T H E TRANSFERENCE NUMBERS OF HYDROCHLORIC ACID IN GLYCEROL-WATER MIXTURES * BY WALTER W. LUCASSE
The transference numbers of an electrolyte can be calculated from the results of measurements of concentration cells without and with liquid junction, In a recent article*results have been published from measurements of cells of the type Hz I HC1 [ AgCl I Ag in which the acid concentration was varied from 0.001 to 4M in solvents of one and five mole percent. glycerol in water. From these measurements it is possible to calculate the electromotive force of cells without liquid junction of the form Ag [ AgCl [ HC1 I Hz [ HCI I AgCl 1 Ag In the present paper are given results of measurements of liquid junction cells of the type Ag 1 AgCl [ HC1 (m) I HCl(o.01 M) [ AgCl 1 Ag in solutions of one and five mole percent. glycerol a t 25' =t0.01. The acid concentration was varied from 0.01 to I M. The hydrochloric acid and glycerol were the same as used in the previous study and the solutions and electrodes were made up in the same manner. The cell used was similar to that described in a previous investigation2, the only change being that the capillary tube connecting the parts B and C was made in the form of a U-tube thus further decreasing the possibility of concentration changes in the solution around the electrode in part C due to diffusion, The results are given in Table I, the values of the electromotive force being the mean of a number of readings taken over a period of several hours after the cell had been allowed to stand in the thermostat for about five hours. The variation in the readings was extremely small, seldom more than a few hundredths of a millivolt. Measurements were also made in each solvent with the electrolyte a t 0.001, 0 . 0 0 2 and 0.005 M. The variations between duplicate determinations were found, however, to be large and from the cells without liquid junction it was seen that the type of electrode used is unreliable a t low concentrations. The results of all measurements between 0.01 and I M are given with the exception of one at 0 . 0 2 M in the second series which was obviously in error. In the first series the values of the electromotive force at 0.1 and a t I M are each the mean of two determinations, the average deviation from the mean being 0.14 and 0.08 mv., respectively. The
* Contribution from the John Harrison Laboratory of Chemistry of the University of Pennsylvania. J. Am. Chem. SOC.,48, 626 (1926). 2 J. Am. Chem. SOC.,47, 743 (1925).
TRANSFERENCE NUMBERS O F HYDROCHLORIC ACID
563
TABLE I Results from Liquid Junc tion Cells Ag 1 AgCl 1 HC1 (m) 1 HCl(o.01 M) I AgCl I Ag Solvent : Five mole Solvent: One mole % glyc. m
E
(0.001)
( (
.005)
.OI
0.00000
.02
.02812
*OS .I
.o6511 .09259
.2
.120go
.28
1
.5
.7 I .o
E
t+
0.814 -0.0195 .817 .2792 .82 I ,6656 .825 * 9552 I. 2420 .828 I . 6160 , ,832 I . 9020 * 834 .838 2.1841 .840 2.3257 .841 2.4566 ' 843 2.5769 .844 2.7327 .846 2.9085
+
.002)
.38
log A
I 3 507 .14811 . I5994 .I7565 .19306
t+
-0.0191
0.845 .844 ' 843
-t0.00000
.oz846 .06530 .09433 ,12165 .I3574 .I4894 .16057 .17671 .I9422
% glyc.
log A
.2746
.6594 9469 1 * 2345 I .6075 I . 8893 2.1726 '
2.3152
2.4477 2.5664 2.7259 2.9036
.842 .841
.840 1839 ,838 .838 .838 '837 .837 .836
value at I M in the second series is the mean of two determinations, the average deviation from the mean being 0.07 mv. The concentrations are expressed in terms of formula weights per 1000grams of solvent. The method used in calculating the transference numbers was that employed by MacInnes and Beattiel. For a uni-univalent electrolyte the equation relating the activity of the electrolyte and the electromotive force of a cell without liquid junction is d E
=- 2
R T dlnak F
and for a cell with liquid junction d Et = t+ 2 R T dlnaA (2) F If the electromotive force be plotted against the logarithm of the geometrical mean activity a straight line will result from the first equation, of constant T; while a curved line of variable slope, t+ T , will result from slope, F F the second equation since t+ is a variable. The ratio of the slopes of these lines a t any given activity yields the cation transference number a t the corresponding concentration. The values of the electromotive forces of the cells without liquid junction were related to the values of log 103 a &(=log A), obtained from the cells without liquid junction, by the empirical equation Et = a b(1ogA) c(logA)2 The values of the constants a, b and c were determined by the method of least squares.
+
+
MacInnes and Beattie: J. Am. Chem. SOC.,42,
1117
(1920).
5 64
WALTER W. LUCASSE
For the one mole percent. solution the equation obtained was Et = -0.092528 0.096289 (log A) 0.00066196 (log A)2
+
+
(3)
and thus the slope of the curve was dE = 0.096289 0.0013239 log A d (1% A) Dividing by the constant slope of the curve without transference (I) gave for the variation of the transference number t t = 0.8139 0.01119 log A (4) The mean deviation, positive and negative, of the observed values from those calcula,ted by equation (3) was 0.11% of the total electromotive force.
+
+
FIG.I The Cation Transference Sumbers of Hydrochloric Acid: I in one mole percent glyc., I1 in five mole per cent glyc., I11 in fifty mole per cent alcohol, IV in absolute alcohol.
For the five mole percent. solution the equation obtained was Et = -0.094589 0.099982 (log A) - 0.00018642 (logA)2 ( 5 ) and thus for the transference numbers t+ = 0.8452 - 0.003152 log A (6) The mean deviation, positive and negative, of the observed values from those calculated by equation ( 5 ) was 0.18% of the total electromotive force. The values of the transference numbers given in Table I were computed from equations (4) and (6). The values of log A there given are, with the exception of those a t 0.001, 0.002 and 0.005 M, from the observed results of the activity coefficient determined from the cells without liquid junction. The values of log A at the bracketed concentrations were obtained from the calculated values of the activity coefficient and the corresponding values of the transference numbers were computed by assuming that the validity of equations (4) and (6) may be extended to these concentrations, although the equations were formed from the data between 0.01 and I M inclusive.
+
TRANSFERENCE NUMBERS O F HYDROCHLORIC ACID
565
The distribution of the curves may be seen from Figure I where the cation transference number X 1000 is plotted against the square root of the molality. There are plotted also, for comparison, the values found by Harned and Fleysherl for the cation transference numbers of hydrochloric acid in 50 mole percent. alcohol and in absolute alcohol. According to the "best values" of Noyes and Fall? the cation transference numbers of hydrochloric acid in water a t 18" rise from 0.832 at 0.005 normal to 0.844 a t I normal. At 2 5 " the values are doubtlessly about 1% lower and rise in about the same manner or perhaps with slightly greater rapidity. It will be noted that the transference number of the hydrogen ion increases with increasing acid concentration in the one mole percent. glycerol solution while in the other three solvents it decreases, the decrease being more rapid the smaller the water content. The distribution of the curves indicates a similar behavior at constant acid concentration to that found by Krumreich3 for the cation transference numbers of 0.01 normal silver nitrate in mixtures of ethyl alcohol and water a t 40'. The transference number of the silver ion was found to increase from 0.482 in pure water to 0.488 in 30% alcohol after which it decreased rapidly to 0.410 in 99.8% alcohol. Had the glycerol content been greater in the present study the curve would doubtlessly have decreased much more rapidly than in the five mole percent. solution and given values of the transference numbers considerably lower than those in water. It is conceivable that measurements in alcoholic solutions of higher water content would give values of the cation transference number which would rise with increasing acid concentration and, indeed, would be greater than those in pure water at the same concentration. Such behavior may be attributed to changes in the relative solvation of the ions in the different solvents.
Summary Measurements at 2 5 " of cells of the form Ag I AgCl I HC1 (m) I HCl(o.01 M) I AgCl I Ag in which m is given a number of values up to one molal in solvents of one and five mole percent. glycerol, have been presented. From these data and the results from corresponding cells without liquid junction, the cation transference numbers of hydrochloric acid have been calculated. Philadelphia, Pennsylvania.
1ISarned and Fleysher: J. Am. Chem. SOC.,47, 92 (1925). 2Soyes and Falk: J. Am. Chem. SOC.,33, 1436 (1911). 3 Krumreich: Z. Elektrochem., 22, 446 (1916).
