the conclusion can be extended to spherical segments of any cross sections, since the hemisphere is the most unfavorable variant for comparison.

Thus, the general scheme for using a parallelepiped as a model for calculating the current at a real mercury spherical electrode may be represented as follows.

1. The shape of the spherical segment is estimated, i.e., the value of the parameter \(\rho\) is found.

2. Using the value of \(\rho\), the parameter \(\alpha\) is chosen, i.e., a parallelepiped is selected whose surface is either equal to the surface of the spherical segment under study or differs from it minimally.

3. For the selected parallelepiped, the current is calculated by formula (I) under the condition \(F_0 < (0.1 \div 0.2)\). The anodic current at the electrode in the form of a truncated sphere is taken to be equal to this value.

Literature

1. V. E. Katyukhin, A. A. Kaplin. Coll. “Chemistry and Chemical Technology,” Tomsk, TPU Press, 1973, p. 57.

2. N. V. Chovnyk, V. V. Vashchenko. ZhFKh, 37, 538, 1963.

EFFECT OF A SUBSEQUENT CHEMICAL COMPLEXATION REACTION ON THE POTENTIAL OF THE REVERSIBLE ANODIC PEAK IN THE ASV METHOD AT A STATIONARY MERCURY DROP ELECTRODE

S. S. Reznikova, Yu. A. Karbainov

In work / 1 / the results were presented of a numerical evaluation of the equation for the reversible anodic peak in the ASV method at a stationary mercury drop electrode for an electrode process complicated by a subsequent chemical complexation reaction.

By interpolating these data, expressions were obtained that relate the potential of the reversible anodic peak to the parameters of the subsequent chemical reaction. The results of these studies are discussed below.

As should be expected, the subsequent chemical complexation reaction occurring in solution causes a shift of the potential of the reversible anodic peak toward more negative-

values. The dependence of the magnitude of this shift \(\Delta \varphi\) on the dimensionless rate constant of the forward complex-formation reaction \(K_f^*\) is rather complex. Here \(\Delta \varphi = -(\varphi_n-\varphi_{\mathrm{pred}})\), and \(\varphi_{\mathrm{pred}}\) is the potential of the reversible anodic peak in the limiting case where \(\gamma = 0\) /2/ and kinetic complications are absent.

\[ \gamma=\frac{RT}{zF}\cdot\frac{D}{\omega r} \qquad K_f^*=\frac{K_f^0/\sigma}{\left(K_f^0/\sigma\right)'} \tag{1} \]

where

\[ \sigma=\frac{zF\omega}{RT},\ \mathrm{s}^{-1} \tag{2} \]

\[ K_f^0=K_f\cdot C_l^p,\ \mathrm{s}^{-1} \tag{3} \]

\(\omega\) is the rate of change of the potential, V/s; \(C_l\) is the concentration of ligand in solution, mol/ml; \(K_f\) is the rate constant of the forward complex-formation reaction, ml/(s·mol). The value \(\left(K_f^0/\sigma\right)'\) corresponds to the limiting case in which the subsequent chemical reaction has practically no effect on the electrode process as a whole. The remaining notation in (1–3) is conventional.

Analysis of the dependence of the potential shift \(\Delta \varphi\) on \(K_f^*\) showed that an increase in \(K_f^*\) causes an enhancement of the potential shift in the negative direction. At sufficiently large values of \(K_f^*\) (fast chemical reactions), the form of this dependence changes sharply; a certain maximum potential shift is attained, the magnitude of which depends on the stability of the complex. A further increase in \(K_f^*\) no longer affects the magnitude of \(\Delta \varphi\); that is, at large values of \(K_f^*\) the peak potential does not depend on \(K_f^*\).

Within the working range of electrode sizes \(r=(0.02\div0.05\,\mathrm{cm})\), the potential of the reversible anodic peak, to an accuracy of 5 mV, does not depend on the electrode radius for any values of \(K_f^*\). The dependence of \(\varphi_n\) on the rate of change of the potential \(\omega\) is accounted for by the dimensionless rate constant of the forward complex-formation reaction \(K_f^*\).

Since, at large \(K_f^*\), the potential of the reversible anodic peak does not depend on the value of \(K_f^*\), in this case \(\varphi_n\) does not depend on the rate of change of the potential. Thus, at large \(K_f^*\), i.e., in the case of fast chemical reactions, the peak potential, just as in the case of linear semi-infinite diffusion, does not depend on \(\omega\) or \(r\).

For small values of the rate constant of the forward reaction com—

complexation \(\left(\lg \dfrac{K_f^*}{K_p} \le 3\right)\), where \(K_p\) is the stability constant of the complex, the interpolation formula is valid

\[ \lg \Delta \Psi = \left(\lg K_f^*\right)^{0.778} + 0.539 \tag{4} \]

In logarithmic coordinates this equation is easily represented as a straight line. The tangent of the angle of inclination of this straight line is 0.778, and the segment cut off on the ordinate axis is 0.445.

For large values of \(K_f^*\left(\lg \dfrac{K_f^*}{K_p} > 3\right)\), one may use the formula

\[ \lg \Delta \Psi = \frac{\lg K_f^*}{0.442 \lg K_f^* + 0.39} \tag{5} \]

Equation (5) in the coordinates \(\lg K_f^*;\ \lg K_f^*/\lg \Delta \Psi\) gives a straight line with tangent of the angle of inclination equal to 0.442. The segment cut off by this straight line on the ordinate axis is 0.38. Equation (5) is valid only for sufficiently strong complexes, \(\lg K_p > 5\).

Expressions (4) and (5) can be used to estimate the parameters of the chemical reaction. The composition of complex \(P\) can be found from equation (3).

Literature

1. Yu. A. Karbainov, S. S. Reznikova, A. G. Stromberg. Elektrokhimiya, 9, 1351 (1973).
2. V. E. Gorodovykh. Izvestiya TPI, 164, II (1967),

ON THE APPLICATION OF NUMERICAL METHODS IN SOLVING DIFFUSION EQUATIONS IN STRIPPING POLAROGRAPHY

A. E. Geineman, M. V. Krasheninnikov, A. A. Kaplin

At the present time, in the ASP method two approaches are used rather widely for solving Fick’s second law with various boundary conditions. The first of these consists in obtaining equations for the anodic current as a function of time in explicit form. In this case the solutions are obtained in the form of series or integrals, the further analysis of which requires calculations on a computer. Sometimes analysis of the general expressions leads to simple approximate analytical expressions, which is the chief advantage of this approach. The second approach is based on the derivation of integral equations with their subsequent solution on a computer.