On Accounting for the Interactions of Electroactive Metals with Mercury in the APN Method

A. A. Kaplin, N. K. Dzhabarova, T. F. Ryashentseva

A characteristic feature of amalgams of electroactive metals, which include first of all the alkali and alkaline-earth metals, is the presence of strong interaction of these metals with mercury, which leads to a substantial deviation of these systems from ideality. An analysis of works \[1, 2\] leads to the conclusion that it is necessary to take into account the interaction in the system $\mathrm{Me}-\mathrm{Hg}$ in theoretical and experimental studies of active metals by the APN method.

For a quantitative accounting of the interaction in the active $\mathrm{Me}-\mathrm{Hg}$ system in the APN method, we have applied the activity method, the use of which in polarography with accumulation was first proposed in works \[3, 4\]. In deriving the equation for the anodic current of a metal with allowance for the change in its activity in the amalgam, the relation for the activity coefficient from the thermodynamics of solutions \[5\] was used:

\[ \ln f_2=-B_o\frac{n}{n-1}N^{\,n-1}+B_oN_2^{\,n}. \tag{1} \]

for the dissolved substance (the active metal). The energy parameters $B_o$ and $n$ characterize the deviation of the system from ideality.

Substituting equation (1) into the parametric equation of the anodic-peak current and passing from the expression for concentration adopted in the APN method to the concentration of the component in mole fractions, we obtain the equation of the anodic oxidation peak of the active metal from the amalgam:

\[ I_a=K_a\cdot S\,\frac{C_oN_2}{N_\infty} \exp\left[-B\frac{n}{n-1}N_2^{\,n-1}+B_oN_2^{\,n}\right], \tag{2} \]

where $C_o$ and $N_\infty$ are, respectively, the concentration and mole fraction of the dissolved substance in the limitingly dilute amalgam.

Using the relations of the parametric theory, which establish through the parameter $\gamma$ the connection between the value of the limiting current and the concentration factors, equation (2) takes the form:

\[ I_a=K_a\cdot\frac{S}{V}\, \frac{C_{u,o}\cdot V\cdot \gamma}{N_\infty} \left(\frac{1}{1+\lambda/C}\right) \exp\left[-B_o\frac{n}{n-1} \left(\frac{1}{1+\lambda/C}\right)^{n-1} +B_o\left(\frac{1}{1+\lambda/C}\right)^n\right] \tag{3} \]

where $C_{u,o}$ is the concentration of metal ions in the solution at which the interaction in the $\mathrm{Me}-\mathrm{Hg}$ system can be neglected; $C$ is the concentration of metal ions in the solution at which the anodic

peak; $\lambda=\dfrac{\nu d_{Hg}}{A_{Hg}\cdot V\cdot S}$; the quantities $K_a$, $\nu$, $V$, $S$, $\gamma$ have the values generally accepted in the APN method.

Equation (3) indicates the complex character of the relationship between the anodic current and the energy parameters $B_o$ and $n$, the parameter $\gamma$, and the concentration of the metal in the amalgam.

A theoretical study of the dependence of the anodic current on the quantities $C$, $B_o$, and $n$ was carried out with the aid of the “Promin’” computer. The quantities $K_a$, $S$, $\nu$, $V$, $\gamma$ were estimated from preliminary experimental data on the study of amalgams of alkali metals on a mercury-film electrode and, in the calculations, were set as constants: $\nu=1\cdot10^{-4}\ \text{cm}^3$; $S=0.15\ \text{cm}^2$; $V=5\ \text{cm}^3$; $\gamma=1\cdot10^{-2}$; $C_{u,o}=4\cdot10^{-8}\ \text{g-ion}/\text{cm}^3$; $K_a=2.5\cdot10^4\ \text{A}/\text{cm}^2\cdot\text{g-atom}$. The values of the parameter $n$ were chosen within the limits $1<n\leq2$; the parameter $B_o$ was chosen on the basis of values known from the literature for amalgams of alkali and alkaline-earth elements and was specified over a broad interval of values: $2.5\div50$.

Theoretical calculations showed that, under constant electrolysis conditions, in the absence of a practical depletion, the interaction in the Me–$Hg$ system leads to a violation of the linearity of calibration plots for active metals. The degree of deviation of the plots from linearity is determined by the bonding energy in the Me–$Hg$ system: as the parameter $B_o$ increases at a given value of $n$, the anodic peak current decreases and the calibration plot passes through a maximum. A similar influence is exerted by a decrease in the quantity $n$. For example, at $C=5\cdot10^{-7}\ \text{g-ion}\cdot\text{cm}^{-3}$, $B_o=20$, and $n=2$, the deviation of the concentration dependence is 10%; at $n=1.4$ the current decreases by a factor of 150.

An experimental study of the influence of interaction in the Me–$Hg$ system on the course of concentration dependences and $i-\tau$ curves was carried out for lithium and potassium against a background of $0.1\ \text{M}\ (C_2H_5)_4NS^3$ in dimethylformamide. The study was performed on a mercury-film electrode ($l=(5\div10)\cdot10^{-4}\ \text{cm}$) and a mercury drop ($r=4\cdot10^{-2}\ \text{cm}$).

A deviation from linearity was found for the dependences of the alkali-metal anodic peak current on concentration and electrolysis time. The calibration plot for potassium over a broad concentration interval passes through a maximum and, in the character of the dependence, coincides with that theoretically calculated from equation (3) for specified values $B_o=30$ and $n=2$. This is consistent with the literature data [1].

As the concentration of the metal in the amalgam increases, other characteristics of the anodic peaks also change: the peak potential shifts into the positive region, and the half-peak width increases. The change in these characteristics leads to a decrease in the sensitivity of the determination and requires correction of the values of the resolving power, which depend on the quantities $\gamma_n$ and $\delta^{1/2}$.

Thus, the experimental data confirm the conclusions drawn from theoretical calculations. The quantitative correlation between the experimental dependences and the theoretical ones, calculated from equation (3), gives grounds to believe that the observed changes in the characteristics of the anodic peaks of alkali metals are caused by the presence of a strong interaction between the metal and mercury.

References

1. V. N. Korshunov, A. B. Grigor'ev, I. P. Gladkikh. Elektrokhimiya, 6, 1204, 1970.

2. C. Wagner. J. Chem. Phys., 19, 626, 1951.

3. A. A. Kaplin. Advances in stripping polarography. Tomsk, TTU Publishing House, 1973, p. 133.

4. A. A. Kaplin, T. F. Ryashentseva. Ibid., p. 137.

5. M. I. Shakhparonov. Introduction to the molecular theory of solutions, Gostekhizdat, Moscow, 1956.

DEVELOPMENT OF A TECHNOLOGY FOR PRODUCING TUMBLING BODIES

V. M. Vityugin, V. A. Lotov, V. V. Koyan, G. S. Frolova, N. I. Poddublyak,
L. V. Sokolov

As a result of the classification of powdered products of chromic electrocorundum, sludge is obtained—the fraction smaller than 160 $\mu$—in an amount of 17% of the weight of the corundum; at present this sludge finds no practical application.

The principal element of the present work is the search for a fundamental possibility of using these sludges for the production of tumbling articles.

Tumbling is a process for cleaning the surface of articles and small-sized parts, carried out in rotating or vibrating drums. In order to accelerate processing, sand, emery, corundum, and other abrasive materials are usually loaded into the drum together with the parts. In addition to the indicated powdered abrasive materials, in tumbling fairly wide use is fo-