EFFECT OF THE VOLUME OF THE BACKGROUND SOLUTION AND THE ELECTROLYSIS TIME ON THE HEIGHT OF THE ANODIC PEAKS OF GALLIUM AND GERMANIUM

O. S. STEPANOVA, M. S. ZAKHAROV

(Presented by the Scientific-Methodological Seminar of the Faculty of Chemical Technology)

The method of amalgam polarography with accumulation makes it possible to determine concentrations of \(10^{-7}\)–\(10^{-8}\) M for a number of elements that form an amalgam with mercury.

Earlier [1—3] the possibility of the amalgam-polarographic determination of gallium and germanium was indicated, and certain physicochemical regularities of their behavior were elucidated.

In the present article results are presented on the influence of the volume of the background solution and the electrolysis time on the height of the anodic peaks of gallium and germanium.

A. G. Stromberg [4] developed a parametric theory of the anodic peak. According to this theory, the depth of the anodic peak is

\[ I_2 = a(1-e^{-b}), \tag{1} \]

where

\[ a = 3\kappa_2 C_1^0 v \frac{1}{r}; \qquad b=\frac{4\pi K_1}{ZF}\, r_2 \frac{t}{v}. \tag{2} \]

Here \(I_2\) is the depth of the anodic peak; \(C_1^0\) is the initial concentration of ions in the solution, mol/ml; \(v\) is the volume of the working solution, ml; \(t\) is the duration of preliminary electrolysis, sec; \(Z\) is the number of electrons participating in the electrode reaction; \(F\) is Faraday’s number; \(r\) is the radius of the drop, cm; \(\kappa_1,\kappa_2\) are constants in the equations

\[ I_1 = K_1SC_1 \quad \text{and} \quad I_2 = K_2SC_2, \tag{3} \]

where \(I_1\) is the current of preliminary electrolysis, A;

\(C_2\) is the concentration of the metal in the amalgam, g-atom/ml.

\(K_1\) depends on the intensity of stirring of the solution. The concentration of the metal in the amalgam \((C_2)\) after electrolysis for \(t\) seconds at a current of \(I_1\) amperes is determined from the relations

\[ C_2=\frac{q}{ZFv_k}; \qquad q=\int_0^t I_1\,dt, \tag{4} \]

(\(q\) is the amount of electricity that has passed through the drop during electrolysis; \(v_k\) is the volume of the drop, cm\(^3\)). At \(b \leqslant 0.1\) [4] the depth of the anodic peak is determined by the expression

\[ I_2 = ab = \frac{12\pi}{ZF}K_1K_2C_1^0rt. \tag{5} \]

This dependence for the depth of the anodic peak is valid for a sufficiently large volume \((v)\) of the background solution, for a sufficiently short electrolysis time \((t)\), and for a small radius of the mercury drop \((r)\), when, in practice, the concentration of ions of the element being determined remains constant. It further follows from formula (5) that, if the inequality

\[ r^2 \frac{t}{v} < 0.1 \frac{ZF}{4\pi K_1} \quad \text{and} \quad C_1 > 0.95 C_1^0, \]

holds, then the depth of the anodic peak does not depend on the volume of the solution \((v)\) and is proportional to the radius of the drop \((r)\) and to the time of preliminary electrolysis \((t)\).

Fig. 1. Effect of the background volume on the depth of the anodic peaks of lead, gallium, and germanium.

For \(b \ge 3\) [4], the depth of the anodic peak is determined by the equation

\[ I_2 = a = 3K_2 C_1^0 v \frac{1}{r}, \]

\[ r^2 \frac{t}{v} > 3 \frac{ZF}{4\pi K_1} \quad \text{and} \quad C_1 < 0.05 C_1^0. \]

It follows from these relationships that, for a sufficiently small volume of solution, a long electrolysis time, and a large drop radius \((0.1\ \text{cm})\), the depth of the anodic peak is proportional to the volume of the solution, inversely proportional to the drop radius, and does not depend on the electrolysis time. At intermediate values of the parameter \((0.1 < b < 3)\), the dependences of the anodic-peak depth on the three factors considered are expressed by formula (1). The theoretical considerations were confirmed by experimental data using lead as an example in works [4, 5]. Since our experiments were carried out under conditions different from those used by the authors, we investigated the effect of the background-solution volume and the electrolysis time not only on the anodic peak of gallium and germanium, but also on the anodic peak of lead. The results obtained for gallium and germanium were compared with the results for lead, as a classical example, and certain conclusions were drawn.

Fig. 2. Plot in the coordinates
\[ I_2/ab - 1/b \]

The investigations were carried out on a Hungarian polarograph 7-77-4B with a recorder, in an electrolyzer with inserted beakers of different sizes [5] and a device allowing the position of the mercury drop inside the solution to be varied. Oxygen was removed from the working solution with purified nitrogen, which was passed through a furnace with copper turnings at

\(t = 200\text{--}300^\circ\mathrm{C}\) and an alkaline pyrogallol solution. Vigorous stirring was carried out only with nitrogen; when the volume of the working solution was changed, the nitrogen feed rate was changed. After each measurement the beaker with the solution under study was replaced by another, into which a fresh portion of the background solution with an addition of the given element at a concentration of \(1 \cdot 10^{-6}\) mole/liter was placed.

The effect of solution volume on the depth of the anodic notch was investigated over the volume range from 0.2 to 5 ml, at a constant electrolysis duration of 10 min and a mercury-drop radius of 0.04 cm.

The experimental data are presented in graphs (1–2) in the coordinates: height of the anodic notch in \(\mu\mathrm{A}\)—background volume, and in the coordinates:

\[ \frac{I_2}{ab} \quad \text{and} \quad \frac{1}{b}(y - x). \]

From graphs (1–2) it is evident that the dependences of \(I_2\) on \(v\) and of \(I_2/ab\) on \(1/b\) are identical in character. Comparing our data with those obtained earlier for lead in [5], it may be concluded that the \(I_2 - v\) dependence fully confirms the theoretical considerations, only in our case it is shifted toward smaller values along the coordinate axes.

Let us consider two particular cases of the limiting values of \(b\) for lead, gallium, and germanium. Substituting into expression (2) the values of \(Z\) and \(F\), as well as the experimentally obtained \(K_1\) and \(t\); \(K_1\) was calculated by formula (3); the electrolysis current was calculated from the area under the anodic notch in electrical units. Then for lead

\[ \text{a) } b = \frac{12.56 \cdot 1.6 \cdot 10^3}{20.96 \cdot 10^5} \, 0.0016 \, \frac{600}{v}, \]

whence

\[ b = \frac{0.1}{v}; \quad \text{if } b \leq 0.1, \]

then

\[ v \geq 1 \ \text{ml}, \]

that is, at \(b \leq 0.1\) the depth of the anodic notch is practically independent of the solution volume at \(v = 1\) ml (Fig. 2);

\[ \text{b) at } b \geq 3, \quad b \geq \frac{0.1}{v}; \quad v \leq \frac{0.1}{3} \leq 0.033 \ \text{ml}, \]

that is, the linear dependence of the depth of the anodic notch will be preserved up to \(v = 0.03\) ml (Fig. 2).

For gallium:

\[ \text{a) } b = \frac{12.56 \cdot 2.9 \cdot 10^3}{3 \cdot 0.96 \cdot 10^5} \, 0.0016 \, \frac{600}{v} = \frac{0.125}{v}; \]

\[ b = \frac{0.125}{v}; \quad \text{if } b \leq 0.1, \text{ then } v \geq 1.25 \ \text{ml}, \]

that is, the depth of the anodic notch is practically independent of the volume of the working solution at \(v \geq 1.25\) ml (Fig. 2);

\[ \text{b) at } b \geq 3, \quad b = \frac{0.125}{v}; \quad v = \frac{0.125}{3} \leq 0.04 \ \text{ml}, \]

that is, the linear dependence of the depth of the anodic notch will be preserved up to \(v = 0.04\) ml (Fig. 2).

For germanium:

\[ \text{a) }\quad b=\frac{12.56\cdot 0.9\cdot 10^{3}}{40.96\cdot 10^{5}}\,0.0016\,\frac{600}{v}=\frac{0.036}{v}; \]

\[ b=\frac{0.036}{v};\quad \text{if } b\leqslant 0.1,\quad \text{then } v\geqslant 0.36\ \text{ml}, \]

that is, the depth of the anodic peak is practically independent of the volume of the solution at \(v\geqslant 0.36\) ml (Fig. 2);

\[ \text{b) at } b\geqslant 3.\quad b\geqslant \frac{0.036}{v};\quad v\leqslant \frac{0.036}{3};\quad v\leqslant 0.01\ \text{ml}, \]

that is, the linear dependence will be preserved down to \(v=0.01\) ml (Fig. 2). Some scatter of the points in the graphs (1–2) can be explained by the fact that it is very difficult to maintain a constant hydrodynamic regime (the error does not exceed 15–20%).

The influence of the electrolysis time was determined under conditions of vigorous stirring of the working solution; the volume of the supporting electrolyte was 0.5 ml, the radius of the mercury drop 0.04 cm, and the time of preliminary electrolysis was varied from 5 min to 2.5 hours. The concentration of Pb, Ga, and Ge was \(1\cdot 10^{-6}\) mole/liter. The experimental data are presented in graphs (3–4) in the coordinates: height of the anodic peak in \(\mu\)A—electrolysis time, and in the coordinates: \(I_{2}/a\) versus \(b\).

For lead the theoretical regularities are fully confirmed (Figs. 3 and 4). The linear dependence is preserved up to \(b=1.26\), that is, this corresponds to \(t=9000\) sec. In the case of gallium it was observed that the anodic peak grows linearly up to \(b=2\), that is \(t=3600\) sec, and then the peak decreases and after two and a half hours disappears completely (Figs. 3 and 4). This phenomenon is apparently connected with the action of surface-active substances (agar-agar bridge). It is known that surface-active substances suppress the cathodic waves of gallium [8].

Fig. 3. Influence of electrolysis time on the depth of the anodic peaks of lead, gallium, and germanium.

Fig. 4. Graph in the coordinates
\[ I_{2}/a—b \]

The possibility of formation of an intermetallic compound of gallium with the contact is excluded, since the mercury drop was suspended on a silver wire, and gallium does not interact with silver [6].

For germanium it was found that, as the time of preliminary electrolysis is increased up to 2.5 hours, the anodic peak of the latter increases (Figs. 3, 4). This can apparently be explained by the fact that the rate of the electrolysis process is determined not by the rate of delivery of the substance to the electrode, but by the rate of dissociation of monogermanate, which is very low. Stashkova and Zelyanskaya [7] had earlier arrived at a similar conclusion. The bend in curve 4 will, in all probability, be observed at a longer electrolysis time.

The data obtained make it possible to establish the optimum conditions for determining microamounts of gallium and germanium in high-purity metals: the volume of the background solution should not exceed 1 ml, and the time of preliminary accumulation should be no more than 1 hour.

Conclusions

1. The theoretical dependence of the depth of the anodic peak on the volume of the background solution and the electrolysis time has been verified for lead, gallium, and germanium.

2. The optimum electrolysis time and background volume for the determination of microamounts of gallium and germanium by the APN method have been established.

Literature

1. M. S. Zakharov. ZhAKh, 18, 4, 450, 1963.

2. A. G. Stromberg, M. S. Zakharov, O. S. Stepanova, S. F. Gurskaya. Methods for the Analysis of Chemical Reagents and Preparations, issue 5–6, IREA, Moscow, p. 95, 1963.

3. O. S. Stepanova, M. S. Zakharov, L. F. Trushina. Polarographic behavior of germanium. ZhAKh, XX, 2, 1965.

4. A. G. Stromberg. Proceedings of the Siberian Branch of the Academy of Sciences of the USSR, No. 5, 76, 1962.

5. A. G. Stromberg, A. A. Kaplin. Factory Laboratory, vol. XXX, No. 5, 1964.

6. M. Hansen, K. Anderko. Constitution of Binary Alloys, vol. 1, Metallurgizdat, p. 209, 1952.

7. N. V. Stashkova; A. I. Zelyanskaya. Proceedings of the Siberian Branch of the Academy of Sciences of the USSR, No. 1, 59, 1959.

8. A. I. Zelyanskaya; N. A. Bausova. Proceedings of the Eastern Branches of the Academy of Sciences of the USSR, No. 7, 51, 1957.