On the temperature dependence of the height of the reversible anodic peak at a stationary mercury drop electrode in the APN method
Abstract Generated abstract
This paper derives mathematical relations describing how the height of a reversible anodic peak at a stationary mercury drop electrode depends on temperature in amalgam polarography with accumulation. The treatment accounts for potential sweep rate, electrode dimensions, diffusion activation energies, and different degrees of solution depletion during preliminary electrolysis, including limiting cases of negligible and nearly complete depletion. Numerical estimates for elevated temperatures indicate that peak height, and therefore method sensitivity, increases more sharply for a stationary mercury drop electrode than for a mercury film electrode, with the magnitude of the effect depending on the activation energy of ion diffusion in the solution.
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PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
OF THE ORDER OF THE OCTOBER REVOLUTION AND THE ORDER OF THE RED BANNER OF LABOR
named after S. M. Kirov
Volume 302 1976
ON THE QUESTION OF THE TEMPERATURE DEPENDENCE OF THE HEIGHT OF A REVERSIBLE ANODIC PEAK AT A STATIONARY MERCURY DROP ELECTRODE IN THE APN METHOD
Yu. A. KARBAINOV, S. N. KARBAINOVA
(Presented by the scientific seminar of the Department of Analytical Chemistry)
The study of the influence of temperature on the rate of the electrode process in the method of amalgam polarography with accumulation (the APN method) is of great interest, since the results of such a study make it possible to obtain valuable information on the regularities of the process of anodic dissolution of a metal from an amalgam. In the present work certain mathematical relationships have been obtained for the dependence of the height of a reversible anodic peak on temperature at a stationary mercury drop electrode (stat. m.d.e.), taking into account the rate of change of the potential \((w)\) and the dimensions of the electrode \((r)\) for different cases of depletion of the solution during the preliminary electrolysis process.
Assuming that the dependence of the height of the anodic peak \((I_a)\) on temperature \((T)\) is determined practically only by the temperature dependence of the anodic-peak coefficient \((K_a)\) and the electrolysis coefficient \((K_e)\), we obtained:
\[ Y=\frac{I_a}{a_T}=\frac{x^{1/2}(1-e^{-Bx})}{G_T+e^{\rho x}}; \qquad (1) \]
\[ x=\frac{E_{D_0}}{2RT}; \qquad (2) \]
\[ \rho=\frac{E_{D_R}}{E_{D_0}}; \qquad (3) \]
\[ B_x=\frac{K_{R,T}}{zF}\cdot S\cdot \frac{\tau}{V}\cdot e^{-x}; \qquad (4) \]
\[ \sigma_T=66.9\cdot D_{R,T}^{1/2}\frac{R^{1/2}}{z^{1/2}\cdot F^{1/2}}\cdot \frac{1}{r\cdot w^{1/2}}; \qquad (5) \]
\[ a_T=\frac{0.446\cdot z^{3/2}\cdot F^{3/2}\cdot w^{1/2}\cdot D_{R,T}^{1/2}\cdot S\cdot C_0\cdot Y}{R^{1/2}\cdot \Theta^{1/2}\cdot v}; \qquad (6) \]
\[ \Theta=\frac{E_{D_0}}{2R}. \qquad (7) \]
Here \(E_{D_0}\) and \(E_{D_R}\) are the activation energies of the diffusion processes of ions in solution and of metal atoms in the amalgam, respectively; \(K_{RT}\), \(D_{RT}\) are constants independent of temperature; \(z\) is the number of electrons participating in the electrode process; \(S\) is the electrode surface; \(v\) is the electrode volume; \(V\) is the volume of solution; \(\tau\) is the electrolysis time; \(F\) is the Faraday constant.
Relation (1) gives the general character of the dependence of the relative height of a reversible anodic peak \((Y)\) on temperature at a stationary mercury drop electrode over a wide range of variation of \(r\) and \(w\).
For the case when \(r\ll 1\) and \(w\ll 1\), \(\sigma_T\gg e^{\rho x}\), then from (1) we have
\[ Y^{**}=\frac{I_a\sigma_T}{a_T}=x^{1/2}(1-e^{-Bx}). \qquad (8) \]
In another limiting case, under conditions of linear semi-infinite diffusion, when \(\sigma_T\ll e^{\rho x}\), instead of (1) one may write
\[ Y^{**}=x^{1/2}\cdot e^{-\rho x}(1-e^{-Bx}). \qquad (9) \]
Let us analyze expression (1) as a function of the magnitude \(B_x\). For the case when \(B_x \ll 0.05\), i.e., depletion of the solution during the preliminary electrolysis process is absent, from (1) we obtain
\[ Y_1=\frac{\chi^{1/2}e^{-\chi}}{\sigma_T+e^{\chi}} \quad (10); \qquad \text{where } \quad Y_1=\frac{I_a}{a_T B_T} \quad (11); \qquad B_T=\frac{k_{l,T}}{zF}\cdot S\cdot \frac{c}{V}. \quad (12) \]
From (10) follow two particular relations for the relative height of the reversible anodic peak at a stationary mercury drop electrode:
a) if the temperature of the solution being analyzed changes only at the electrolysis stage, from (10) we have:
\[ Y_{1,e}=\frac{I_a}{a\cdot B_T}=e^{-\chi}; \tag{13} \]
b) if the temperature of the solution changes only at the stage of anodic dissolution of the amalgam, then
\[ Y_{1,0}=\frac{I_a}{a_T\cdot B}=\frac{\chi^{1/2}}{\sigma_T+e^{\chi}}. \tag{14} \]
When \(B_x \gg 3\), i.e., practically complete depletion of the solution takes place during electrolysis, from (1) we obtain:
\[ Y_2=\frac{\chi^{1/2}}{\sigma_T+e^{\chi}} \quad (15). \tag{15} \]
The height of the reversible anodic peak in this case, according to (15), changes with a change in temperature only at the stage of anodic dissolution of the amalgam.
A numerical estimate of the degree of increase in the height of the reversible anodic peak with temperature when it is raised from 25 to \(75^\circ\mathrm{C}\) at different values of \(E_{D_0}\), carried out for a mercury film electrode and a stationary mercury drop electrode, shows that a sharper increase in the peak height with increasing temperature, and consequently in the sensitivity of the method, is observed in the case of the mercury drop electrode.
Using equations (10), (13), and (14), the dependence of the relative height of the reversible anodic peak on temperature at a mercury drop electrode was calculated. The calculated data were obtained over the temperature range \(25—100^\circ\mathrm{C}\) under the following conditions: \(r=4.25\cdot 10^{-2}\ \mathrm{cm}\); \(v=1.4\cdot 10^{-2}\ \mathrm{V/sec}\); \(D_R=5.92\cdot 10^{-5}\cdot e^{-472/T}\); \(z=2\); \(E_{D_0}=6\cdot 10^3\ \mathrm{cal/mol}\).
From analysis of these data it follows: when the temperature of the solution being analyzed changes only at the electrolysis stage, the height of the reversible anodic peak under the indicated conditions increases by a factor of 2.8. If, however, the temperature of the solution being analyzed changes both at the electrolysis stage and at the stage of anodic dissolution of the amalgam, an increase in the height of the reversible anodic peak when the temperature changes from 25 to \(100^\circ\mathrm{C}\) is observed by a factor of 2.9.
Conclusions
Mathematical relations have been obtained connecting the height of the reversible anodic peak at a stationary mercury drop electrode with temperature (through the quantity \(\chi\)), taking into account the rate of change of potential and the dimensions of the electrode for different cases of solution depletion during preliminary electrolysis.
It has been shown that a sharper increase in the sensitivity of the APN method when elevated temperatures are used is observed in the case of a stationary mercury drop electrode. The degree of increase in sensitivity due to temperature depends on the nature of the solvent, i.e., on the magnitude of the activation energy of the process of ion diffusion in the electrolyte solution.