best accepted values of other investigators. This work resulted 
 in the establishment of the value and reliability of the method when 
 hydrogen gas cells are used. This is in direct contradiction to the con- 
 clusion arrived at by Macintosh eighteen years earlier. 
 
 There is no accurate work, thus far, on the application of the method 
 to uni-bivalent electrolytes. 
 
 Theortical 
 
 The determination involves the measurement of the potentials of a 
 concentration cell without diffusion; a concentration cell with diffusion 
 and reversible with respect to the cation; and a concentration cell with 
 diffusion and reversible with respect to the anion. 
 
 The total potential of the concentration cell, reversible with respect 
 to the cation, Pt H | H 2 SC>4 d \ H 2 SO 4 c 2 1 Ptn consists of the algebraic 
 sum of the two electrode potentials and the potential at the boundary 
 of the solutions. On the assumption that sulfuric acid dissociates into 
 two hydrogen ions and one sulfate ion, the algebraic sum of the electrode 
 potentials is expressed by the well-known formula 
 
 &-5Tft,s. a, 
 
 b cz 
 
 The potential at the liquid boundary is expressed by the formula 
 
 2Uc-Ua RT ci 
 
8 
 
 The hydrogen electrode in the concentrated solution is positive with re- 
 spect to the hydrogen electrode in the dilute solution. At the boundary 
 of the solutions, the sulfuric acid diffuses from the concentrated to the 
 dilute side, and since the hydrogen ion moves faster than the sulfate 
 ion, the dilute side is positively charged with respect to the concentrated. 
 This means that the potential developed at the boundary opposes the 
 potential of the hydrogen electrodes. The total potential of the hydrogen 
 concentration cell is, therefore, expressed by the equation 
 
 RT a 2U C - U a RT ci 
 
 [2U C - Ua'} RT ci _ 3 U a 
 1 '" 2(U C + Ua)\ F H c* ~ 2 U a + 
 
 RT 
 Uc F 
 
 By the substitution of the transference number of N fl , of the anion for 
 
 U a /(U a + U c ) the equation 
 
 Et^N.Zjln* (3) 
 
 is obtained. 
 
 The total potential of the concentration cell, reversible with respect 
 to the anion Hg | Hg 2 SO 4 , H 2 SO 4 Ci | H 2 SO 4 c 2 , Hg 2 SO 4 | Hg, consists of the 
 algebraic sum of the two electrode potentials and the potential at the 
 boundary of the solutions. The algebraic sum of the electrode potentials 
 is expressed by the formula 
 
 The boundary potential is the same as in the hydrogen concentration cell, 
 and is in the same direction. The algebraic sum of the sulfate electrode 
 potentials is also in this direction. Therefore the total potential of the 
 sulfate concentration cell is expressed by the equation 
 
 _ RT ci 2U C - Ua RT ci 
 
 [1 2U C - Ua "1 RT 1 _ 3 Uc RT ^ ci 
 2 + 2(U C + Ua)] F H c,~ 2 Uc + Ua F H c 2 ' 
 
 By the substitution of the transference number, N c , of the cation for the 
 expression U c /(U a -+- U c ) the equation becomes 
 
 E&o 4 = - Nc 17 In - . (5) 
 
 2, r C'2 
 
 The potential of the concentration cell without diffusion, Pt H | 0.1 M 
 H 2 SO 4 , Hg 2 SO 4 , | Hg 1 Hg 2 SO 4 , 0.01 M H 2 SO 4 | Pt H , is represented by the 
 equation 
 
 E = \ R i ln l (6) 
 
9 
 
 The value E may be obtained experimentally from the difference between 
 the potentials of the cells Pt H 1 0.1 M H 2 SO 4 , Hg 2 SO 4 | Hg, and Pt H 1 
 0.01 M, H 2 S0 4 , Hg 2 S0 4 1 Hg. 
 
 Equation 5 divided by Equation 6 gives E SO JE = N c , which expresses 
 the transference number of the cation in terms of E S04 and E. In a. simi- 
 lar way the expression E H /E = N a , is obtained, as N a + N c = 1, there- 
 fore E so JE-\-E u /E = L; and 
 
 so 4 + H = E. (7) 
 
 It is evident from Equation 7 that the same value should be obtained 
 by the sum of the potentials E SOt and EH as by the difference of the po- 
 tentials EQ.QI and 0-1. 
 
 Since, to obtain the total potential, Es 0t , the boundary potential is added 
 to the electrode potentials, while for the total potential, E u , it is subtracted, 
 then, by a combination of these as shown below, a formula is obtained 
 which expresses the boundary potential in terms of E SOi and E H - 
 
 RT ci (2-3Ng)RT i Ci . RT Cl (2-3NJRT ci 
 
 EH = In --- - -- In - ; E SOt = - In - H -- - -- In -; 
 
 F cz 2 F ci 2F c 2 2 F ci 
 
 RT ci , 2(2-3N a )RT ci 
 2E S04 = *- + - -- -/- 
 
 2 S04 - H (2-3N a )RT i a 
 
 
 Therefore the value for the boundary potential may be obtained by the 
 substitution of the measured potentials E SOt and E H in the above equation. 
 
 Apparatus and Materials. 
 
 The potential measurements were made with an Otto Wolff 15,000-ohm 
 potentiometer, using a certified Weston cell as a standard. The solutions 
 were prepared from a commercial c. P. sulfuric acid of 1.84 sp. gr. and 
 were standardized by means of sodium carbonate prepared by the fusion 
 of c. P. sodium hydrogen carbonate in an atmosphere of carbon dioxide. 
 The mercurous sulfate was electrolytically prepared by the Hulett 2 method. 
 The hydrogen was obtained by the electrolysis of 5 N sodium hydroxide 
 solution using a generator similar to that of Bodenstein and Pohl, 3 and 
 the hydrogen electrodes were of the ordinary foil type. The mercury 
 used was twice distilled. All measurements were made with the cells 
 contained in an electrically heated and regulated oil thermostat main- 
 tained at a constant temperature of 25. 
 
 The concentration cell method, as previously shown, requires the con- 
 secutive measurement of 4 distinct potentials which must be extremely 
 constant and reproducible. Much experimental work was required before 
 the satisfactory system of cells shown in Fig. 1 was developed. In this 
 
 2 Hulett, Phys. Rev., 32, 257 (1911). 
 
 3 Bodenstein and Pohl, Z. Elektrochem., 11, 373 (1905). 
 
10 
 
 arrangement the connections, between the separate cells, are made by 
 means of siphons (M, N, H and G). A method whereby they could be 
 filled with the proper solutions before being connected with the arms of 
 the containers was considered essential. In this way new boundaries 
 could be introduced without disturbing the electrodes. Connections 
 were made with the cells through the reservoirs (R BI R b , R c , R d , Fig. 1) 
 on the arms of the containers. 
 
 Arrangement of Cells and Method of Procedure. 
 
 In Fig. 1, A and B are the mercurous sulfate electrodes; C and D are 
 the hydrogen electrodes. A and C contain O.I M and B and D 0.01 M 
 sulfuric acid. The electrodes A and C are connected by the siphon H, 
 B and D by the siphon G. The two sulfate electrodes are connected by 
 the siphon M; the two hydrogen electrodes by the siphon N. 
 
 The containers were fastened in their proper position and filled with the 
 electrode materials. The siphons H and G were put in place and filled by 
 suction. The stopcocks J and O, P and K were then closed. The hydro- 
 gen was admitted to C and D through the inlets S and S' and bubbled 
 through the solutions. It escaped through the outlets W and W' into 
 
 M H 6 V 
 
 R a^aegfe- 
 
 Fig. 1. Arrangement of cells as used. 
 
 chambers (not shown) of about 10 cc. capacity. When the hydrogen 
 electrodes became constant, the stopcock O was opened long enough to 
 measure the potential E i between the sulfate and hydrogen electrodes 
 in 0. 1 M sulfuric acid solution. In a similar way the measurement E O.QI 
 
11 
 
 was made for the sulfate and hydrogen electrodes in 0.01 M sulfuric acid. 
 By the proper manipulation of the stopcocks, the solutions in those halves 
 of siphons H and G connected to the sulfate electrodes were emptied. 
 The arms of the siphons M and N with the rubber stoppers attached were 
 immersed in 2 beakers which contained 0.1 M and 0.01 M sulfuric acid. 
 The solutions were drawn into the arms of the siphons and formed the 
 boundary within the stopcocks t and q. These siphons were then placed 
 in their proper positions connecting the cells. 4 The stopcock q was opened 
 and the potential E H of the hydrogen concentration cell measured. In 
 a similar way the potential of the sulfate concentration cell (.EsoJ was 
 measured. 
 
 The leads from the electrodes were permanently connected to a switch- 
 board so the potentials between any two electrodes could be measured 
 by the manipulation of a switch connected to the potentiometer. 
 
 In the first part of the work the measurements showed considerable 
 fluctuation, which was traced to the leakage of current from the high 
 potential electrical circuits in connection with the thermostat. The 
 difficulty was overcome by the replacement of the water by kerosene. 
 
 During the development of this work some information was obtained 
 which may be of assistance to others concerned with similar investigations. 
 It was found that the length of time required for the mercurous sulfate 
 electrodes to reach a condition of equilibrium could be greatly reduced 
 by vigorously shaking the sulfuric acid and mercurous sulfate in a me- 
 chanical shaker before using in the cells. The first cells constructed con- 
 tained the hydrogen electrodes in the same chamber as the mercurous 
 sulfate electrode and the potentials were found to vary greatly. This 
 was believed to be due to the catalytic effect of the platinum black which 
 was loosened by the action of the hydrogen on the electrode and fell on 
 to the mercurous sulfate. The difficulty was eliminated by the use of 
 separate chambers for the electrodes. 
 
 Experimental Results with Sulfuric Acid. 
 
 The final measurements were made and are given in four tables of which 
 I and II are examples. 
 
 In these tables Col. E H contains the potentials of the hydrogen con- 
 centration cell with diffusion, Pt H | 0.1 M H 2 SO 4 | 0.01 M H 2 SO 4 1 Pt H ; 
 Col. E S04 those of the sulfate concentration cell with diffusion, Hg Hg 2 SO 4 
 0.01 M H 2 SO 4 | 0.1 M H 2 SO 4 , Hg 2 SO 4 | Hg; Col. E .i the potentials of 
 the cell Pt H | 0.1 M H 2 SO 4 , Hg 2 SO 4 | Hg; and Col. EQ.OI the potentials 
 of the cell, Pt H I 0.01 M H 2 SO 4 , Hg 2 SO 4 | Hg. The column headed "E 
 by E H + 304" contains the sums of the values recorded in Cols. E H 
 4 In the measurement for the transference numbers of HaSC^ the reservoirs (R a , Rb> 
 RC, Rd) were filled above the openings of the side arms. In the later work when 
 gelatin was used they were filled as shown in the diagram. 
 
12 
 
 TABLE I. 
 
 by by 
 
 No. Date. Time. Bar. E H . E SO4 . EQ^. E OQ1 . E H +E SOt .E Q 01 - EQ j. 
 
 Mm. 
 
 1 10/13 3:00 P.M. 741.6 0.742020.80260 
 
 2 10/13 4:00 741.6 0.74200 0.80260 
 
 3 10/13 7:30 740.4 0.01137 0.04933 0.74205 0.80275 0.06070 0.06070 
 
 4 10/13 9:00 740.0 0.01139 0.04930 0.74210 0.80274 0.06069 0.06064 
 
 5 10/13 10:30 740.0 0.01139 0.04929 0.74212 0.80276 0.06068 0.06064 
 
 6 10/13 11:30 739.5 0.01141 0.04928 0.74212 0.80279 0.06069 0.06067 
 
 7 10/14 10:00 A.M. 736.0 0.01136 0.04900 0.74203 0.80249 0.06036 0.06036 
 
 8 10/14 1:30 P.M. 734.5 0.01133 0.04913 0.74201 0.80246 0.06046 0.06035 
 
 9 10/14 3:30 734.5 0.01130 0.04918 0.74203 0.80245 0.06048 0.06042 
 
 Av. 0.01136 0.04922 0.74207 0.80263 06058 0.06056 
 
 The cell was set up at 9:00 A.M. on October 13, 1919. 
 
 TABLE II. 
 
 1 10/15 10: 00 A.M. 739.3 0.741660.80192 
 
 2 10/15 1:30 P.M 0.74209 0.80263 
 
 3 10/15 5:45 0.742000.80268 
 
 4 10/15 7:15 0.742050.80269 
 
 5 10/15 10:00 737.3 0.01136 0.04922 0.74195 0.80256 0.06058 0.06061 
 
 6 10/15 12:00 737.0 0.01127 0.04921 0.74212 0.80257 0.06048 0.06045 
 
 7 10/16 9: 00 A.M. 736.30.011200.049270.742090.802530.060470.06044 
 
 8 10/16 10:30 736.5 0.01121 0.04923 0.74210 0.80247 0.06044 0.06037 
 
 Av. 0.01126 0.04923 0.74206 0.80253 0.06049 0.06047 
 
 The cell was set up at 11 P.M. on October 14, 1919. 
 
 and E SOi . The column "E by EO.OI HO.I" contains* the differences 
 between the values recorded in E .oi an d E } . 
 
 The 0.1 M and 0.01 M cells were prepared and placed in the thermostat 
 where they remained for about 12 hours to come to equilibrium before 
 the boundaries were introduced. This accounts for the blank spaces in 
 the tables. 
 
 As pointed out in the theoretical discussion the values recorded in column 
 EH + E SOi should be equal to those recorded in column E .oi ^o.i- 
 The close agreement of these values indicates the accuracy of the potential 
 measurements. The differences between the successive values in each 
 column indicates the degree of constancy of the cells. The differences 
 in columns E .oi an d 0.1 may be attributed, in part, to changes in 
 barometric pressure, for which corrections have not been applied, as such 
 corrections are unnecessary for the calculations in which the measurements 
 are used. 
 
 The remarkable agreement between the averages in the different tables 
 indicates the reproducibility of the work. 
 
 In the theoretical treatment formulas were given by means of which 
 the values of E, E H , ESO an d E B can be calculated. Table III contains 
 a summary of such calculated values together with the measured values. 
 
13 
 
 TABLE III. COMPARISON BETWEEN CALCULATED AND MEASURED POTENTIALS. 
 
 E'. Ef. E. E B . E sot . B . 
 
 Calc. from / Cond. 0.10511 0.06693 0.08883 0.014716 0.06407 0.03781 
 \Fz.Pt.0.08072 ....... 0.06054 0.011301 0.04918 0.02908 
 
 Measured .............. 0.06054 0.011310 0.04925 0.02906 
 
 These calculations involve the ratio otid/otjCs. It has been customary 
 to use conductivity values in its calculation. Since the work of Jones 
 is probably the most reliable on the conductivity of sulfuric acid, his re- 
 sults were used in these calculations. This ratio may also be obtained 
 from freezing-point data. The values obtained from these two sources 
 are decidedly at variance. No freezing-point data are available for the 
 degree of dissociation of 0.1 M sulfuric acid. However, a complete 
 table is given by Lewis and Linhart 5 for concentrations between 10 ~ 2 
 and 10~ 6 molar. The degree of dissociation given by Lewis and Linhart 
 for 0.01 M sulfuric acid was substituted in the equation for E together 
 with the measured potential (0.06054), and the equation solved for the 
 degree of dissociation for 0.1 M sulfuric acid. In the curve of Fig. 2 
 the abscissas are the molar concentrations and the ordinates the degrees 
 
 of dissociation. The portion indicated 
 by the solid line was obtained from the 
 freezing-point data and the broken 
 portion is an extension to include the 
 value calculated from the potential 
 measurements. Since this is a smooth 
 curve, the indication is that the point 
 obtained from the potential measure- 
 ments is approximately the same as 
 would have been obtained from the 
 freezing-point determination. In every 
 instance the results obtained when the 
 freezing-point values are used in the 
 ratio aiCi/azCz show better agreement 
 with the measured potentials than when 
 the conductivity values are used. The 
 latter results are in all cases higher than 
 the measured. It should be noticed, 
 
 however, that the exact agreement between the measured and calculated 
 values for E is to be expected, since it was from this measured value of E 
 that G was calculated. The close agreement between the measured and 
 calculated values of E H , SO4 and E B is a true indication of the correctness 
 of the value 0.2973 for the degree of dissociation of 0.1 M sulfuric 
 acid. 
 
 5 Lewis and Linhart, J. Am. Chem. Soc., 41, 1959 (1919). 
 
 /oo 
 
 90 
 
 80 
 
 70 
 
 60 
 
 50 
 
 40 
 
 30, 
 
 MOLAR CONCENTKATION 
 
 D./ 0.O/ O.OOt O.OOOI O.OOOOI O.OOOOOI 
 
 Fig. 2. Dissociation-concentration 
 curve. 
 
14 
 
 It is important to note that all of the values thus far calculated are based 
 on the assumption that sulfuric acid dissociates entirely into two hydrogen 
 ions and one sulfate ion. Column E f shows the values for E calculated 
 on the assumption that the sulfuric acid dissociates into one hydrogen 
 ion and one hydrogen sulfate ion. The fact that the measured potentials 
 agree so well with those calculated on the first assumption and do not agree 
 with those calculated on the second assumption is a strong indication that the 
 sulfuric acid dissociates almost entirely into 3 ions at these concentrations. 
 
 It has been noticed by others that the calculated values for potential 
 measurements are always higher than the measured values when conduc- 
 tivity dissociation ratios are used. Ferguson 6 in his work on hydrochloric 
 acid attributed the difference to the fact that the formula assumes the 
 complete dissociation of the acid. As the acid is not completely dissociated 
 the formula does not exactly represent the facts and must be corrected 
 so as to include the undissociated acid. Such a correction was made for 
 hydrochloric acid and, when applied to the formulas involving conductivity 
 ratios, gave values which agreed more closely with those measured. A 
 similar correction can be developed for the sulfuric acid concentration cell. 
 
 When two faradays of electricity pass through a sulfuric acid concentra- 
 tion double cell, one mol of acid is transferred from one concentration to the 
 other. The electrical work which accompanies this change is represented 
 by W = 2 EF. The osmotic work required to effect this same change 
 is usually represented by W - 3 RT In Ci/c z . This assumes that the acid 
 is completely dissociated into 3 ions. Since it is not completely dissociated 
 what actually happens is (1) the transference of an amount of hydrogen 
 ion equal to twice the concentration times the dissociation of the acid; 
 (2) the transference of an amount of sulfate ion equal to the concentration 
 times the dissociation of the acid; (3) the transference of an amount of un- 
 dissociated acid equal to the concentration of the undissociated acid. The 
 general expression which represents the sum of the osmotic work in (1) 
 
 and (2) is Wi = aZRT ln c 
 
 Cz 
 
 Similarly the osmotic work in (3) is W = (I a)RT In -. In the appli- 
 
 Cz 
 
 cation to sulfuric acid (d) in (Wi) becomes 2ciH+ = 2 CIOL' = CiSO 4 ~~; 
 and Cz becomes 2c 2 H+ = 2c z a" = c 2 SO 4 . 
 
 Similarly Ci in W z becomes CiH 2 SO 4 = Ci (1 a'); and c z becomes c 2 H 2 - 
 SO 4 = c 2 (l a*)\ and, as the total electrical work is equal to the total 
 osmotic work, 
 
 W = 2EF = <x3RTln ff + (l- 
 Cict 
 
 E = - 
 
 2 F 
 
 6 J. Phys. Chem., 20, 326 (1916). 
 
15 
 
 This formula cannot be taken as absolutely correct since it assumes that 
 the dissociation is the same in both concentrations, which is not true. 
 
 The most reliable value that can be used for a is ' in which a' 
 
 A 
 
 is the degree of dissociation in c\ and a" is the degree of dissociation in c*. 
 
 Col. E" Table III shows the result of the application of this correction. 
 It is evident that the correction is an improvement since the difference 
 (0.00639) between the measured value and that calculated from the cor- 
 rected formula is much less than the difference (0.01829) between the 
 measured value and that calculated from the usual formula. 
 
 In the theoretical part of this work is was shown that the boundary 
 
 o _ o AT J2T* r 
 
 potential can be calculated from the formula E B = - - In ; 
 
 2 F c 2 
 
 9 T 77" 
 
 also that E B = . Column E B contains the results from the 
 3 
 
 calculation by the first formula. Again the close agreement between 
 the measured and calculate values in the case of the freezing-point 
 ratio and lack of agreement in the case of the conductivity ratio are 
 evident. 
 
 Maclnnes 7 has developed a formula for boundary potentials of uni- 
 univalent electrolytes which involves the transference number of the cation 
 and the potentials of the cells with and without diffusion. He states 
 that it "contains no assumption regarding the concentration of the ions 
 of the solutions." In the following development the same reasoning is 
 applied to the uni-bivalent acid, sulfuric acid, on the assumption that it 
 dissociates into two hydrogen ions and one sulfate ion. 
 
 When two faradays of electricity pass through the cell the net result 
 is the transference of one mol of sulfuric acid from the concentrated to the 
 dilute side. The current is carried across the boundary between the two 
 solutions by the transference of 2 N c gram ions of hydrogen ions in one 
 direction and 1 N c gram ions of sulfate ions in the opposite. The osmotic 
 work at the boundary is proportional to the algebraic sum of the number 
 of gram ions that have passed through it. Therefore the osmotic work 
 W is proportional to 3N C 1. The electrical work which accompanies 
 the transference of one mol of sulfuric acid from the concentrated to the 
 dilute side is equal to the product of the electromotive force of the cell 
 and the number of faradays required to effect the transference. Since 
 this is so, the following relation holds. 
 
 2EF:2EsF::3:3N c - 1 
 
 a.ndE B = E(3N C - l)/3; forE, -^p may be substituted since it has been 
 7 Maclnnes, /. Am. Chem. Soc., 37, 2301 (1915). 
 
16 
 
 shown that N = ^ 4 . The formula then becomes 
 iSt 
 
 E B = so< (3N C - 1) /3N C . 
 
 Substituting the correct values for N c and E S04 as measured, the value 
 0.02904 is obtained. This is in almost perfect agreement with the meas- 
 ured value 0.02906 and proves the validity of the formula. 
 
 That this expression E B = E SOt (3N C 1) /3N e is but another form of 
 
 c\ QAT 7? "7"" r 
 
 the usual expression E B = - - - In - for boundary potential, can 
 
 2 r 2 
 
 readily be shown, since 
 
 EB = jj^ 4 (3N e - 1) (9) 
 
 and 
 
 Substituting in (9) 
 
 Nc In - RT r . 
 
 EB = 2 F c 2 (3Nf _ !) = . tn * (3Nc _ 1} 
 
 3N< F 
 
 is obtained; as (3N C - 1) = (2 - 3N a ) 
 
 RT a 2 - 3N a RT , Cl 
 
 EB In- (3N C 1) = In-. 
 
 F c 2 2 F c 2 
 
 Therefore 
 
 2 - 3N a RT 7 Cl 2E 80i - E 
 
 t /OA7 , 
 EB = _ (3Nc _ D = 
 
 3N e N 2 F c 2 3 
 
 A consideration of these formulas indicates the advantage of the formula 
 (2 S04 -E H )/3 since it contains no assumption regarding the concentration 
 of the ions, nor does it require a knowledge of the transference numbers. 
 The averages of E H , E SOt , and E from a few of the tables obtained are 
 contained in Table IV, together with the transference numbers calculated 
 from them. 
 
 TABLE IV. 
 
 SUMMARY OP POTENTIALS AND TRANSFERENCE NUMBERS. 
 T KI j? j? Eor N "- Na - 
 
 Table. /. -rWu- 
 
 II 
 
 0.01136 
 
 0.04922 
 
 0.06056 
 
 0.1875 
 
 0.1875 
 
 III 
 
 0.01126 
 
 0.04923 
 
 0.06047 
 
 0.1862 
 
 0.1862 
 
 IV 
 
 0.01137 
 
 0.04929 
 
 0.06059 
 
 0.1875 
 
 0.1874 
 
 V 
 
 0.01126 
 
 0.04927 
 
 0.06053 
 
 0.1868 
 
 0.1868 
 
 Av. 
 
 0.01131 
 
 0.04925 
 
 0.06054 
 
 0.1868 
 
 0.1868 
 
 To facilitate the comparison of the value obtained in this investiga- 
 tion with those obtained on others, a summary of such values is contained 
 in Table V. 
 
17 
 
 Attention should be called to the fact that the values recorded in columns 
 En/E and 1E SO JE of Table IV are determined from separate and dis- 
 tinct potential measurements. The agreement between the successive 
 values in each column and between the averages of the two columns demon- 
 strates the reliability of the concentration cell method for the determination 
 of the transference numbers of sulfuric acid. 
 
 TABUS V. 
 SUMMARY OP TRANSFERENCE NUMBERS OF SULFURIC ACID. 
 
 Investigator^ Concentration. Te ^ p - N *' **%*** 
 
 Bein 1898 0.24% 11 0. 175=^=3 0.1804 
 
 Mclntosh 1898 1.0-0. 001 M 18 0.174=*= 18 0.1817 
 
 Starck 1899 0.5-0.6% 17-20 0.145=*=? 
 
 Jahn and Huybrechts 1902 0.06-0. 005 M 18 0.176==4 0.1837 
 
 Eisenstein 1902 Q.124M 18 0.168 3 0.1757 
 
 Eisenstein 1902 0.01M 30 0.188=*=! 0.1825 
 
 Tower 1904 0.1 M 20 "0.1805 0.1860 
 
 Tower 1904 0.01 If 20 0.1809 0.1864 
 
 Whetham and Paine 1908 0.05M 18 0.184 0.1917 
 
 France 1920 0.1-O.OlJlf 25 0.1868 0.1868 
 
 Experimental Results with Sulfuric Acid Containing Gelatin. 
 
 The properties of hydrophile colloids have been the subject of many 
 investigations during the past few years. So far, no entirely satisfactory 
 explanation has been offered for their action in the presence of electrolytes. 
 The theories advanced are based largely on the measurements of osmotic 
 pressure, conductivity, swelling and transference numbers. 
 
 There appear to be but three articles in the literature dealing with the 
 influence of colloids on transference numbers and in each instance the 
 analytical method was used. 
 
 Paul Richter 9 investigated the influence of gelatin, gum arabic, agar- 
 agar, and peptone on the transference number of the chloride ion of lithium, 
 potassium and hydrogen chlorides. 
 
 A. Mutscheller 10 investigated the influence of gelatin on the transfer 
 ence numbers of silver nitrate, cupric sulfate and zinc sulfate solution 
 which contained definite quantities of a 1% gelatin solution. 
 
 According to his results the transference numbers of the nitrate and 
 
 8 The values and the limits of accuracy of the first six investigations are taken 
 from MacBain's abstract of transference data (/. Wash. Acad. Sci., 9, 11 (1905)). In 
 the first six investigations the analytical method was employed. According to Mac- 
 Bain the results of Jahn and Huybrechts and of Tower are probably the most reliable. 
 Whetham and Paine employed the conductivity method. The values in the last column 
 were obtained from the values in the preceding column by the application of the tem- 
 perature coefficients given by Tower (/. Am. Chem. Soc., 26, 1038 (1904). 
 
 9 Richter, Z. physik. Chem., 80, 449 (1912). 
 
 10 Mutscheller, Met. Chem. Eng., 13,353 (1915); J. Am. Chem. Soc., 42, 442 (1920). 
 
18 
 
 sulfate ions decrease with an increase in the quantity of gelatin solution 
 added. By the addition of sufficient quantities of gelatin solution, even 
 negative values were obtained. He states that when the transference 
 number of the anion is zero the conditions are most favorable for the 
 deposition of the metal. The effect of the gelatin is accounted for on the 
 assumption that it is positively charged and forms an "absorption com- 
 pound" with the anions. This results in the partial or complete neu- 
 tralization or even reversal of the original charge on the ions. The re- 
 sults obtained by Mutscheller for the sulfate and nitrate ions show effects 
 of gelatin far in excess of those observed by Richter for the chloride ion. 
 
 It is well to emphasize here that the results obtained by Mutscheller, 
 if correct, are indeed remarkable, but it is the opinion of the author that 
 an error has been made in the calculations or in the recorded data. This 
 subject is under investigation at the present time. 
 
 Mutscheller 10 explains the effect of gelatin on the transference numbers 
 of silver nitrate, cupric sulfate and zinc sulfate by the assumption that 
 gelatin is positively charged and "absorbs" the negative ions. This 
 causes a decrease in their velocity. According to Nernst the potential 
 at the boundary of two solutions of different concentration depends upon 
 the difference in velocities of the ions. If the theory of Mutscheller is 
 true the presence of gelatin in such solutions should change the boundary 
 potential. Then measurements of the transference numbers of sulfuric 
 acid by this method would determine whether gelatin affected the boundary 
 potential. 
 
 Since gelatin precipitates the heavy metals, it was obvious that precipi- 
 tation would result if it were added to a sulfuric acid solution saturated with 
 mercurous sulfate. Since, however, the influence of the gelatin on trans- 
 ference numbers is due only to its effect on the boundary potential, it is 
 unnecessary to introduce gelatin into the electrode containers. 
 
 The cells were prepared as described and the siphons connect'ng the 
 hydrogen and sulfate electrodes were filled with 0.1 M and 0.01 M sol- 
 utions of sulfuric acid which contained a definite concentration of gelatin. 
 They were then placed in the reservoirs, with the ends immersed in solu- 
 tions of the same concentrations as that which surrounded the electrodes. 
 The measurements were made as before, but showed a gradual progres- 
 sive change. It was discovered that this was due to the diffusion of 
 the gelatin from the siphons into the reservoirs and then into the solu- 
 tion which surrounded the electrodes. This made it necessary to devise 
 a method which would prevent the diffusion and at the same time intro- 
 duce no new potentials. Several devices were tried in which use was 
 made of glass wool, filter paper, glass capillaries, and cotton wicks, 
 before the following satisfactory method was found. 
 
 Ordinary cotton lamp-wicks were carefully washed by boiling in acid 
 
19 
 
 of the same concentration as used in the cells. After washing and dry- 
 ing they were kept in 0.1 M and 0.01 M sulfuric acid solutions. Cells 
 were prepared and so filled that the solution rose in the inner tube to the 
 level L indicated in Fig. III. Gelatin solution identical 
 with that in the siphon S was filled in the reservoirs to 
 the level L. A wick W previously saturated with acid 
 solution containing no gelatin was hung over the side of 
 the inner tube so that one end of it was immersed in the 
 plain solution of the inner tube and the other in the gela- 
 tin solution in the reservoir. This arrangement effectively 
 eliminated the diffusion, provided the solutions in the 
 inner tube and in the reservoir were maintained at the 
 same level. No new potentials were introduced by this 
 arrangement. All of the measurements were made with 
 cells prepared in this manner. Measurements were 
 made with concentrations of gelatin over a range of 
 0.5 to 20.0%. The results of these measurements 
 are contained in 18 tables of which Table I is a 
 sample. 
 
 Fig. Ill Detail 
 of reservoir. 
 
 Expt. Date. Time. 
 
 1 1/14 12: 30 A.M. 
 
 2 1/24 9:30 
 
 3 1/24 11:50 
 
 TABLE VI. TYPICAL EXPERIMENTS. 
 
 Bar. E n- E so*- E 0.1- E 0.l. 
 
 Mm. Using 0.5% gelatin. 
 
 743.8 0.74189 0.80260 
 
 748.4 0.74205 0.80264 
 
 748.4 . . 0.74203 0.80260 
 
 Ehn 
 
 Eby 
 
 Using 5% gelatin siphons introduced at 1 .P.M 
 
 4 1/24 1:00 P.M. 
 
 5 1/24 5:00 
 
 6 1/24 11:00 
 
 7 1/25 10: 30 A.M. 
 
 Av. 
 
 747.8 0.01295 0.04750 0.74199 0.80235 
 749.6 0.01290 0.04743 0.04210 0.80220 
 751.0 0.01292 0.04740 0.74217 0.80237 
 754.2 0.01290 0.04779 0.74213 0.80260 
 0.01290 0.04754 0.74213 0.80239 
 
 0.06033 0.06010 
 
 0.06032 0.06020 
 
 0.06069 0.06047 
 
 0.06044 0.06026 
 
 The cell was set up on Jan. 23 at 2: 30 P.M. The averages do not include the first 
 four sets of readings. 
 
 In these tables the same arrangement of the data has been followed as 
 in the previous tables. In order that a comparison of the values recorded 
 in the separate tables may readily be made the average values in each 
 table together with the transference numbers calculated thereform have 
 been summarized in Table VII. 
 
 The headings of Cols. 2, 3, 4, and 5 have the same significance 
 as before. Cols. 6, 7, 8, and 9 contain the transference numbers cal- 
 culated from the values in Cols. 2, 3, 4, and 5, as indicated in the head- 
 
20 
 
 c >o 
 
 38 
 
 Tf C^ CO 
 
 0^ O^ O^ 
 OOO 
 
 i f>- Ot^O5 t~- 00 00 I s - CO >C 
 
 **^ CO O^ O^ CO CO CO lp ~ * CO CM 
 'O O C5 O5 OOO OOO 
 
 O I-H O I-H i i i- i i O O 
 
 !>!>!> 
 
 o o o' o o o' 
 
 iC O I 00 "tf i ( 
 (Mi-*i-< (MCOCO 
 OCOCO lO lO 1C 
 
 o o o o o o o o o 
 
 CO Cl 00 
 
 t^- I-H O5 O5C1O5 
 
 COT^CO COCOCO 
 
 o o o o o' o 
 
 CO lO O^ O5 <N i ( 
 
 t^OO CO"t"* 
 
 COCOCO COCOCO 
 
 o'oo ooo 
 
 t> o ca oo Oi Oi ic ic ic cococo 
 
 CO T+I CO CO CO CO CO CO CO CO CO CO 
 
 o o o ooo ooo ooo ooo odd odd ooo ooo 
 
 O O i-HCO 
 <N (M O T-I 
 
 co co co co 
 
 CO CJ5 
 O 
 CO CO 
 
 o' o ooo 
 
 CO CO CO OOOl> 1C 
 
 I-IT-H^ "^TfriTti 
 
 i-< W (M ci <N (N (N 
 
 d odd odd o 
 
 O CO 1-1 !> Oi I> (N O CO 
 iCC (MCO(M (MOii-H I-H 
 
 OOo OOO 
 
 OOO OOO 
 
 OOO OOO 
 
 ^f t^* i* O^ 1C CO C^Q Oi CO O^ *C 
 
 Oi O t^COO OCOCO CQCOTti 
 
 COCO >CCtC tCCOcO COCOCO COCOCO 
 
 OO OOO OOO OOO OOO 
 
 ooo ooo ooo ooo ooo ooo ooo ooo ooo 
 
 ^o t^osco b-oo 
 
 ..I-ITI ??^^ ^?tr 
 
 CO CO CO CO CO CO C^ CQ C^ C^ C^l ' 
 
 ooo ooo odd odd o'o'o". ddo ooo ooo ooo 
 
 Ob~ T} 
 
 OOO O5 
 
 CO CO 
 
 8: 
 
 00 
 
 L-O 
 
 1C ( 
 
 p p p o pop p < 
 
 d odd odd odd dod o'oo odd ooo odd odd 
 
 * 
 
 V 
 
 
21 
 
 ings. Col. 10 contains the sum of the N a and N c values of Cols. 7 and 9 
 and should always be equal to unity. The deviation from unity is an 
 indication of the small error of the potentials used in their calculation. 
 The accuracy with which the potentials of E H and 5 S04 can be dupli- 
 cated in the presence of gelatin, is shown by the closeness with which the 
 averages for any two tables of the same concentration agree. From a 
 comparison with similar values in the previous tables, it is plainly 
 evident that when gelatin is present the agreement is less satisfac- 
 tory than when it is not. This lack of agreement becomes greater 
 the higher the concentration of gelatin. Table VIII is a summary of the 
 averages of the potentials and transference numbers contained in Table 
 VII. 
 
 TABLE VIII. SUMMARY OF POTENTIALS AND TRANSFERENCE NUMBERS. 
 
 % Gel. 
 0.0 
 0.5 
 1.0 
 2.0 
 2.5 
 3.0 
 5.0 
 
 10.0 
 
 15.0 
 
 20.0 
 
 *. 
 
 0.01136 
 0.01290 
 0.01494 
 0.02741 
 0.02682 
 0.03181 
 0.03755 
 0.03735 
 0.04065 
 0.04155 
 
 0.04918 
 0.04784 
 0.04563 
 0.03749 
 0.03266 
 0.02824 
 0.02408 
 0.02410 
 0.02243 
 0.02068 
 
 0.187 
 0.213 
 0.247 
 0.407 
 0.442 
 0.524 
 0.620 
 0.613 
 0.668 
 0.685 
 
 0.02906 
 0.02746 
 0.02544 
 0.01676 
 0.01283 
 0.00822 
 0.00354 
 0.00362 
 0.00140 
 -0.00006 
 
 A consideration of the values recorded for N a shows that they increase 
 with increase in concentration of gelatin. The relation between the trans- 
 ference number of the anion and concentration of gelatin is shown by the 
 curve in Fig. 4. In this curve the transference numbers are plotted a s 
 
 0.700 
 0.600 
 0.500 
 0.400 
 0300 
 
 1 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 p 
 
 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 O./OD 
 
 
 
 
 Ff/i 
 
 ? CfNT. 
 
 6i.AT 
 
 H 
 
 
 
 
 Q /> J2 t4 /6 
 
 Fig. 4. JVa-gelatin curve. 
 
 ordinates and the concentrations of gelatin as abscissas. The change 
 in transference number with increase in gelatin is rapid at low gelatin 
 concentrations, is gradual between 3 and 5%, and above this is not appreci- 
 
22 
 
 able. If this represents an actual increase in the migration velocity of 
 the anion, then there must be a corresponding decrease in the boundary 
 potential (B)- The values in the columns headed E B and N a indicate 
 such changes. ^ Since the boundary potential is opposed to the electrode 
 potentials in the case of the hydrogen concentration cell (E H ) and is 
 added to the electrode potentials in the case of the sulfate concentration 
 cell (E SOi ) a decrease in E B would result in an increase in the value of 
 EH and a decrease in E SOi . That such changes do take place is indicated 
 by the values in the columns headed E H and E SOi . 
 
 It has been shown that the boundary potential depends on the trans- 
 ference numbers of the ions and the ratio of their concentrations in the 
 two solutions. Therefore a change in E-Q would result from a change in 
 concentration or a change in transference number. 
 
 The value of EB would be reduced by making the concentration of the 
 solutions more nearly equal. When exactly equal EB would be zero, and 
 when the concentration of the 0.1 M solution became less than that of the 
 0.01 M, the direction would be reversed. 
 
 To determine whether or not concentration changes are produced by the 
 gelatin, concentration cells of the type Pt H I 0.1 M H 2 SO 4 )KC1 0.1 M 
 H 2 SO 4 + gel. | Pt H and Pt H ] 0.01 M H 2 SO 4 1 KC1 | 0.01 M H 2 SO 4 + gel. 1 
 Pt H were used. The data from these measurements are summarized 
 in Table IX. 
 
 TABLE IX. 
 
 0.1 M. 0.01 M. 
 
 %Gel. C lf x . C 2 E z . 
 
 0.05946 0.012340 
 
 1 0.05694 0.00070 0.007684 0.01216 
 
 2 0.05670 0.00122 0.002172 0.04458 
 
 3 0.05542 0.00181 0.000430 0.08609 
 
 4 0.05356 0.00268 0.000144 0.11418 
 
 It was impossible to work with concentrations of gelatin above 4% because of the 
 excessive foaming of the solutions. 
 
 The first column contains the percentage of gelatin in the acid in one- 
 half the cell. The columns E x and E z contain the measured potentials 
 of the cells E x and E 2 when 0.1 M and 0.01 M solutions are used. In 
 columns C\ and C z are the hydrogen-ion concentrations in 0.1 M and 
 0.01 M solutions with gelatin, calculated by the use of the formula for con- 
 centration cells in which boundary potential has been eliminated. The 
 results in columns C\ and C 2 show that gelatin produces a relatively small 
 decrease in the hydrogen-ion concentration of the 0.1 M solution, and a 
 much greater relative decrease in the 0.01 M solution. The hydrogen-ion 
 concentration of the 0.1 M solution is always greater than that of the 
 0.01 M; therefore the reversal of the boundary potential (E B ) as shown 
 in Table VIII cannot result from the concentration changes produced by the 
 
23 
 
 gelatin. Since E B can be decreased or reversed only by a change in con- 
 centration or transference number, the observed change must be due to 
 a change in the transference number. 
 
 Since it has been shown above that the gelatin produces changes in the 
 hydrogen-ion concentration, new potentials are developed at the boundaries 
 between the solutions in the wicks and the gelatin solution in the reser- 
 voirs. The locations and directions of the boundary potentials, E B , 
 E x and E z together with .E H an d ESO* are represented digrammatically 
 in Fig. 5. The location of the boundary potentials is shown also by the 
 same letters in Fig. 1. E B represents the potential within the siphon, that 
 is, the potential which has been considered thus far. E x and E z repre- 
 sents the potentials at the contact of the solutions in the reservoirs. 
 EH and E$Q4 are the measured potentials and are the algebraic sums of 
 the potentials at the electrodes and the boundary potentials E x , E B , 
 and E z . 
 
 The potentials E x , E B , and E z which result from the presence of the 
 gelatin can be calculated from the data in Table IX by the use of the usual 
 formula for boundary potential. These calculations were made and the 
 results are included in Table X. The potentials at E x and E z are oppo- 
 sitely directed and the resultant potential is therefore their difference. 
 These differences are recorded in the column headed E Z E X . The total 
 potential at E B is opposed to the resultant potentials E Z E X and may be 
 considered as the sum of the original boundary potential E B (0.02906) 
 
 and the potential resulting from 
 
 the changes in concentration pro- 
 duced by the gelatin. Therefore the 
 differences between the total poten- 
 tials E' B and the original potential 
 E B (0.02906) is that due to the 
 changes in concentration produced 
 by the gelatin. The values of 
 these differences are recorded in 
 the column headed E' B -0.02906. 
 As the values in the column headed 
 E' B - 0.02906 are practically iden- 
 tical with those in E Z E X and op- 
 positely directed, their combined Fig. 5.-Diagram of potentials, 
 effect must be zero. This shows that the potentials E x and E z at the 
 contacts between the solutions in the wicks and the gelatin solutions in the 
 reservoirs are entirely compensated by the potential (E' B 0.02906) 
 simultaneously developed at the boundary E B . Therefore any boundary 
 potential produced by the introduction of gelatin cannot result from 
 changes in concentration. The experimental data, however, show that 
 
24 
 
 the boundary potential E B is changed by the addition of gelatin. Since 
 this cannot be due to concentration changes it must result from a change 
 in the transference numbers of the hydrogen and sulfate ions or from an 
 actual change in the kind of ions present. This may be effected in sev- 
 eral ways; (1) by the removal of either ion as the result of its being 
 selectively adsorbed by the gelatin ; (2) by a change in the velocity of 
 either ion ; (3) by chemical reaction with the gelatin resulting in the forma- 
 tion of new ions. 
 
 TABLE X. BOUNDARY POTENTIAL CALCULATIONS. 
 
 %Gel. EH. Es 04 . EB. E*. E z E z - E x E B -0.02906.E' B 
 
 1 0.01494 0.04563 0.02544 0.00077 0.00878 0.00801 0.00804 0.0371 
 
 2 0.02941 0.03749 0.01676 0.00085 0.03215 0.03107 0.03124 0.0603 
 
 3 0.03181 0.02824 0.00822 0.00132 0.06210 0.06078 0.06094 0.0900 
 
 4 0.00196 0.0825 0.08054 0.08054 0.1095 
 
 Since the conductivity of a solution is affected by any change in the 
 number and the mobility of its ions, it was thought that conductivity 
 measurements would furnish information as to the nature of the influence 
 of the gelatin. Measurements were made of the conductivity of . 1 M 
 and 0. 01 M sulfuric acid solutions which contained different concentrations 
 of gelatin. The concentration of gelatin was varied from to 20%. As 
 it was necessary to apply a correction for the conductivity of the gelatin 
 in conductivity water, a series of measurements was made with gelatin 
 solutions over this same range of concentration. The corrected conduc- 
 tivity values are recorded in Table XI. 
 
 TABLE XI. CONDUCTIVITY OF SULFURIC ACID SOLUTIONS IN PRESENCE OF GELATIN 
 
 %Gel. 0.1M. 0.01 M. 
 
 0.037704 0.005011 
 
 1 0.033695 0.002413 
 
 2 0.030608 0.000948 
 
 3 0.027516 0.000755 
 
 4 0.02423 0.000686 
 10 0.009907 0.000462 
 15 0.003987 0.000349 
 20 0.002800 0.000233 
 
 The effect of the gelatin on the conductivity of the 0. 1 M and 0. 01 M 
 sulfuric acid solutions is also shown by the curves in Figs. 6 and 7. The 
 conductivities are plotted as ordinates and the concentrations of gelatin 
 as abscissas. These curves show that the gelatin produces a greater 
 relative change in the conductivity of the 0.01 M sulfuric acid solution 
 than in the conductivity of the 0. 1 M solution. It should be recalled that 
 in the concentration-cell measurements, recorded in Table IX, the gelatin 
 produced a much greater relative change in the hydrogen-ion concentration 
 of the 0.01 M solution than in the 0. 1 M. In fact, by the addition of 
 about 3 to 4% of gelatin, the concentration of the 0.01 M solution was 
 
25 
 
 reduced practically to zero. From Fig. 7 it is readily seen that by the 
 addition of about 3% of gelatin the conductivity has been reduced almost 
 to zero. This indicates that not only is the hydrogen-ion concentration 
 reduced by the addition of gelatin but that sulfuric acid is removed as 
 a whole. 
 
 0.036 
 0.034 
 0-032 
 030 
 O.O28 
 0.026 
 0.024 
 O.O22 
 0.020 
 00/8 
 O.O/6 
 O.OI4 
 0.012 
 O.OIO 
 OOO8 
 O006 
 
 O OO4 
 O.O02 
 O.OOO 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 
 - 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 fc 
 
 \ 
 
 \ 
 
 
 
 fc 
 
 1 
 
 
 \ 
 
 
 
 l 
 
 
 \ 
 
 \ 
 
 
 / 
 
 7 ffC-/V 
 
 T GIL* 
 
 T/NE 
 
 ^ < 
 
 2 4 6 8 /O /2 /4 /& f8 2O 
 
 Fig. 6. Conductivity-gelatin curve 
 for o.i M H 2 SO 4 . 
 
 0.0026 
 
 0.0000 
 
 PER ClNTGfLATlNE 
 
 20 
 
 02 4 6 8 /O /2 /4 J6 /6 
 
 Fig. 7. Conductivity-gelatin curve 
 for o.oi M H2SO4. 
 
 Several calculations were made involving the conductivity data and 
 potential data in an effort to determine whether the gelatin produced an 
 actual change in the mobility of the ions, but it was impossible to conclude 
 from these calculations whether the effects obtained were due to concentra- 
 tion changes alone or to concentration changes together with changes in 
 mobility or the presence of new ions. 
 
 Two explanations have been offered to account for the action of gelatin, 
 
 one of which assumes that the ions of the acid are "absorbed" by the gelatin, 
 
 and the other that a highly dissociable chemical compound is formed. 
 
 Supporters of the first theory are H. G. Bennett 11 and A. Mutscheller; 10 
 
 11 Bennett, /. Am. Leather Chem. Assoc., 13, 270 (1918). 
 
26 
 
 and favoring the second theory are H. R Procter, 12 H. R. Procter and J. A. 
 Wilson, 13 J. Loeb, 14 and W. O. Fenn. 15 
 
 It has been shown in this investigation that some of the properties of 
 sulfuric acid are altered by the presence of gelatin. A summary of the data 
 obtained in the work on its influence on the transference number of the 
 anion of sulfuric acid is contained in Table VIII. It may be observed that 
 the boundary potential (E B ) is reduced from +0 . 02906 to - . 00006. Cor- 
 responding to this decrease in boundary potential, there is an increase in the 
 potential of the hydrogen concentration cell (E H ) from 0. 01136 to 0. 04155 
 and a decrease in the potential of the sulfate concentration cell (E SOt ) 
 from 0.04918 to 0.02068. There is an apparent increase in the trans- 
 ference number of the anion from 0.187 to 0.685. Any factor which 
 would increase the numerical value of EH and decrease E SOt would 
 give the observed effect of a decrease in the boundary potential and an in- 
 crease in the transference number of the anion. This factor was at first 
 believed to be the result of changes in concentration which are recorded 
 in Table IX, due to the presence of the gelatin. A careful consideration 
 of the boundary potentials E x , E B , and E z which result from these changes 
 in concentration leads, to the conclusion that they should neutralize each 
 other. The data in Table XI show this to be the fact. Therefore this 
 effect was not due to the concentration changes brought about by the 
 introduction of the gelatin. This led to the conclusion that the observed 
 changes in the potentials of the concentrations cells resulted from a change 
 in the boundary potentials. This decrease in the boundary potential 
 could be produced by any one of three factors. An actual change in the 
 transference numbers; a decrease in the concentration of the 0.1 M so- 
 lution such that it was less than the 0.01 M solution; or by a change 
 in the kind of ions present. Since the second of these factors is eliminated 
 by the data recorded in Table IX, which shows that such concentration 
 changes are impossible, it appears that the decrease in boundary potential 
 must be due to the other factors. 
 
 As there is a possibility that a chemical compound which ionizes is 
 formed, the facts are considered also from this point of view. If such is 
 the case there should be a fairly close relation between the amount of 
 gelatin added and the amount of acid removed. This would explain 
 the decrease in hydrogen-ion concentration and decrease in conductivity 
 observed. If such a reaction occurs new compounds are formed and some 
 of the hydrogen ions are replaced by complex gelatin ions which results 
 in the increase in the transference number of the anion as observed. No 
 
 12 Procter, /. Chem. Soc., 100, 342-3 (1911); 105, 313 (1914). 
 
 13 Procter and Wilson, ibid., 109, 307 (1916). 
 
 " Loeb, /. Gen. Physiol. 1, 39-60, 237-54 (1918) ; 2, 363-85, 483-504, 559-80 (1919) . 
 15 Fenn, /. Biol. Chem., 33, 279-94, 439-51 (1918); 34, 141-60, 415-28 (1918). 
 
27 
 
 data were obtained from which the exact amount of sulfuric acid removed 
 by a definite weight of gelatin could be determined. 
 
 From the curve for the conductivity of the 0.1 M sulfuric acid solution, 
 Fig. 6, it appears that the conductivity of the solution is reduced a definite 
 amount for each additional per cent of gelatin. The addition of the first 
 per cent of gelatin in the 0.01 M solution also produces about the same 
 reduction in conductivity. This indicates that a definite quantity of 
 gelatin removes a definite amount of sulfuric acid from the solutions. 
 If the compound formed dissociates, and some evidence has been obtained 
 from other sources that it does then the conductivity curves will tend to 
 flatten at the higher concentrations of gelatin. Loeb 14 has been led to be- 
 lieve that in acid solutions gelatin reacts to form gelatin salts of the acid 
 and in the case of sulfuric acid he states that the gelatin sulf ate formed has 
 the composition represented by the formula gel 4 (SO 4 )2. The dissociation 
 of such a salt would result in the formation of a slowly moving complex 
 colloidal gelatin cation and a sulf ate anion. The transference number 
 of the anion of such a compound would be greater than that of the cation. 
 This conforms to the observed facts. Furthermore, such a compound 
 would show some conductivity, so that for the higher concentrations of 
 gelatin the decrease in conductivity would no longer be proportional to 
 the gelatin added. This is borne out by the flattening of the conductivity 
 curves at the higher concentrations of gelatin. It should be pointed out 
 that the sharp bend in the conductivity curve of the 0.01 M solution, 
 Fig. 7, occurs at about the same concentration as a similar bend in the gela- 
 tin transference-number curve, Fig. 4; furthermore it is shown from the 
 gelatin concentration cells, Table IX, that the sulfuric acid in 0. 01 M solu- 
 tion is practically all removed at this same concentration of gelatin. 
 
 These facts indicate that sulfuric acid as such is removed by the addition 
 of gelatin to the solution. Accordingly the apparent change in transference 
 numbers is due not to an actual change in the velocity of the H + and SO* 
 ions, but to the presence of new ions in the solution resulting from the dis- 
 sociation of the gelatin sulf ate compound. 
 
 It is the opinion of the author that the aqtion of gelatin and sulfuric 
 acid results in the formation of a single dissociable product in which the 
 H + ion of the acid loses its identity. It is further believed that in the 
 presence of a base a similar product would result in which the identity 
 of the OH~ ion would be lost and that in the presence of a neutral salt 
 solution no similar action would result. At the present time investigations 
 are being conducted by the author to confirm this hypothesis. 
 
 Summary. 
 
 1. A method has been described for the determination of the trans- 
 ference numbers of a uni-bivalent electrolyte by the measurement of the 
 potentials of concentration cells. 
 
28 
 
 2. The transference number of the anion of sulfuric acid for concentra- 
 tions between 0.1 M and 0.01 M has been measured and found to be 
 0.1868 .7 at 25. 
 
 3. It has been shown that dissociation values determined from freezing- 
 point data are more satisfactory for calculating the potentials of concen- 
 tration cells than those obtained from conductivity data. 
 
 4. A correction to the formula for the potential of a concentration cell 
 has been developed which takes into account the undissociated part of 
 the acid. 
 
 5. It has been shown that the concentration-cell method is entirely 
 satisfactory for the determination of the transference numbers of sulfuric 
 acid. 
 
 6. The effective concentration of 0.1 M and 0.01 M sulfuric acid 
 solutions has been found to be reduced by the addition of gelatin. 
 
 7. The transference numbers of 0.1 M and 0.01 M sulfuric acid so- 
 lutions have been found to be altered by the presence of gelatin. 
 
 8. The conductivities of sulfuric acid solutions have been found to be 
 reduced by the presence of gelatin. 
 
 9. An hypothesis has been offered to account for the action of gelatin 
 in the presence of electrolytes. 
 
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