PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE NAMED AFTER S. M. KIROV,
ORDER OF THE OCTOBER REVOLUTION AND ORDER OF THE RED BANNER OF LABOR

Vol. 215 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1974

STUDY OF MIXED POTENTIAL IN IRREVERSIBLE REDOX SYSTEMS

A. I. KARTUSHINSKAYA, Yu. N. ZHIKHAREV

(Presented by the scientific seminar of the MPG laboratory)

This work is devoted to a polarographic study of the mixed potential in nonequilibrium systems. In the polarographic literature there are few data on the mixed potential [1, 2, 3, 4, 5, 6]. This question is important in theoretical studies and also has practical application in studying the corrosion of amalgams in amalgam metallurgy. The aim of the study includes investigation of the mutual influence of the components of complex redox systems (the ratio of their concentrations, half-wave potentials, etc.) at a dropping amalgam electrode and explanation of the results obtained on the basis of the theory of irreversible anodic–cathodic waves [7].

Two redox systems were studied:

1) Zn(Hg), Zn(2+), O₂, OH⁻ in a 1 M KOH solution,
2) Zn(Hg), Zn(2+), Cu(2+) in a solution of 1 M NH₄Cl + 1 M NH₄OH.

The work used an LP—60 recording polarograph and a polarographic cell with a dropping amalgam electrode, described in [8]. Zinc amalgam was prepared in the upper electrolyzer; the cathode was a mercury dropping electrode, the anode a zinc electrode (a platinum plate electrolytically coated with zinc), and the electrolyte a 0.2 M ZnSO₄ solution. Another capillary was sealed into the bottom of the upper electrolyzer; it served as the dropping amalgam electrode and was immersed in the lower polarographic cell. The characteristic of the dropping amalgam electrode was \(m^{1/3}t^{1/6} = 5.22\ \text{mg}^{2/3}\cdot \text{sec}^{1/6}\). The anode and auxiliary electrode in the lower cell was a saturated calomel electrode. The concentration of zinc in the amalgam (in different series of experiments) was varied in the first system from \(2\cdot 10^{-5}\) to \(53\cdot 10^{-5}\) g-atom/l, and in the second system from \(4.8\cdot 10^{-5}\) to \(35\cdot 10^{-5}\) g-atom/l; it was determined from the height of the anodic wave using the Ilkovič equation. The concentration of zinc ions in solution in the first system remained constant in all experiments and was equal to \(2\cdot 10^{-4}\) g-ion/l; in the second system it was varied in a definite correspondence with the concentration of zinc in the amalgam. The concentration of oxygen in the solution was determined from the first oxygen wave using a calibration graph constructed from the solubility of oxygen in 1 M KOH in equilibrium with air at 25°C.

The complex polarograms of the first system had four waves. The si-

the system \(\mathrm{Zn(Hg)}, \mathrm{Zn(2+)}, \mathrm{O_2}, \mathrm{OH^-}\) is nonequilibrium, and two coupled electrochemical reactions proceed in it:

\[ \begin{aligned} &\mathrm{Zn(Hg)} - 2\bar e \longrightarrow \mathrm{Zn(2+)} &&(1)\\ &\tfrac{1}{2}\mathrm{O_2}+\mathrm{H_2O}+2e \longrightarrow 2\mathrm{OH^-} &&(2)\\ \hline &\mathrm{Zn(Hg)}+\tfrac{1}{2}\mathrm{O_2}+\mathrm{H_2O}\longrightarrow \mathrm{Zn(2+)}+2\mathrm{OH^-} &&(3) \end{aligned} \]

With an increase in the concentration of dissolved oxygen, the rate of this reaction increases; moreover, the second oxygen wave grows more slowly than the first; the anodic zinc wave decreases, the cathodic zinc wave increases, and the total anodic-cathodic zinc wave remains unchanged.

The complex polarograms of the second system also give four waves. The first two waves correspond to the stepwise reduction of copper complexes. The overall process may be represented as

\[ \mathrm{Cu^{2+}}+2\bar e \longrightarrow \mathrm{Cu(Hg)}, \tag{4} \]

the third wave is the anodic dissolution of zinc:

\[ \mathrm{Zn(Hg)}-2\bar e \longrightarrow \mathrm{Zn(2+)}, \tag{5} \]

and the fourth wave is the reduction of zinc ions:

\[ \mathrm{Zn(2+)}+2\bar e \longrightarrow \mathrm{Zn(Hg)}. \tag{6} \]

Simultaneously with the electrochemical processes, a chemical process takes place on the surface of the mercury drop, which may be represented in the form

\[ \mathrm{Cu^{(2+)}}+\mathrm{Zn(Hg)}\longrightarrow \mathrm{Zn^{(2+)}}+\mathrm{Cu^0}, \tag{7} \]

the probability of which is indicated by a decrease in the anodic zinc wave and the cathodic copper wave in equivalent amounts.

Since the systems under consideration are nonequilibrium systems, a mixed potential is established in them. Its magnitude depends on the concentration of oxygen or copper in solution and can be determined directly potentiometrically (in the absence of current in the circuit) or polarographically as the potential corresponding to the point of intersection of the polarogram with the residual current. With increasing concentration of oxygen or copper in solution, the anodic-cathodic zinc wave “rises,” and the point of intersection of the polarogram with the residual current (the mixed potential) shifts into the positive region of potentials—first along the anodic zinc wave, then along the second oxygen or copper wave, and finally along the first oxygen or copper wave, tending in the limit to their equilibrium potentials. The mixed potential can be calculated from the equation of an irreversible wave, derived on the basis of the theory of slow discharge and ionization [7]. To calculate the mixed potential shifting along the anodic zinc wave, the equation used was

\[ \varphi_{c.m}=\varphi_{1/2,a}+\frac{b}{\beta}\lg\frac{h_{\Sigma}}{h_a-h_{\Sigma}}. \tag{8} \]

For the case of displacement of the mixed potential along the second wave of oxygen or copper, the equation used was

\[ \varphi_{c.m}=\varphi''_{1/2}-\frac{b}{\alpha''}\lg\frac{h_a-h_1}{h_{\Sigma}-h_a}. \tag{9} \]

And in the case of displacement of the mixed potential along the first wave of oxygen or copper, the calculation was carried out according to the equation

\[ \varphi_{c.m}=\varphi'_{1/2}-\frac{b}{\alpha'}\lg\frac{h_a}{h_1-h_a}, \tag{10} \]

where \(\varphi_{1/2,a}\) is the potential of the anodic half-wave of zinc; \(\varphi''_{1/2}\) is the potential of the second half-wave of oxygen or copper; \(\varphi'_{1/2}\) is the potential of the first half-wave of oxygen or copper; \(b = 2.3 \dfrac{RT}{zF} = 0.0295\) (at \(25^\circ\mathrm{C}\)); \(\beta\) is the ionization coefficient of zinc atoms; \(\alpha'\), \(\alpha''\) are the discharge coefficients for the 1st and 2nd waves of oxygen or copper, respectively; \(h_a\) is the height of the anodic wave of zinc; \(h_1\) is the height of the 1st wave of oxygen or copper; \(h_\Sigma\) is the total height of the two waves of oxygen or copper.

The values of the mixed potential obtained by calculation from the above formulas agree with the values of the mixed potentials obtained experimentally. The deviations that occur at relatively high concentrations of oxygen or copper in solution are explained by the occurrence of reactions (3) for the first system and (7) for the second system.

At high amalgam concentrations, the values of the mixed potential deviate from the equilibrium value by a comparatively small amount (\(\sim 0.20\) V) when the oxygen content changes from values \(<1\cdot 10^{-5}\) to \(15\cdot 10^{-5}\) mol/l and from \(<5\cdot 10^{-5}\) to \(50\cdot 10^{-5}\) mol/l for copper. At low amalgam concentrations, the value of the mixed potential changes by 1.2 V when the oxygen concentration is increased from \(1\cdot 10^{-5}\) to \(1.8\cdot 10^{-5}\) mol/l, and by 0.9 V when the copper concentration is increased from \(5\cdot 10^{-5}\) to \(15\cdot 10^{-5}\) mol/l.

The experimental data obtained show that in the two oxidation–reduction systems considered, at comparable concentrations of zinc in the amalgam and of oxygen or copper in solution, it is not the equilibrium potential that is measured, but the mixed potential. The results presented explain the deviation of experimental values [9, 10] of the equilibrium potential from the values of potentials calculated by the Nernst formula in other systems where electropositive impurities are present.

REFERENCES

1. J. Kolthoff, J. Lingane. Polarography. Vol. 2. Intersc. Publ. New York, London, 1952, ch. VI.

2. J. Heyrovský, J. Kuta. Principles of Polarography. Moscow, “Mir,” 1965, ch. 13, p. 116.

3. J. Kolthoff. C. Miller. J. Am. Chem. Soc. 62, 2171 (1940).

4. J. Lingane. J. Am. Chem. Soc. 65, 870 (1943).

5. A. G. Stromberg. In the collection Theory and Practice of Polarographic Analysis, Kishinev, “Shtiintsa” Publishing House, 1962, p. 177.

6. A. G. Stromberg, A. Kartushinskaya. Elektrokhimiya, 1965, 1, 1291.

7. A. G. Stromberg. Fizicheskaya khimiya, 1955, 29, 409, 2152.

8. A. G. Stromberg. Proceedings of the 4th All-Union Electrochemical Conference. Moscow, Publishing House of the Academy of Sciences of the USSR, 1959, p. 213.

9. B. Miller. Helv. chim. acta 46, 671, 1963.

10. F. Chao, M. Costa. Compt. rend. 261, 990, 1965; 262, 1357, 1966.