EFFECT OF THE $\psi'$-POTENTIAL ON THE ANODIC PEAK POTENTIAL

A. G. STROMBERG, V. E. GORODOVYKH, T. V. GOMZA

The rate of irreversible electrochemical reactions is greatly affected by changes in the near-electrode concentration of electroactive particles. The greater the potential jump in the diffuse part of the double layer, $\psi'$, the more the bulk and surface concentrations of ions differ. In addition, a change in the $\psi'$-potential causes a change in the effective potential jump between the electrode surface and the discharging particle [1].

A change in the $\psi'$-potential may be the result of changes in the concentration and composition of the supporting solution. When surface-active organic substances are introduced into the solution, the change in the $\psi'$-potential may be so large that it has a decisive influence on the course of the electrode process as a whole. A very vivid example in this respect is the influence of camphor on the amalgam-polarographic behavior of cadmium, described by Stromberg and Zagainova [2].

In the practice of amalgam polarography with accumulation, sufficiently concentrated supporting solutions are usually used, which makes it possible to disregard the influence of the $\psi'$-potential. Theoretically, the influence of the $\psi'$-potential on irreversible anodic peaks has likewise not been considered.

Let us use the equation for an irreversible anodic peak [3]:

\[ I_{\mathrm{p}}=\frac{z^2 F^2 C_R v \beta \omega}{RT}\cdot e^{-\frac{z^2 F^2 C_R v \beta \omega}{RT i_0}}-1, \tag{1} \]

where $C_R$ is the concentration of the metal in the amalgam, $v$ is the electrode volume, $\omega$ is the rate of change of potential, $\beta$ is the transfer coefficient, and $i_0$ is the exchange current.

In deriving the equation it was assumed that the electrode potential changes linearly with time in the anodic direction, beginning from the equilibrium potential:

\[ \varphi=\varphi_p+\omega t. \tag{2} \]

We shall assume that, for a given concentration of surfactant in the solution, the equilibrium potential corresponds to $\psi'_p$.

A change of the potential from the equilibrium value is accompanied by a change in the $\psi'$-potential:

\[ \psi'_{\varphi}=\psi'_p+\Delta\psi', \tag{3} \]

where \(\psi'_\varphi\) corresponds to the electrode potential \(\psi\).

Equation (2) will take the following form:

\[ \omega t = \varphi - \varphi_p - \psi'_\varphi + \psi'_p . \tag{4} \]

Substitute the expression for the time required to reach the peak [3]

\[ t_p = \frac{RT}{zF\beta\omega}\ln \frac{z^2F^2 C_R \beta\omega}{i_0 RT} \tag{5} \]

into equation (4)

\[ \varphi_p - \psi'_p = \varphi_p - \psi'_p + \frac{RT}{zF\beta}\ln \frac{z^2F^2 C_R \beta\omega}{i_0 RT}. \tag{6} \]

Substituting, in place of the apparent value of the exchange current, the exchange current at \(\psi' = 0\), \(i_0^*\), we obtain

\[ \varphi_p - \varphi_p = \psi'_p + \frac{RT}{zF\beta}\ln \frac{z^2F^2 C_R \beta\omega}{i_0^* RT}. \tag{7} \]

The dependence described by equation (7) can serve as an experimental criterion which, in the case of adsorption of organic surface-active substances, makes it possible to establish whether the change in the rate of the anodic process is only the result of a change in the \(\psi'\)-potential, or whether the decrease in the exchange current is also caused by a change in the activation energy of the process [4]. In the first case, in the coordinates \((\varphi_p-\varphi_p)-\psi'_p\), a straight line with a slope equal to unity should be obtained, cutting off on the ordinate axis a segment from whose magnitude the exchange current can be calculated (for known \(\beta\)). A change in the activation energy of the electron-transfer reaction will cause the indicated dependence to deviate from linearity.

We previously studied the influence of adsorption of \(\beta\)-naphthol on electrochemical processes involving cadmium under conditions of anodic–cathodic polarography. It was established that, in the process of cadmium ionization, adsorption of \(\beta\)-naphthol on the electrode, along with a change in the \(\psi'\)-potential, causes an increase in the activation energy of the electron-transfer reaction. The experimental criterion following from equation (7) makes it possible to test these conclusions under conditions of amalgam polarography with accumulation.

The anodic peaks of cadmium were obtained using a mercury-film electrode with a silver-plated platinum substrate [5a]. The background was 0.1 N sulfuric acid. The \(\beta\)-naphthol introduced into the solution was first purified by triple distillation with steam. The polarization curves were recorded using an OH-101 polarograph equipped with a device for automatic recording of the anodic peak [6a]. Potential measurements were performed relative to a saturated calomel electrode.

The adsorption of \(\beta\)-naphthol on mercury [7a] and the calculation of the \(\psi'\)-potential at various electrode potentials and \(\beta\)-naphthol concentrations had been carried out by us previously.

To avoid the influence of \(\beta\)-naphthol adsorption on the cadmium accumulation process, i.e., in order to maintain a constant initial concentration of the metal in the amalgam, the electrolysis potential was chosen outside the range of \(\beta\)-naphthol adsorption [7a] and was equal to \(-1.4\) V.

The height of the anodic peaks of cadmium obtained in the presence of various amounts of \(\beta\)-naphthol in the solution remains constant to within 15%. The peak potential changes, as shown in Fig. 1. The dependence \((\varphi_p-\varphi_p)-\psi'_p\) (Fig. 2) is nonlinear, which indicates

on the change in the activation energy of the electron-transfer reaction along with the $\psi'$-effect. Thus, the conclusions about the influence of $\beta$-naphthol adsorption on processes involving cadmium, obtained using anodic-cathodic polarography, are confirmed.

Fig. 1. Change in the potential of the anodic peak of cadmium with increasing concentration of $\beta$-naphthol in solution

Fig. 2. Change in the shift of the potential of the anodic peak of cadmium from the equilibrium potential as a function of the value corresponding to the peak potential

REFERENCES

1. A. N. Frumkin, V. S. Bagotskii, Z. A. Iofa, B. N. Kabanov. Kinetics of Electrode Processes. Moscow, Moscow State University Press, 1952.

2. A. G. Stromberg, L. S. Zagaynova. Journal of Physical Chemistry, 31, 1042, 1957.

3. V. A. Igolinskii. Izvestiya TPI, vol. 148, Tomsk, Tomsk State University Press, 1967, p. 14.

4. A. G. Stromberg, V. E. Gorodovykh, T. V. Gomza. Double Layer and Adsorption on Solid Electrodes. Proceedings of the III Symposium, Tartu, 1972, p. 235.

5. L. V. Mishchenko, V. A. Trukhacheva, R. Yu. Bek. TsNIIolovo, 1967, No. 1, p. 61.

6. V. V. Gomza, T. V. Gomza. “Zavodskaya laboratoriya,” 38, 668, 1972.

7. Yu. N. Oblivantsev, T. V. Gomza, V. E. Gorodovykh. Advances in Stripping Polarography. Tomsk, Tomsk State University Press, 1973, p. 101.