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

Volume 250

1975

MIXED POTENTIAL AND MIXED CURRENT IN A NONEQUILIBRIUM MIXTURE OF THREE ELECTROCHEMICAL SYSTEMS AT AN AMALGAM ELECTRODE

A. I. KARTUSHINSKAYA, Yu. N. ZHIKHAREV

(Presented by the scientific-methodological seminar of the Faculty of Chemical Technology)

In previous works [1] we considered cases of coupled electrochemical processes occurring on the surface of an amalgam dropping electrode in dilute solutions and amalgams, when there are two nonequilibrium oxidation-reduction systems: ions of the more electropositive metal \(M_1\) in solution (an impurity) and atoms of the more electronegative metal \(M_2\) in the amalgam (and ions of this metal in solution).

Let us consider a more complex case of mixed currents and mixed potentials, when there are three nonequilibrium electrochemical systems. For definiteness, let us assume that the principal oxidation-reduction system gives an anodic-cathodic irreversible wave (Fig. 1) with equilibrium potential \(\varphi_{p2}\). In addition, a more electropositive impurity of metal \(M_1\) is present in solution, and in the amalgam, together with atoms of the base metal \(M_2\), there are atoms of an impurity of the more electronegative metal \(M_3\).

Depending on the relative magnitude of the limiting currents \(I_1, I_2, I_3, I_4\), the mixed potential may vary over a wide range of potentials from \(\varphi_{p1}\) to \(\varphi_{p3}\). Let us further assume that the heights of the cathodic and anodic waves of the irreversible oxidation-reduction system \(M_2(\mathrm{Hg}), M_2^{z+}\) are constant in magnitude, and only the cathodic limiting current \(I_1\) of the metal ions \(M_1\) in solution and the anodic limiting current \(I_4\) of the metal \(M_3\) in the amalgam vary.

We assume that a dropping amalgam electrode is used as the amalgam electrode, and that an excess of indifferent electrolyte is present in the solution.

If the limiting currents have the relation \(I_1+I_3<I_4\), with \(I_4 \gg I_1\), then the mixed potential (1) lies on the anodic wave of the metal \(M_3\) (region IV, Fig. 1, curve 1). The mixed current is equal to the sum of the cathodic limiting currents \(I_1+I_3\). The rate of the cementation process is limited by the diffusion of metal ions \(M_1\) (current \(I_1\)) and \(M_2\) (current \(I_3\)) to the surface of the amalgam. The value of the mixed potential can be calculated from the formula derived on the basis of the theory of slow discharge-ionization [2, 3]

\[ \varphi_{\mathrm{mix}}=\varphi_{1/2,4}+\frac{b}{z_3\beta_4}\lg\frac{I_1+I_3}{I_4-(I_1+I_3)}, \tag{1} \]

where \(\varphi_{1/2,4}\) is the anodic half-wave potential of metal \(M_3\);

\[ b=\frac{2.3RT}{F}; \]

\(z_3\) is the number of electrons participating in the electrode reaction involving metal \(M_3\);

\(\beta_4\) is the electron-transfer coefficient in the ionization process;

\(I_1\) is the limiting cathodic current of metal \(M_1\);

\(I_3\) is the limiting cathodic current of metal \(M_2\);

\(I_4\) is the limiting anodic current of metal \(M_3\).

If the limiting currents are related by \(I_4-I_1<I_3\), with \(I_4>I_1\), then the mixed potential lies on the cathodic wave of metal \(M_2\) (region III, Fig. 1, curve 2). In this case the mixed current flowing through the amalgam–solution phase boundary is equal to \(I_3-(I_4-I_1)\).

The rate of the cementation process in this case is limited by diffusion of atoms of metal \(M_3\) (current \(I_4\)) and ions of metal \(M_1\) (current \(I_1\)) to the amalgam surface. The expression for the mixed potential then has the form

\[ \varphi_{\mathrm{cm}}=\varphi_{1/2,3} -\frac{b}{a_3z_2}\lg\frac{I_4-I_1}{I_3-(I_4-I_1)}, \tag{2} \]

where \(\varphi_{1/2,3}\) is the cathodic half-wave potential of metal \(M_2\); \(a_3\) is the discharge coefficient of metal \(M_2\) (region II, Fig. 1, curve 4). The magnitude of the mixed current is determined by the relation: \(I_2-(I_1-I_4)\). The rate of the cementation process is limited by diffusion of ions of metal \(M_1\) (current \(I_1\)) and atoms of metal \(M_3\) (current \(I_4\)) to the amalgam surface. The value of the mixed potential can be calculated from the equation

Fig. 1. Theoretical form of a polarogram at a dropping amalgam electrode in a nonequilibrium mixture of three electrochemical systems at different ratios among the limiting currents \(I_1\), \(I_2\), \(I_3\), and \(I_4\). Curve 1 — \(I_1<I_4\) and \(I_1+I_3<I_4\). Curve 2 — \(I_1<I_4\) and \(I_4-I_1<I_3\). Curve 3 — \(I_1=I_4\). Curve 4 — \(I_1>I_4\) and \(I_1-I_4<I_2\). Curve 5 — \(I_1>I_4\) and \(I_2+I_4<I_1\).

\[ \varphi_{\mathrm{cm}}=\varphi_{1/2,2} +\frac{b}{z_2\beta_2}\lg\frac{I_1-I_4}{I_2-(I_1-I_4)}, \tag{3} \]

where \(\varphi_{1/2,2}\) is the anodic half-wave potential of metal \(M_2\); \(\beta_2\) is the electron-transfer coefficient in the ionization process of metal \(M_2\); \(I_2\) is the limiting anodic current of metal \(M_2\).

\(^{1)}\) The mixed potentials in the figure are located at the intersections of the polarogram with the zero current value, i.e., it is assumed that the residual current of the dropping mercury electrode in the solution of indifferent electrolyte has been subtracted from the experimentally measured currents at each potential.

And, finally, if the limiting currents satisfy the relation \(I_2 + I_4 < I_1\), with \(I_1 > I_4\), then the mixed potential lies on the cathodic wave of metal \(M_1\) (region \(I\), Fig. 1, curve 5). The mixed current passing through the amalgam surface is equal to \(I_2 + I_4\). In this case, the rate of the cementation process is limited by diffusion of the atoms of metal \(M_2\) (current \(I_2\)) and \(M_3\) (current \(I_4\)) to the phase boundary. The mixed potential for this case can be calculated from the equation

\[ \varphi_{\mathrm{mix}} = \varphi_{1/2,1} - \frac{b}{\alpha_1 z_1}\lg \frac{I_2 + I_4}{I_1 - (I_2 + I_4)}, \tag{4} \]

where \(\varphi_{1/2,1}\) is the cathodic half-wave potential of metal \(M_1\); \(\alpha_1\) is the electron-transfer coefficient in the discharge of ions of metal \(M_1\).

The most interesting case is that in which the height of the cathodic wave of impurity ions of metal \(M_1\) in solution is equal to the height of the anodic wave of the impurity metal \(M_3\) in the amalgam. In this case, as is evident from the figure (Fig. 1, curve 3), the potential measured experimentally is equal to the equilibrium potential, but there is no equilibrium in the system, since a mixed potential is established in the system that is numerically equal to the equilibrium potential.

It should be noted that the formulas given above, (2), (1), (3), (4), are valid not only for a dropping amalgam electrode, but also for any amalgam electrode, provided that a stationary electrode process takes place on it, i.e., for example, at the amalgam–solution interface when the solution and the amalgam are stirred.

In conclusion, we express our gratitude to Professor A. G. Stromberg for valuable comments in preparing the manuscript of this article for publication.

REFERENCES

1. A. G. Stromberg, A. I. Kartushinskaya. — Electrochemistry, 1, 1291, 1965.

2. A. G. Stromberg. Theory and Practice of Polarographic Analysis. Shtiintsa Publishing House, Kishinev, p. 177, 1962.

3. A. G. Stromberg. — Physical Chemistry, 29, 409, 2152, 1955.