CONSTANTS OF THE ANODIC PEAK ON A MERCURY FILM ELECTRODE IN AMALGAM POLAROGRAPHY WITH ACCUMULATION (APA)

L. F. Trushina, V. M. Pichugina

The theory of amalgam polarography with accumulation on a stationary mercury film electrode for reversible processes was developed in [1]. That work also presented solutions to a number of methodological questions of APA on a mercury film electrode and studied the influence of certain factors on the height and shape of anodic peaks. The theory of anodic voltammetry on a planar mercury film electrode and theoretical numerical calculations of the influence of a number of factors (rate of potential change, film thickness) on the height and shape of the anodic peak are also given in [2, 3].

The purpose of the present work is the experimental determination of the constants of the anodic peak in the APA method on a stationary mercury film electrode for a number of elements in various supporting electrolytes, and the refinement of certain propositions of [1] on the basis of broader experimental material.

For the peak current of a reversible process occurring on a mercury film electrode, we shall use the theoretical limiting formula from [1], which is valid at small values of the rate of potential change:

\[ I=\frac{8F}{\pi^2(RT/F)}\cdot z^2\omega\cdot l\cdot S\cdot C_a, \tag{1} \]

Expression (1) may be represented as follows:

\[ I=K_{\text{pl}}\cdot\omega\cdot Q, \tag{2} \]

where

\[ K_{\text{pl}}=\frac{8F}{\pi^2(RT/F)}\cdot z^2=3.05\cdot 10^6 z^2\ (25^\circ\mathrm{C}). \tag{3} \]

\[ Q=l\cdot S\cdot C_a. \tag{4} \]

Here \(K_{\text{pl}}\) is the constant of the anodic peak on a film electrode, coul/volt·g-atom; \(q\) is the area under the peak, coulomb; \(z\) is the number of electrons participating in the process of anodic dissolution of the amalgam; \(l\) is the thickness of the mercury film, cm; \(S\) is the surface area of the film electrode, cm\(^2\); \(C_a\) is the concentration of metal atoms in the amalgam, g-at/cm\(^3\); \(\omega\) is the rate of potential change, in sec; \(F\) is the Faraday number, 96500 coul/cm\(^2\).

Expression (1) is valid, as follows from [1], under the following conditions:

\[ \frac{zF\omega}{RT} \ll \frac{\pi^2 D_R}{l^2}, \]

or

\[ \omega \ll \frac{\pi^2 RT}{F}\cdot \frac{D_R}{z\cdot l^2}, \tag{5} \]

where \(D_R\) is the diffusion coefficient of metal atoms in the amalgam, \(\mathrm{cm^2/sec}\).

From relation (3) it is seen that the constant of the anodic peak on a film electrode \(K_{\mathrm{pl}}\) does not depend on the thickness of the mercury film or on the rate of change of potential (within the limits in which condition (5) is valid).

On the other hand, from the parametric theory of the method of amalgam polarography with accumulation [4], we have the empirical formula:

\[ I_a = K_a\cdot S\cdot C_a, \tag{6} \]

where \(K_a\) is the constant of the anodic peak, \(\mathrm{a\cdot cm/g\text{-}atom}\). Taking into account (4) and the relation \(K_a=K'_a\omega\), we reduce (6) to the form (2):

\[ I_a = K_{\mathrm{pl}}\cdot \omega\cdot Q . \tag{2a} \]

Then the following relations will hold between \(K_{\mathrm{pl}}\) and \(K_a\):

\[ K_{\mathrm{pl}}=\frac{K_a}{l\cdot \omega}=\frac{K'_a}{l}. \tag{7} \]

From these expressions it is seen that the constant of the anodic peak on a stationary mercury drop electrode (hanging drop) depends on the size of the electrode and the rate of change of potential.

The value of the anodic peak constant on a mercury film electrode can be obtained using relations (2a) and (4):

\[ K_{\mathrm{pl}}=zF\frac{l}{\omega\cdot q}. \tag{8} \]

By this formula, knowing the magnitude of the area under the peak \(q\), the peak depth \(l\), and the rate of change of potential \(\omega\), one can determine \(K_{\mathrm{pl}}\). It should be noted that, at a constant value of the area occupied by the anodic peak when the voltammetric curve is recorded, the ratio \(\frac{l}{\omega}\) must remain constant.

Using the concept of the effective half-width of the peak, given in [5], we have:

\[ \frac{\delta_{\mathrm{ef}}}{\omega}=\frac{\delta\cdot \nu}{\omega}=\frac{q}{I}, \]

or

\[ \delta\cdot \nu=\frac{q\omega}{I}; \tag{9} \]

where \(\nu\) is the coefficient of the width of the anodic half-peak, \(\nu=\frac{\delta_{\mathrm{ef}}}{\delta}\). From expressions (8) and (9) we find:

\[ K_{\mathrm{pl}}\cdot \delta\cdot \nu=zF=\mathrm{const}, \]

whence

\[ \nu=\frac{zF}{\delta\cdot K_{\mathrm{pl}}}. \tag{10} \]

Table 1

* 1—0.1 M KNO\(_3\); 2—0.1 M KOH; 3—0.1 M KCl; 4—0.25 M KOH + 0.5 M EDA (ethylenediamine); 5—0.5 M KOH; 6—0.05 M KCl + 0.25 M KOH; 7—6 M HCl.

Thus, the coefficient of the width of the anodic half-wave can be determined using the values of the half-wave width and of the anodic-wave constant on a film electrode.

Experimental Part

We determined the values of the anodic-current constants on a film electrode \(K_{\text{pl}}\) for the elements Tl, Cd, Cu, Pb, Zn, Bi, In in various supporting electrolytes. The experiments were carried out with an electrolyzer whose design is described in [6]. Oxygen was removed from the analyzed solutions with purified nitrogen. The electrolysis potential (relative to a saturated calomel electrode) was different for the various elements and is indicated in Table 1. A mercury film electrode with surface area \(S = 0.2\ \text{cm}^2\), prepared from a silver wire of radius \(0.05\ \text{cm}\), was used. The concentration of metal ions in solution for the various elements ranged from \(5 \cdot 10^{-10}\ \text{g-ion}/\text{cm}^3\) to \(1 \cdot 10^{-9}\ \text{g-ion}/\text{cm}^3\). The electrolysis time was 5 min. Stirring of the solution during electrolysis was carried out by a stream of nitrogen (50 ml/min). The rate of potential change was \(4 \cdot 10^{-3}\ \text{V/sec}\) in determining \(K_{\text{pl}}\) for all elements except Bi, where \(\omega = 9 \cdot 10^{-3}\ \text{V/sec}\). The results of the investigations are given in Table 1.

Table 2

The effect of the rate of potential change and of the thickness of the mercury film on the magnitude of the anodic-wave constant \(K_{\text{pl}}\) was studied experimentally. In the range of potential-change rates \(2 \cdot 10^{-3}\)—\(16 \cdot 10^{-3}\ \text{V/sec}\), the investigations were carried out on a polarograph 7-77-4B.

(Hungary), in the range 0.125–1 V/sec—on an oscillographic polarograph OH-2 (Table 2). The influence of the rate of potential change on the value of \(K_{\text{pl}}\) was studied for Tl and Cd against a background of \(0.1N\ \mathrm{KNO_3}\). The volume of the solution was 5 ml. The concentration of thallium and cadmium ions in the solution was \(2\cdot 10^{-7}\) g-ion/l. The duration of electrolysis was 2 min. In all experiments the value of the dimensionless parameter \(B<0.03\), which indicates the absence of depletion of the solution. The thickness of the mercury film was \(10\ \mu\). The electrolysis potential for Tl and Cd was \(-1.2\) V (sat. cal. el.). The holding time before recording the anodic polarogram was 20 sec. The peaks obtained on the oscillographic polarograph were photographed on photographic film.

In experiments to determine the influence of the thickness of the mercury film on the value of \(K_{\text{pl}}\) (Table 3), the conditions remained the same. The thickness on the mercury

Table 3

film was increased successively from \(4\ \mu\) to \(12\ \mu\). Each experiment was repeated at least three times. The thickness of the mercury film was controlled by the amount of electricity passing through the electrode during the electrolytic growth of the mercury film. The rate of potential change in this series of experiments was \(4\cdot 10^{-3}\) V/sec.

Table 1 presents the results of numerical calculations of the constants of the anodic peak on a film electrode for various elements, obtained from our experimental data, and their comparison with \(K_{\text{pl}}\) values obtained from the theoretical limiting formula (1).

Discussion of Results

The new experimental data obtained on the film electrode confirm the experimental and theoretical conclusions obtained in [1] concerning the independence of the anodic-peak constant on the film electrode, \(K_{\text{pl}}\), from the thickness of the mercury film and the rate of potential change. As can be seen from Table 1, the ratio of the magnitude of the depth of the anodic peak to the rate of potential change remains approximately constant over the entire range of variation of \(\omega\).

A comparison of the value \(\dfrac{K_{\text{pl}}}{z^2}=3.05\cdot 10^6\) coul/(V·g-atom), obtained in [1], with our experimental data makes it possible to conclude that,

that the theoretical values calculated by Igolinsky’s limiting formula are 3–4 times higher than the experimental ones; moreover, for multivalent ions \((z = 2; z = 3)\) and irreversible processes (for Zn, for example) this discrepancy is greater. Attention should also be drawn to the fact that the dependence of \(K_{\text{pl}}\) on the number of electrons \(z\) is weaker than quadratic.

As can be seen from Table 4, the constancy of the quantity \(\dfrac{K_{\text{pl}}}{z^{3/2}}\) is observed better.

It also follows from Tables 1 and 2 that the value of the half-width \(\delta\) remains approximately constant when \(\omega\) and the film thickness are varied, and, as a consequence of (10), the coefficient of the width of the anodic half-wave \(\nu\) also does not depend on \(\omega\) and \(l\) over the entire range of variation of these quantities.

It should be noted, however, that with an increase in the rate of change of the potential and in the thickness of the mercury film, the shift of the potentials of the anodic peaks of thallium and cadmium in the positive direction is manifested more strongly than in [1] (Figs. 1, 2). This fact is in better agreement with the data obtained in [3].

Fig. 1. Dependence of \((\varphi_{\text{p}} - \varphi_{1/2})\) on the rate of change of potential, \(\omega\), V/min. Curve 1 — \(l = 4\mu\); 2 — \(l = 6\mu\); 3 — \(l = 8\mu\); 4 — \(l = 10\mu\); 5 — \(l = 12\mu\). Experimental conditions: \(\psi_{\text{el}} = -1.2\) V (sat. calomel electrode), electrolysis time — 5 min; \(S = 1 \cdot 10^{-3}\ \text{a}/\text{mm}\); \(U = 2\ \text{m}\Omega\).

Fig. 2. Dependence of \((\varphi_{\text{p}} - \varphi_{1/2})\) on the thickness of the mercury film \(l\), microns. Curve 1 — \(\omega = 2 \cdot 10^{-3}\) V/sec; 2 — \(\omega = 4 \cdot 10^{-3}\) V/sec; 3 — \(\omega = 6 \cdot 10^{-3}\) V/sec; 4 — \(\omega = 9 \cdot 10^{-3}\) V/sec; 5 — \(\omega = 1.2 \cdot 10^{-2}\) V/sec; 6 — \(\omega = 1.6 \cdot 10^{-2}\) V/sec.

It must be emphasized that the value of the coefficient \(\nu\) for different elements is approximately constant and varies within narrow limits, \(\nu = 1.1\text{–}1.2\). At the same time, no effect is noticeable of irreversibility or of the number of electrons participating in the electrode process on the value of \(\nu\).

In summary, it may be said that although the theoretical limiting formula was derived for reversible processes and low rates of change of potential, it is also valid for irreversible processes and for larger values of the rate of change of potential; that is, this formula proves to be valid under broader conditions than was assumed in its derivation.

In conclusion, we express our gratitude to Doctor of Chemical Sciences Professor A. G. Stromberg for his constant attention to this work and for valuable advice during its discussion.

Conclusions

1. The concept of the constant \(K_{\text{pl}}\) of the anodic peak on a mercury film electrode has been introduced (coul/g-atom).

2. For two elements (thallium and cadmium), on a new supporting electrolyte, Igolinsky’s theoretical and experimental conclusion has been confirmed concerning the independence of the constant \(K_{\text{pl}}\) from the rate of potential change \((4 \cdot 10^{-3}—4.0\ \text{V/sec})\) and from the film thickness \((4—12\ \mu\text{m})\).

3. For seven elements on different supporting electrolytes, numerical values have been determined for the anodic-peak constant \(K_{\text{pl}}\), the width of the anodic half-peak, and the coefficient of the anodic half-peak width.

4. The limits of applicability and the agreement with experiment of Igolinsky’s theoretical limiting formula for the height of the anodic peak on a mercury film electrode at a low rate of potential change have been discussed.

5. It has been shown that the coefficient of the anodic half-peak width \(\nu\) does not depend on the rate of potential change or on the film thickness and, for different elements and supporting electrolytes, varies within narrow limits \((1.2 \pm 0.1)\).

Literature

1. V. A. Igolinsky. Dissertation. Tomsk Polytechnic Institute, Tomsk, 1963.

2. W. de Vries, E. van Dalen, J. Electroanal. Chem. 8, 366, 1964.

3. W. de Vries, J. Electroanal. Chem. 9, 448, 1965.

4. A. G. Stromberg. Izvestiya SO AN SSSR, No. 5, 76, 1962.

5. A. G. Stromberg. Izvestiya TPI, 128, 13, 1964.

6. A. G. Stromberg, M. S. Zakharov, V. E. Gorodovykh, L. F. Zaichko. Zavod. labor., 27, 517, 1961.