M. S. ZAKHAROV, M. I. FARTYGINA, T. D. KONOPITSINA, N. Ya. BONDAREVA

AMALGAM POLAROGRAPHY METHOD. ANODIC CURRENT CONSTANTS

(Presented by the scientific seminar of the Department of Physical Chemistry, TPI)

In work [1] the possibility was shown of applying a calculation method in carrying out analysis by the method of amalgam polarography with accumulation. The calculation method is based on the use of the anodic peak constant \(K_2''\). The latter is calculated by the formula

\[ K_2''=\frac{I_a}{C_1}\cdot\frac{1}{12\pi K_1' r\tau\sqrt{\omega}}, \tag{1} \]

where \(I_a\) is the height of the anodic peak (anodic current), A;

\(C_1\) is the concentration of the ion in solution, g-mole/cm\(^3\);

\(r\) is the radius of the mercury-droplet stationary electrode, cm;

\(\tau\) is the electrolysis time, sec;

\(\omega\) is the rate of change of potential, V/sec;

\[ K_1' \]

is the electrolysis constant;

\[ K_1'=\frac{1}{zFS}\left(\frac{i_e}{c_1}\right); \]

\(z\) is the number of electrons participating in the electrode process per ion of substance;

\(F\) is the Faraday number;

\(S\) is the electrode surface, cm\(^2\);

\(i_e\) is the electrolysis current, A.

From formula (1) it is seen that the constant \(K_2''\) should depend only on the diffusion coefficient of metal atoms in the amalgam (\(D_2\)), the number of electrons (\(z\)), and the reversibility of the electrode process.

The present work is devoted to determining the anodic peak constants (\(K_2''\)) for cadmium, lead, thallium, bismuth, indium, tin, antimony, and others. In addition to \(K_2''\), the half-peak width \((\delta)\), the enrichment factor

\[ \frac{c_2}{c_1},\quad \frac{I_a}{i_e},\quad m=\frac{c_2/c_1}{I_a/i_e} \]

and others were determined. The magnitude \((\delta)\) can characterize the degree of irreversibility of the process of anodic dissolution of an element from an amalgam.

Experimental Part

The experiments were carried out in an electrolyzer whose design is described in [2]. To obtain correct results, oxygen was removed from the solution with purified hydrogen. All experiments were performed in the absence of depletion of the solution (the concentration of the depolarizer in the solution remains constant). All the quantities indicated above were determined at three concentrations of the element in the solution \((1,\ 2,\ 3 \cdot 10^{-5}\ M)\). The radius of the mercury drop in all experiments was \(0.045—0.05\ \mathrm{cm}\). The rate of change of potential was \(0.016\ \mathrm{V/sec}\), the volume of solution \(5\ \mathrm{ml}\), and the electrolysis time \(5\ \mathrm{min}\).

When an element is accumulated in the mercury electrode from solutions with a low concentration of the element, the Faradaic current is very small and becomes comparable with the condenser current. Therefore the electrolysis current is calculated from the area of the anodic peak. In [1] it is shown that the electrolysis currents calculated from the area of the anodic peak and those measured directly coincide. As is known,

\[ \int_0^\tau i_{\mathrm{e}}\,d\tau = Q; \]

\(Q\) is the quantity of electricity, in coulombs, that has passed through the solution during preliminary accumulation. Numerically this quantity is equal to the area of the anodic peak, expressed in coulombs.

Hence,

\[ i_{\mathrm{e(av)}}=\frac{Q}{\tau}; \]

\(i_{\mathrm{e(av)}}\) is the average electrolysis current.

The concentration of the element in the amalgam was calculated from the expression

\[ c_2=\frac{i_{\mathrm{e}}\tau}{zFV_{\mathrm{k}}}, \tag{3} \]

where \(V_{\mathrm{k}}\) is the volume of the mercury drop (sphere).

The results of the study are presented in Table 1.

It should be noted that, in carrying out the studies, we did not seek to stir the solution intensively (there was no need for this). Therefore a slight increase was observed in the concentration of atoms of the substance in the mercury drop as compared with the concentration of ions in the solution

\[ \left(\frac{c_2}{c_1}\right). \]

Discussion of Results

It can be seen from Table 1 that, for an element at different concentrations in solution, the magnitude of the anodic-peak constant \((K_2)\) on the same supporting electrolyte remains practically constant. On different supporting electrolytes, the values of the constants may differ considerably. Thus, for \(\mathrm{Tl}^+\) in \(0.1\ \mathrm{N}\ \mathrm{KOH}\), \(K_2\) is on average 750, whereas in \(0.1\ \mathrm{N}\ \mathrm{KNO}_3\) it is 450. The same is observed for other elements as well. This difference between the constants, as will be shown below, is due to the different degree of irreversibility of the anodic process of the element on different supporting electrolytes.

For most elements the ratio \(\dfrac{c_2}{c_1}\) is greater than the ratio \(\dfrac{I_{\mathrm{a}}}{i_{\mathrm{e}}}\). This is due to the fact that the cathodic-current constant \((K_1)\) is greater than the anodic-current constant \((K_2')\) [1]. However, for polyvalent elements \((\mathrm{Sn}\ (\mathrm{IV}),\ \mathrm{Sb}\ (\mathrm{V}))\), the value of \(m\) on some supporting electrolytes is even less than unity.

As follows from [1], there is a direct relationship between the anodic-current constant and the number of electrons \(z\) participating in the electrode oxidation–reduction process: the larger \(z\), the grea—

Table 1

Continuation of Table 1

Continuation of Table 1

Continuation of Table 1

the value \(K_2''\) for monovalent elements, \(K_2''\) lies in the range 450–750, for divalent elements—1100–2000, for trivalent elements—2700–4700, for tetravalent elements—4000–5500, and for pentavalent elements—about 6500.

The absence of a strict relationship between \(z\) and \(K_2''\) is due to the dependence of \(K_2''\) on the degree of irreversibility of the anodic process.

In [1] it was shown that the irreversibility of the anodic process can be characterized by the ratio of the half-peak width \(\delta\) of the element. For one and the same element on different supporting electrolytes, the values

\[ \frac{K_{2,1}''}{K_{2,2}''} \]

should be approximately equal to

\[ \frac{\delta_2}{\delta_1}. \]

Here \(K_{2,1}''\), \(\delta_1\); \(K_{2,2}''\), \(\delta_2\) are the constants of the anodic peak and the half-peak width in the first and second electrolytes for one and the same element. As an example, the indicated values for several elements are given in Table 2.

Table 2

Values of the ratios \(\dfrac{K_{2,1}''}{K_{2,2}''}\) and \(\dfrac{\delta_2}{\delta_1}\) for one element on different supporting electrolytes

It is seen from Table 2 that, for the elements cited, the magnitudes of the ratios of the constants almost coincide with the magnitudes of the ratios of the half-peak widths. The same is observed for other elements as well; consequently, the difference between the constants \(K_2''\) is determined by the degree of irreversibility of the electrode process (the different half-peak width). For different elements of the same valence, the following relation should hold [1]:

\[ \frac{K_{2,1}''}{K_{2,2}''} = \frac{D_{2,1}^{1/2}\delta_2}{D_{2,2}^{1/2}\delta_1}, \]

where \(D_{2,1}\) and \(D_{2,2}\) are the diffusion coefficients of atoms of the first and second elements in mercury. The values of these ratios for several elements are given in Table 3.

Table 3

Values of the ratios \(\dfrac{K_{2,1}''}{K_{2,2}''}\) and \(\dfrac{D_{1,2}^{1/2}\delta_2}{D_{2,2}^{1/2}\delta_1}\)

From Table 3 it is evident that the values of the ratios \(\dfrac{K''_{2,1}}{K''_{2,2}}\) and \(\dfrac{D_{2,1}^{1/2}\cdot \delta_2}{D_{2,2}^{1/2}\delta_1}\) are close to one another. Similar ratios are also observed for other elements of the same valence. This means that the anodic current (the depth of the anodic notch) and the anodic-current constant \(K'_2\) are directly proportional to \(\sqrt{D_2}\).

In conclusion, we express our deep gratitude to Professor A. G. Stromberg for valuable advice during the performance and discussion of the work.

REFERENCES

1. M. S. Zakharov, A. G. Stromberg, “Anodic-current constants and calculated amalgam polarography,” ZhFKh 38, 130 (1964).

2. A. G. Stromberg, M. S. Zakharov, V. E. Gorodovykh, L. F. Zaichko. “Determination of microconcentrations of copper, lead, and zinc in high-purity tin.” Zavod. labor., issue 5, 517 (1961).