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Full text of "A study of the transference numbers of sulfuric acid and the influence of gelatin on the transference numbers by concentration cell method .."






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EXCHANGE 




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8061 '12 NVP Itfd 
'A 'M 'asnoEjA 



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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