Tomsk Order of the October Revolution and Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov
Volume 197, 1975

ANODIC AMALGAM VOLTAMPEROMETRY AT CONSTANT CURRENT ON MERCURY FILM AND SPHERICAL ELECTRODES. A CALCULATION METHOD

M. S. Zakharov, V. V. Pnev, V. I. Bakanov

(Submitted by the scientific seminar of the Department of Physical and Colloid Chemistry)

In the present work a calculation method is proposed for anodic amalgam voltamperometry with constant current (AAVC) for determining the concentration in solution of elements whose amalgams are oxidized reversibly.

For reversible electrode processes on mercury film electrodes (at $\vartheta' \ge 0.35$) and spherical electrodes (at $\vartheta' \ge 0.24$), the dependence of the electrode potential $\varphi$ on time is expressed respectively by the equations [1, 2]:

\[ \varphi^{\mathrm{pl}}_{(\vartheta)} = \varphi_1 - \frac{RT}{zF} \ln \frac{q\left[\vartheta'-\vartheta+\Phi(\vartheta)\right]} {C_0^{0}-\frac{2q}{\pi^{1/2}}\vartheta^{1/2}}, \tag{1} \]

\[ \varphi^{\mathrm{sph}}_{(\vartheta)} = \varphi_1 - \frac{RT}{zF} \ln \frac{3\lambda(\vartheta'-\vartheta)+\lambda\Phi(\vartheta)} {C_0^{0}+\lambda\left(1-\exp \vartheta\, \operatorname{erfc}\vartheta^{1/2}\right)}. \tag{2} \]

where

\[ q=\frac{i_0 l}{zFDS}, \qquad \lambda=\frac{i_0 r_0}{zFDS}, \qquad \Phi(\vartheta)=\sum_{n=1}^{\infty}\frac{2}{\mu_n^2}\exp(-\mu_n^2\vartheta). \]

From equations (1) and (2) it is evident that the half-wave potential for a reversible process is attained when the expression under the logarithm is equal to unity. From this condition one can obtain equations for calculating the time of attainment of the half-wave potential. After simple transformations we obtain:

for the film electrode

\[ \Psi(\bar{\vartheta}) = q\left[ \bar{\vartheta} + \frac{2\bar{\vartheta}^{1/2}}{\pi^{1/2}} + \Phi(\bar{\vartheta}) \right] = \vartheta'-C_0^{0}, \tag{3} \]

for the spherical electrode

\[ \Psi(\bar{\vartheta}) = \bar{\vartheta} + 0.333\left[ 1-\exp \bar{\vartheta}\operatorname{erfc}\bar{\vartheta}^{1/2} - 0.333\Phi(\bar{\vartheta}) \right] = \vartheta' - \frac{C_0^{0}}{3\lambda}, \tag{4} \]

where $\bar{\vartheta}$ is the dimensionless time of attainment of the half-wave potential.

From equations (3) and (4) it is evident that the time of attainment of the half-wave potential and the concentration of the element in solution are interrelated. Graphs of this dependence in the coordinates $\Psi(\bar{\vartheta})=q\vartheta'-C_0^{0}$, $\bar{\vartheta}$ (for

film electrode) and \(\Psi(\vartheta)=\vartheta' - \dfrac{C_0^0}{3\lambda}\), \(\vartheta\) (for a spherical electrode) are shown, respectively, in Figs. 1 and 2. For the film electrode at \(\overline{\vartheta}\ge 0.32\) and for the spherical electrode at \(\overline{\vartheta}\ge 0.4\), the graphs in the indicated coordinates are straight lines with a slope tangent close to unity. In this case one may write:

\[ \text{for the film electrode}\qquad \vartheta' - \overline{\vartheta}=\frac{C_0^0}{q}; \tag{5} \]

\[ \text{for the spherical electrode}\qquad \vartheta' - \overline{\vartheta}=\frac{C_0^0}{3\lambda}. \tag{6} \]

Having determined experimentally the quantities \(\overline{\vartheta}\) and \(\vartheta'\), one can, without using the method of additions or a calibration graph, determine \(C_0^0\) or, using Fig. 1 (for the film) and Fig. 2 (for the sphere), for any \(\vartheta\), calculate—

Fig. 1. Dependence of the quantity
\[ \vartheta' - \frac{C_0^0}{q} \]
on \(\overline{\vartheta}\) for a mercury film electrode

Fig. 2. Dependence of the quantity
\[ \vartheta' - \frac{C_0^0}{3\lambda} \]
on \(\overline{\vartheta}\) for a mercury spherical electrode.

... from expressions (3) for the film and (4) for the sphere, or, for \(\vartheta \ge 0.32\) (for the film), calculate from expression (5), and for \(\vartheta \ge 0.4\) (for the sphere), calculate from expression (6).

Conclusions

A computational method is proposed for determining the concentration of solutions by anodic amalgam voltammetry at constant current on mercury film and spherical electrodes for amalgams that are oxidized reversibly.

References

1. M. S. Zakharov, V. I. Bakanov. (This collection).
2. M. S. Zakharov, V. V. Pinev. (This collection).