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
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE
UNIVERSITY OF MICHIGAN IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF DOCTOR
Wesley George I France
ESCHENBACH PRINTING COMPANY
A Study of the Transference Numbers of
Sulfuric Acid and the Influence of
Gelatin on the Transference
Numbers by the Concen-
tration Cell Method
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE
UNIVERSITY OF MICHIGAN IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF DOCTOR
Wesley George France
ESCHENBACH PRINTING COMPANY
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
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
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.
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.)
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
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
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
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
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.
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
The potential at the liquid boundary is expressed by the formula
2Uc-Ua RT ci
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 +
By the substitution of the transference number of N fl , of the anion for
U a /(U a + U c ) the equation
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
E = \ R i ln l (6)
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).
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
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
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
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.
No. Date. Time. Bar. E H . E SO4 . EQ^. E OQ1 . E H +E SOt .E Q 01 - EQ j.
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.
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
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
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.
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
5 Lewis and Linhart, J. Am. Chem. Soc., 41, 1959 (1919).
D./ 0.O/ O.OOt O.OOOI O.OOOOI O.OOOOOI
Fig. 2. Dissociation-concentration
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
Similarly the osmotic work in (3) is W = (I a)RT In -. In the appli-
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
W = 2EF = <x3RTln ff + (l-
E = -
6 J. Phys. Chem., 20, 326 (1916).
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'
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
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
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).
shown that N = ^ 4 . The formula then becomes
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)
Substituting in (9)
Nc In - RT r .
EB = 2 F c 2 (3Nf _ !) = . tn * (3Nc _ 1}
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
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
SUMMARY OP POTENTIALS AND TRANSFERENCE NUMBERS.
T KI j? j? Eor N "- Na -
Table. /. -rWu-
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.
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.
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).
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
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
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
Fig. Ill Detail
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
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.
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
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-
Tf C^ CO
0^ O^ O^
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 (
OCOCO lO lO 1C
o o o o o o o o o
CO Cl 00
t^- I-H O5 O5C1O5
o o o o o' o
CO lO O^ O5 <N i (
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
o' o ooo
CO CO CO OOOl> 1C
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
^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
p p p o pop p <
d odd odd odd dod o'oo odd ooo odd odd
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
TABLE VIII. SUMMARY OF POTENTIALS AND TRANSFERENCE NUMBERS.
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
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-
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.
0.1 M. 0.01 M.
%Gel. C lf x . C 2 E z .
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
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
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.
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
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
2 4 6 8 /O /2 /4 /& f8 2O
Fig. 6. Conductivity-gelatin curve
for o.i M H 2 SO 4 .
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).
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).
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.
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.
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
5. It has been shown that the concentration-cell method is entirely
satisfactory for the determination of the transference numbers of sulfuric
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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