PHYSICAL CHEMISTRY

E. A. MAZNICHENKO, B. B. DAMASKIN, and Z. A. IOFA

EFFECT OF ALKALI-METAL CATIONS ON THE HYDROGEN OVERVOLTAGE ON MERCURY IN ACID SOLUTIONS

(Presented by Academician A. N. Frumkin, February 8, 1961)

A study of the dependence of the capacitance of the electrical double layer on the nature of the alkali-metal cations \((^{1,2})\) indicates a certain superequivalent adsorption of the larger-radius cations on the surface of the mercury electrode. This conclusion is in agreement with the effect of cations on the kinetics of electrochemical processes \((^{3-9})\). It was of interest to investigate the effect of alkali-metal cations on the cathodic evolution of hydrogen on mercury, the theory of which has been developed most fully.

We measured the hydrogen overvoltage \(\eta\) on a dropping mercury electrode in the following solutions: in pure \(0.01N\) HCl, in HCl with additions of LiCl, NaCl, KCl, RbCl, CsCl at concentrations of \(0.1;\ 0.33;\ 1N\), and also in \(0.001N\) HCl with additions of LiCl, KCl, CsCl at concentrations of \(0.001;\ 0.01;\ 0.033N\).

At an HCl concentration of \(0.001N\), the polarization curves were corrected for concentration polarization by the method of Meiman and Bagotskii \((^{10})\). In \(0.01N\) HCl the measured current \(\bar I\) is considerably below the limiting current, so that concentration polarization may be neglected. In this case the current density \(i\), corresponding to a definite \(\eta\), was calculated from the measured current \(\bar I\) and the mean drop area, computed from the formula \(\bar s = 0.509 (m\tau)^{2/3}\), where \(m\) is the rate of outflow of mercury from the capillary and \(\tau\) is the drop time of mercury at the given potential. The curves \(\eta,\ \lg i\) obtained in this way coincided with curves recorded on a stationary mercury electrode, since this method of calculation takes into account the correction associated with the regime of the dropping electrode \((^{11})\).

In dilute solutions the ohmic potential drop was taken into account according to the formula

\[ \Delta \varphi = \frac{\bar I}{4\pi \chi} \left[ \frac{4.82a}{m^{1/3}\tau^{1/3}} - 1 \right], \]

where \(\chi\) is the specific electrical conductivity, and \(a\) is the distance between the tip of the Luggin capillary and the center of the drop.

In the range of current densities investigated, \(10^{-4.8}—10^{-3.5}\ \text{A}/\text{cm}^2\), a linear dependence was observed between \(\eta\) and \(\lg i\). The slope of the curves for salt concentrations up to \(0.33N\) is \(0.110—0.111\ \text{V}\); for the normal solution, \(0.116\ \text{V}\). The experiments were carried out at negative potentials, at which adsorption of the anion \(\mathrm{Cl}^-\) should not occur. The reproducibility of the values of \(\eta\) from experiment to experiment was \(\pm 3\ \text{mV}\).

Table 1 gives the values of \(\eta\) for all investigated concentrations of HCl and salts at \(\lg i = -4\) and \(t = 22^\circ\). It is evident from the table that, for solutions of the same concentration, \(\eta\) increases from \(\mathrm{Li}^+\) to \(\mathrm{Cs}^+\). According to the basic equation of the slow-discharge theory,

\[ \eta = \mathrm{const} + \frac{RT}{\alpha F}\ln i + \frac{1-\alpha}{\alpha} \left( \psi_1 - \frac{RT}{F}\ln [\mathrm{H}^+] \right) \tag{1} \]

Table 1

Hydrogen overvoltage \(\eta\) (in volts)

the increase in \(\eta\) is associated with a shift of the \(\psi_1\)-potential in the positive direction. Since the total electrolyte concentration remains constant, the \(\psi_1\)-potential takes on more positive values, apparently as a result of increased adsorption of cations with increasing radius.

Let us consider the dependence of \(\eta\) on the background concentration for each cation and compare it with the increase in overvoltage \(\Delta\eta\) on going from pure acid to a solution of the given composition, calculated from the equations of the theory of the diffuse double layer. If the nature of the cations is not taken into account, the value of \(\Delta\eta\) can be calculated from the approximate formula

\[ \Delta\eta=\frac{1-\alpha}{\alpha}\frac{RT}{F}\ln\frac{C}{[\mathrm{H_3O^+}]}, \tag{2} \]

where \(C\) is the total electrolyte concentration; moreover, this formula gives values close to the theoretical ones at \(\alpha=0.527\) \((^{13})\).

It follows from equation (1) that at \(\ln i=\mathrm{const}\) and \(\mathrm{pH}=\mathrm{const}\), \(\Delta\eta=\Delta\psi_1\). Therefore we can compare our experimental values of \(\Delta\eta\), as well as \(\Delta\eta\) determined by formula (2), with the corresponding \(\Delta\psi_1\), i.e., the increases in \(\psi_1\) on going from pure HCl to HCl of the same concentration but with added salt, calculated according to Grahame’s theory from capacitance data. The experimental and calculated results for acidic solutions of LiCl, KCl, and CsCl are given in Table 2. It is evident from the table that for all concentrations

Table 2

electrolyte, except for the highest one, the theoretical values of $\Delta\eta$ and $\Delta\psi_1$ in KCl solutions are closest of all to the experimental $\Delta\eta$. Our experimental $\Delta\eta$ for KCl is approximately 10% lower than the values given in Bagotskii’s work [15], which may be explained by the higher $\eta$ in pure HCl in our experiments.

All experimental values of $\Delta\eta$ for LiCl are lower, and for CsCl higher, than the theoretical ones, so that one may suppose that the concentration of cations in the double layer in the case of Li$^+$ is lower, and in the case of Cs$^+$ higher, than for K$^+$. Thus, Li$^+$ ions apparently exhibit negative specific adsorption, which can be explained by the greater hydration of Li$^+$ ions, so that it is relatively more advantageous for Li$^+$ cations to be in the bulk of the solution, where they are completely hydrated, than in the double layer, where partial dehydration of the cations is possible. The increased concentration of Cs$^+$ ions in the double layer, in agreement with literature data, is probably due to its specific adsorption.

As can be seen from Table 2, when the background concentration is increased to $1N$, the experimental values of $\Delta\eta$ in KCl solutions become considerably lower than the calculated ones, which in this case coincide with the experimental values of $\Delta\eta$ for CsCl. According to literature data on differential capacitance [2], this result can be explained by the drawing of Cl$^-$ anions into the double layer, which removes the effect of the specific adsorption of Cs$^+$ cations.

It is of interest to compare the experimental values of $\Delta\Delta\eta$ upon replacing Li$^+$ ions by K$^+$ ions and K$^+$ ions by Cs$^+$ ions in solutions of the same concentration with the theoretical $\Delta\Delta\psi_1$ for these same solutions. It is seen from Table 3 that the electrostatic calculation of $\Delta\Delta\psi_1$ according to Grahame’s theory, which assumes the absence of specific adsorption of cations, gives negative values of $\Delta\Delta\psi_1$, which contradicts the kinetic experimental data.

Table 3

Note. a — according to Grahame’s theory; b — according to the theory of Brodskii—Shtrehlov.

Tables 2 and 3 give $\Delta\psi_1$ and $\Delta\Delta\psi_1$ for K$^+$ and Li$^+$ ions, calculated according to the theory of Brodskii and Shtrehlov [16, 17]. The calculation was carried out graphically; for the ions the following values of effective ionic radii were adopted: for H$^+$ and Li$^+$, $r = 5$ Å, and for K$^+$ and Cs$^+$, $r = 3$ Å$^\*$. The values of $\Delta\psi_1$ for the case of increasing the background concentration according to this theory are close to $\Delta\psi_1$ calculated by the theory of the diffuse double layer (Table 2). On the other hand, $\Delta\Delta\psi_1$ in going from Li$^+$ to K$^+$ of the same concentration has the same sign as the experimental $\Delta\Delta\eta$ (Table 3). In dilute solutions even quantitative agreement between calculation and experiment is observed.

* The values of the effective ionic radii adopted here were roughly equated by us to the radii of the anions F$^-$ and Cl$^-$, since only for these ions had they been determined. The ratio of ionic radii (with the exception of H$^+$) was determined by the ratio of mobilities. Calculation of absolute values of the effective ionic radii by Stokes’ formula from mobility values [18] leads to considerably smaller quantities, for which the difference between the theories of Grahame and Brodskii—Shtrehlov is erased.

The increase in \(\eta\) on going from \(\mathrm{Li}^+\) to \(\mathrm{K}^+\), according to the theory \((^{16,17})\), can be explained by a more positive value of \(\psi_1\) in KCl, owing to the higher concentration of \(\mathrm{K}^+\) ions in the double layer because of their smaller effective volume. However, it follows from this theory that the effect of increasing \(\eta\) on going from \(\mathrm{Li}^+\) to \(\mathrm{K}^+\) should be greater than from \(\mathrm{K}^+\) to \(\mathrm{Cs}^+\), since the difference in effective ionic radii, calculated from mobilities \((^{19})\), is much larger in the first case than in the second. As is seen from Table 3, this conclusion contradicts the experimental data: thus, the experimental \(\Delta \Delta \eta_{\mathrm{Cs}^+—\mathrm{K}^+}\) values exceed \(\Delta \Delta \eta_{\mathrm{K}^+—\mathrm{Li}^+}\) by more than a factor of two. Thus, in order to explain the magnitude of \(\Delta \Delta \eta_{\mathrm{Cs}^+—\mathrm{K}^+}\), the theoretical premises of Brodowsky and Strelov are insufficient. Apparently, allowance must be made for the influence of specific adsorption.

In our experiments a smaller specific influence of cations on the rate of the process was observed than in the case of reduction of \(\mathrm{S}_2\mathrm{O}_8^{2-}\) anions. This can be partly explained on the basis of the theory of delayed discharge, since the influence of cations is the greater, the larger in absolute value is the coefficient at the \(\psi_1\)-potential. For the \(\mathrm{S}_2\mathrm{O}_8^{2-}\) anion it is equal to \(\frac{n-\alpha}{\alpha} =\)

\[ = -8.1, \]

whereas in hydrogen reduction \(\frac{1-\alpha}{\alpha} = +1\). At the same time \(\Delta \Delta \psi_1\), calculated by the theory of delayed discharge for the transition from \(0.01N\) KCl to \(0.01N\) CsCl at a potential of \(-1.4\) V, amounts, in the case of reduction of \(0.001N\ \mathrm{S}_2\mathrm{O}_8^{2-}\), to 65 mV, and in the case of reduction of \(0.001N\ \mathrm{H}^+\), to 37 mV. Apparently, this discrepancy is connected with the approximate nature of the calculation of the \(\psi_1\)-potential and indicates the need to take into account the local value of the \(\psi_1\)-potential near adsorbing ions.

We express our deep gratitude to Academician A. N. Frumkin for his exceptional attention to the work and for valuable advice in discussing the experimental data.

Moscow State University
named after M. V. Lomonosov

Received
3 II 1961

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