Method of Amalgam Polarography with Accumulation. Polarographic Behavior of Antimony, II

M. S. Zakharov, L. F. Zaichko

(Presented by the scientific-methodological seminar of the KhTF)

In continuation of work on the study of the amalgam-polarographic behavior of antimony \([1, 2]\), in the present work the coefficients \(\gamma_{\mathrm{p}}^{0}\), \(\gamma_{\mathrm{e}}^{0}\), \(\gamma_{\mathrm{ch}}^{0}\), \(\gamma_{\phi}^{0}\), \(\gamma_{0}^{0}\), \(\gamma_{\mathrm{k}}^{0}\) (coefficients of stirring, electrolysis, sensitivity, form, attenuation, and concentration for \(\mathrm{Sb}^{3+}\)) have been determined under standard conditions: \(t^{0}=25^\circ\mathrm{C}\), \(w=10^{-2}\ \mathrm{V/sec}\), \(\kappa_{1}=500z\cdot D^{0.45}\ \mathrm{A\cdot cm\cdot mol^{-1}}\) \([3, 4]\), in a hydrochloric-acid medium \([3]\).

\[ \gamma_{\phi}^{0}=\frac{\kappa_{2}^{0}}{\kappa_{3}^{0}}=\frac{\kappa_{2}}{\kappa_{3}}, \qquad (1); \qquad \gamma_{\mathrm{p}}^{0}=\frac{500zD^{0.45}}{\kappa_{3}^{0}}, \qquad (2); \qquad \gamma_{\mathrm{k}}^{0}=100, \qquad (3). \]

\[ \gamma_{0}^{0}=\frac{\gamma_{\phi}^{0}}{\gamma_{\mathrm{p}}^{0}}, \qquad (4); \qquad \gamma_{\mathrm{e}}^{0}=100\gamma_{0}^{0}, \qquad (5); \qquad \gamma_{\mathrm{ch}}^{0}=100\gamma_{\phi}^{0}, \qquad (6); \qquad \kappa_{3}^{0}=\kappa_{3}\frac{0.1}{w^{1/2}}, \qquad (7). \]

\[ \kappa_{3}=\frac{I_{3}}{Sc_{1}}, \qquad (8); \qquad \kappa_{2}=\frac{zFr}{3}\frac{I_{2}}{g}, \qquad (9); \qquad \kappa_{2}^{0}=\kappa_{2}\frac{w^{1/2}}{0.1}. \qquad (10). \]

The meaning of the coefficients is explained in \([4]\). The results of the calculations are given in Table 1.

Table 1

Polarographic coefficients for \(\mathrm{Sb}^{3+}\) in a hydrochloric-acid medium

These data indicate that the sensitivity of the determination of antimony in \(1N\), \(3N\), and \(6N\ \mathrm{HCl}\), at the same concentration coefficient (100), is practically the same. This is due to the fact that the reversibility of the oxidation–reduction process of antimony in all three media investigated is almost identical, as is shown by the practically identical values of \(\gamma_{\phi}^{0}\), \(\gamma_{0}^{0}\), \(\gamma_{\mathrm{p}}^{0}\), \(\gamma_{\mathrm{e}}^{0}\). Next, the number of electrons participating in the process of anodic oxidation of the amalgam was determined.

of antimony obtained by electrolysis on a stationary mercury electrode. The number of electrons was determined in 2 ways.

1. The areas under the voltammetric curves for the reduction and oxidation of antimony in \(1N\) HCl were compared. From the literature data it is known [5] that, on a hydrochloric-acid background, \(\mathrm{Sb}^{3+}\) is reduced to \(\mathrm{Sb}^0\), i.e., 3 electrons participate in the reduction process. The areas under the voltammetric curves were measured with a planimeter; the mean value from 3 measurements was taken. According to the experimental data, the areas under the voltammetric curves of the cathodic and anodic processes are respectively \(6.7 \cdot 10^{-5}\) and \(6.3 \cdot 10^{-5}\) coulombs. Hence it follows that

\[ \frac{g_{\mathrm{cat}}}{g_{\mathrm{an}}}=\frac{3}{n}\sim\frac{1}{1}. \]

Consequently, the anodic process of oxidation of the antimony amalgam on the investigated background proceeds with the participation of three electrons.

1. A method has been described in the literature for determining the number of electrons in amalgam oxidation by comparing the areas under the voltammetric curves of the anodic process under study and of a process with a known number of participating electrons [6]

\[ z_a' = z_a'' \frac{q_a'}{q_a''}\left(\frac{D_p'}{D_p''}\right)^{0.5}. \tag{11} \]

In this work the following factors are not taken into account: a) it is assumed that the electrolysis current at a stationary spherical electrode is directly proportional to the diffusion coefficient of ions in solution to the power 0.5. The authors [3] showed that the electrolysis current is proportional to \(D^{0.45}\).

The formula does not take into account the dependence of the anodic oxidation current of the amalgam of an element on the diffusion coefficient of atoms in mercury for the ARA method with a dropping stationary electrode. In [7] it was shown that the anodic oxidation current is proportional to \(\sqrt{D_2}\). Taking the above into account, for the more general case we propose the following formula for calculating the number of electrons participating in the anodic process at \(c_{1,x}=c_{1,2}\):

\[ z_x = z_2 \frac{q_x}{q_2} \left(\frac{D_{1,2}}{D_{1,x}}\right)^{0.45} \cdot \left(\frac{D_{2,2}}{D_{2,x}}\right)^{0.5 *}, \tag{12} \]

where \(z_x, z_2\) are the numbers of electrons of the anodic process under study and of the process with a known number of electrons;

\(q_x, q_2\) are the areas under the peaks (coul.) of the indicated anodic processes;

\(c_{1,x}, c_{1,2}\) is the concentration of ions in solution;

\(D_{1,x}, D_{1,2}\) are the diffusion coefficients of ions in solution;

\(D_{2,x}, D_{2,2}\) are the diffusion coefficients of atoms in mercury.

Using the indicated equation, the number of electrons was calculated for the anodic oxidation process of antimony in \(1N\) HCl. The value of the diffusion coefficient of \(\mathrm{Sb}^{3+}\) in \(1N\) HCl is \(0.93 \cdot 10^{-5}\ \mathrm{cm}^2\,\mathrm{sec}^{-1}\) (determined from the Ilkovič equation). The diffusion coefficient for thallium in the same electrolyte is \(2.5 \cdot 10^{-5}\ \mathrm{cm}^2\,\mathrm{sec}^{-1}\). The ratio of the areas under the voltammetric anodic curves is

\[ \frac{q_{\mathrm{an}}^{\mathrm{Sb}}}{q_{\mathrm{an}}^{\mathrm{Tl}}}=7.5. \]

The value \(z_x\), calculated from equation (12), corresponds to \(2.7 \sim 3\).

The effect of temperature on the cathodic process of reduction of Sb was studied by the method of classical polarography in the temperature range

\[ *)\quad \frac{D_{2,\mathrm{Tl}}}{D_{2,\mathrm{Sb}}}=0.73\ [8]. \]

\(+20 \div +80^\circ\mathrm{C}\). The experiments were carried out in a thermostat; the temperature was measured with an accuracy of \(\pm 1^\circ\mathrm{C}\). The results of studies of the effect of temperature on the cathodic waves of antimony in \(1N\) HCl, in coordinates \(\lg H - \dfrac{1}{T}\), are presented in Fig. 1. It is evident from the figure that the plot consists of two intersecting straight lines. This indicates that at \(t \simeq 40^\circ\) a change occurs in the mechanism of the electrode reaction of the cathodic process. The activation energy calculated for the cathodic process of antimony on a hydrochloric-acid background is \(4.2\ \mathrm{kcal/mol\cdot g}\) and \(1.1\ \mathrm{kcal/deg\cdot mol}\) for the temperature intervals \(20\text{--}40^\circ\mathrm{C}\) and \(40\text{--}80^\circ\mathrm{C}\), respectively.

Fig. 1. Plot of the dependence of the height of the polarographic wave on \(\dfrac{1}{T}\) in \(1N\) HCl. Sb concentration \(=4\cdot 10^{-4}\ M/l\).

Later data on the study of the effect of temperature on the anodic cathodic current by the APC method will be presented in another paper [9].

Conclusions

1. The polarographic coefficients for the anodic peak of \(\mathrm{Sb}^{3+}\) in \(1N\), \(3N\), and \(6N\) HCl have been calculated.

2. Using the proposed formula, the number of electrons participating in the process of anodic oxidation of antimony in \(1N\) HCl has been determined \((n=3)\).

3. The activation energy of the cathodic process of Sb in \(1N\) HCl has been calculated.

Literature

1. L. F. Zaichko, M. S. Zakharov. In: Methods of Analysis of Chemical Reagents and Preparations, Moscow, IREA, p. 37, 1963.

2. L. F. Zaichko, M. S. Zakharov. Journal of Analytical Chemistry, 21, 65 (1966).

3. M. S. Zakharov, A. G. Stromberg. Journal of Analytical Chemistry, 20, 1279 (1965).

4. M. S. Zakharov, A. V. Kon'kova. Polarographic coefficients of certain elements in the APC method (this collection).

5. T. A. Kryukova, S. I. Sinyakova, T. V. Aref'eva. Polarographic Analysis, Moscow, 1959.

6. E. K. Spirin, A. G. Stromberg. Determination of the number of electrons participating in cathodic and anodic polarization in the APC method (this collection).

7. M. S. Zakharov, A. G. Stromberg. Journal of Physical Chemistry, 38, 130 (1964).

8. A. G. Stromberg, E. A. Zakharova. Electrochemistry, 1, 1036 (1965).

9. L. F. Zaichko, M. S. Zakharov. Journal of Analytical Chemistry, 22, 876, 1967.