Reports of the Academy of Sciences of the USSR
1963. Vol. 150, No. 3

PHYSICAL CHEMISTRY

O. K. STEFANOVA, E. A. MATEROVA,
Corresponding Member of the Academy of Sciences of the USSR B. P. NIKOLSKII

ION-EXCHANGE AND ELECTROCHEMICAL PROPERTIES OF SULFOCATIONITES IN SOLUTIONS OF CERTAIN 1–1 CHARGE ELECTROLYTES

In the preceding communication \((^1)\) an approximate equation was discussed which expresses the dependence of the e.m.f. of the cell

\[ \mathrm{Ag}\,|\,\mathrm{AgCl},\,\mathrm{ACl},\,\mathrm{BCl} \underset{\text{solution I}}{\big|} \text{ cationite membrane } \big|\, \mathrm{ACl},\,\mathrm{BCl},\,\mathrm{AgCl} \underset{\text{solution II}}{\big|} \,\mathrm{Ag} \tag{1} \]

on the compositions of solutions I and II:

\[ E=\frac{RT}{F}\ln \frac{ a_{\pm(\mathrm{BCl})_2}^{2} +K_{\mathrm{A-B}}\frac{U_A}{U_B}a_{\pm(\mathrm{ACl})_2}^{2} }{ a_{\pm(\mathrm{BCl})_1}^{2} +K_{\mathrm{A-B}}\frac{U_A}{U_B}a_{\pm(\mathrm{ACl})_1}^{2} }. \tag{2} \]

Here \(a_{\pm(\mathrm{ACl})_1}\), \(a_{\pm(\mathrm{ACl})_2}\), \(a_{\pm(\mathrm{BCl})_1}\), and \(a_{\pm(\mathrm{BCl})_2}\) are the mean activities of the corresponding chlorides in solutions I and II; \(U_A\) and \(U_B\) are the mobilities of ions \(A^+\) and \(B^+\) in the membrane; \(K_{\mathrm{A-B}}=\dfrac{C_A a_B}{C_B a_A}\) is the exchange constant of ions \(A^+\) and \(B^+\) between the cationite and the solution; \(C_A\) and \(C_B\) are the concentrations of ions \(A^+\) and \(B^+\) in the cationite, and \(a_A\) and \(a_B\) are their activities in the solution.

Fig. 1. Cell for measuring transport numbers (schematic)

This equation can be obtained from the general thermodynamic relation given in \((^2)\). The assumptions made in deriving equation (2) were discussed in detail in \((^1)\). For the systems investigated in the present work, the most important is the following: it is assumed that the membrane is impermeable to anions, that the activity coefficients and mobilities of the cations inside the membrane are constant, and that solvent transport may be neglected.

For the special case in which each of the solutions contains only one electrolyte, i.e., for the galvanic cell

\[ \mathrm{Ag}\,|\,\mathrm{AgCl},\,\mathrm{ACl} \underset{\text{solution I}}{\big|} \text{ cationite membrane } \big|\, \mathrm{BCl},\,\mathrm{AgCl} \underset{\text{solution II}}{\big|} \,\mathrm{Ag} \tag{3} \]

equation (2) is transformed into the following:

\[ E=\frac{RT}{F}\ln \frac{ a_{\pm(\mathrm{BCl})_2}^{2} }{ K_{\mathrm{A-B}}\frac{U_A}{U_B}a_{\pm(\mathrm{ACl})_1}^{2} } = \frac{2RT}{F}\ln \frac{a_{\pm(\mathrm{BCl})_2}}{a_{\pm(\mathrm{ACl})_1}} - \frac{RT}{F}\ln K_{\mathrm{A-B}}\frac{U_A}{U_B}. \tag{4} \]

The present communication is devoted to studying the applicability of equations (2) and (4) to specific systems including HCl—NaCl, HCl—KCl, NH₄Cl—KCl solutions and heterogeneous membranes based on KU-2 and SBS-1 sulfocationites.*

On the basis of the results of independent measurements, the parameters \(K_{A-B}\) and \(\dfrac{U_A}{U_B}\), entering equations (2) and (4), were determined. From these data the e.m.f. of galvanic cells (1) or (3) containing solutions of known composition was calculated. The values obtained were compared with the e.m.f. values determined experimentally. \(K_{A-B}\) was calculated from data on the equilibrium compositions of the solution and the corresponding granular ion exchanger; the ratio of the activity coefficients of the cations in solution was calculated by Harned’s method (⁴).

The ratio of the mobilities of cations inside the ion exchanger was determined on the basis of measurements of transport numbers through a membrane (or resin) in mixed form, or from the change in the electrical conductivity of the membrane when it was converted from one ionic form into another. The ion transport numbers \((\mathrm{H}^+, \mathrm{Na}^+, \mathrm{Cl}^-)\) were determined analytically from the change in their content in the cathodic solution after passing a definite quantity of electricity through the system. The cell in which the measurements were carried out is shown in Fig. 1a.

Fig. 2. Setup for measuring electrical conductivity (schematic)

When calculating the ratio of the mobilities of \(\mathrm{H}^+\) and \(\mathrm{Na}^+\) ions inside the membrane from the values of their transport numbers, it was assumed that the ionic composition of the membrane corresponds to equilibrium with the anodic solution.** The latter condition is not fulfilled if concentration polarization arises at the boundary between the membrane and the anodic solution. To avoid its possible influence, we investigated ion transport through a layer of granular ion exchanger (packed membranes). In this case, between the chambers of the cell (Fig. 1b) there was placed a layer of ion exchanger of known ionic composition, separated from the solutions by the corresponding heterogeneous membranes. During the experiment, the constancy of the composition of the ion-exchanger layer adjacent to the cathodic solution was monitored. Under this condition, possible polarization at the membrane boundary with the anodic solution will not affect the results.

The electrical conductivity was measured using direct current. The layout of the apparatus is presented in Fig. 2. The resistance of the layer of solution adjacent to the membrane was taken into account by a blank experiment in which the membrane was removed from the cell. During resistance measurements the system was thermostated; all other quantities were determined at room temperature (18–20°).

When measuring the e.m.f. of cell (1) or (3), the solutions separated by the membrane were buffered by adding to them 10–20 g of resin previously brought into equilibrium with the given solution. The contents of the chambers were stirred vigorously. The results obtained are presented in Table 1.

In the last three columns of the table are given the e.m.f. values of the cells

* The characteristics of these resins and membranes are given in work (³).
** The theoretical and experimental justification of this assumption will be given in a more detailed communication.

Table 1

Note. In all cases, subscript 1 refers to that electrolyte or cation which is written first in the second column.

(1) or (3), obtained experimentally ($E_{\mathrm{expt}}$), calculated from equation (2) or (4) ($E'_{\mathrm{theor}}$), and also from the equation of the ion-exchange theory of the glass electrode (⁵), which does not take into account the influence of ion mobilities on the magnitude of the e.m.f. ($E_{\mathrm{theor}}$). The agreement between the values of $E_{\mathrm{expt}}$ and $E'_{\mathrm{theor}}$ may be considered satisfactory if one takes into account the considerable scatter in the values of the exchange constants and the ratios of the ion mobilities, especially for the SBS-1 resin.* The e.m.f. values calculated from the equation of ion-exchange theory for all systems containing the hydrogen ion show greater discrepancies with experiment, clearly exceeding the experimental error. Consequently, in this case the diffusion potential inside the membrane, caused by the different mobilities of counterions, makes a substantial contribution to the e.m.f. of the cell.

The satisfactory agreement between the e.m.f. values determined experimentally and calculated from equations (2) and (4) indicates the applicability of these equations to the systems studied: HCl—NaCl, NH₄Cl—KCl, and, to a lesser extent, HCl—KCl. Consequently, the assumptions (¹) made in deriving these equations may, for the first two systems, be considered valid within the accuracy of our experiment.

As has already been noted in the literature (see, for example, (⁶)), the magnitude of the bi-ionic potential (or of the e.m.f. of cell (3) in our case) is a measure of the specificity of the membrane electrode with respect to ion B⁺ in the presence of ion A⁺. In the systems we studied, one can speak only of a certain slight specificity of the membrane electrodes with respect to the hydrogen ion, which is determined by its increased mobility in the ionite phase.

The authors express their deep gratitude to E. B. Trostyanskaya, A. S. Tevlina, K. M. Saldadze, B. A. Pashkov, and E. I. Semenova, who provided the resins and membranes for this work.

Leningrad State University
named after A. A. Zhdanov

Received
16 I 1963

REFERENCES

¹ O. K. Stefanova, M. M. Shults et al., Vestn. Leningr. Univ., No. 4 (1963).
² G. Scatchard, J. Am. Chem. Soc., 75, 2883 (1953).
³ K. M. Saldadze, A. B. Pashkov, V. S. Titov, Ion-Exchange High-Molecular Compounds, Moscow, 1960.
⁴ G. Harned, B. Owen, The Physical Chemistry of Electrolyte Solutions, Moscow, 1952, p. 427.
⁵ B. P. Nikolsky, ZhFKh, 10, 495 (1937).
⁶ F. Helferich, Ionites, Moscow, 1962, p. 341.

* The low accuracy of the results obtained for the SBS-1 resin is evidently due to the fact that the latter has lower chemical stability, lower capacity than the KU-2 resin, and is also not strictly monofunctional.