Theory of the Mercury-Graphite Electrode
Abstract Generated abstract
This paper develops a theoretical description of electrochemical processes at a mercury graphite electrode formed by preliminary electrolysis, focusing on the kinetics and mechanism of mercury deposition on graphite. The authors model deposition as governed by nucleation and nucleus growth, deriving different time dependences for concentrated and dilute mercury ion solutions and arguing that the apparent mercury film consists of spherical drops that can merge and later detach. Experimental verification indicates that below about 5 by 10^-8 g-ion/l deposition is controlled by nucleus growth, while above about 5 by 10^-6 g-ion/l it is controlled by nucleus formation. The study also reports that anodic peak behavior during electrodissolution of antimony, lead, and copper from the mercury film agrees with Igolinsky’s equation over a broad range of film thicknesses.
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Theory of the Mercury–Graphite Electrode
B. F. Nazarov, E. M. Mal’kov
(Presented at the scientific-methodological seminar of the KhTF)
The literature contains information on the use of the mercury–graphite electrode in analytical practice; however, the theory of the mercury–graphite electrode has not yet been developed [1].
The aim of the present work is to develop a theory of the electrochemical processes occurring at a mercury–graphite electrode. Since the mercury–graphite electrode is formed in the course of preliminary electrolysis, the kinetics of mercury deposition on graphite and the elucidation of the mechanism of formation of the mercury “film” acquire great significance (as will be shown below, the mercury “film” consists of separate spherical drops of mercury, which during electrolysis can merge into conglomerates that break down with time, leading to the detachment of mercury from the graphite).
We shall assume that the rate of mercury deposition on graphite is determined by two factors. The first factor is the rate of formation of nuclei; the second factor is the rate of growth of the individual nuclei, i.e.:
\[ \frac{dQ}{dt}=n\frac{dq}{dt}+q_0\frac{dn}{dt}, \tag{1} \]
where \(Q\) is the amount of substance deposited during electrolysis, g-atom;
\(q\) is the amount of substance in one nucleus at time \(t\);
\(q_0\) is the initial amount of substance in a nucleus, g-atom;
\(n\) is the number of nuclei.
Let us consider two cases of formation of the mercury–graphite electrode during electrolysis.
At a sufficiently high concentration of mercury ions in the solution, the rate of electrodeposition over a certain time interval will occur only through the formation of nuclei (the limiting
stage). Since the rate of formation of nuclei in the initial interval of time does not depend on time, the following relation will be valid for the amount of mercury deposited on the electrode:
\[ Q=q_0\frac{dn}{dt}\Delta t , \tag{2} \]
where
\[ \frac{dn}{dt}=\mathrm{const}, \]
\(\Delta t\) is the time of deposition of the nuclei.
After the entire surface of the graphite has been filled with mercury nuclei, further electrodeposition of mercury will take place through the supply of substance to the electrode surface. In this case the amount of mercury deposited can be calculated by the following formula:
\[ Q^1=KSC\Delta t^1+q_0\frac{dn}{dt}\Delta t \tag{3} \]
where \(Q^1\) is the amount of mercury deposited on the mercury surface;
\(\Delta t^1\) is the time of deposition of mercury on the mercury surface; \(K\) is the proportionality coefficient;
\(S\) is the surface area of the electrode;
\(C\) is the concentration of mercury ions in the solution. That is, the dependence of the amount of deposited substance on the electrolysis time should be a curve passing through the origin and having an inflection corresponding to the filling of the graphite with mercury nuclei.
Another mechanism of formation of the mercury–graphite electrode is possible during electrolysis of sufficiently dilute solutions. In this case the rate of electrodeposition of mercury will be limited by the growth rate of the nuclei and by their shape. We have obtained various expressions for the rate of electrodeposition of mercury depending on the shape of the nuclei being formed. A common feature of the expressions obtained is that they contain terms in which the time enters to the third power:
\[ Q=At+Bt^2+Ct^3 \tag{4} \]
where \(A\), \(B\), \(C\) are certain constants; for a spherical nucleus \(A=B=0\).
Having reached a certain size, individual nuclei will begin to merge with one another, forming a mercury “film.” In this case the dependence “amount of deposited substance—electrolysis time” is a complex curve (at short electrolysis times the curve is a cubic parabola, which, as the electrolysis time increases, changes into a straight line corresponding to the deposition of mercury on the film).
As a result of experimental verification it has been shown that, when the mercury concentration in the solution is less than \(5\cdot10^{-8}\) g-ion/l, the rate of mercury deposition on the electrode is determined by the growth of individual nuclei, whereas when the mercury concentration is greater than \(5\cdot10^{-6}\) g-ion/l, the rate of mercury deposition is determined by the rate of formation of nuclei.
During the electrodissolution of metal from the mercury “film” of the graphite electrode, the height of the anodic peak should obey the equations obtained by Devries or Igolinskii [2, 3]. Our data, obtained using the examples of antimony, lead, and copper, show that the dependence of the height of the anodic peak on the number of electrons participating in the electrode process, the rate of change of potential, etc., is in good agreement with Igolinskii’s equation. The ratio of the height of the anodic
the ratio of the current to the amount of substance on the electrode is constant over a wide range of thicknesses of the mercury “films.”
Conclusions
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It has been shown that the rate of mercury deposition on a graphite electrode at short electrolysis times and high mercury concentrations is determined by the rate of formation of spherical nuclei, whereas at short electrolysis times and low mercury concentrations it is determined by the rate of growth of the nuclei.
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It has been found that the dependence of the height of the anodic peak during the electrodissolution of metal from a mercury film on a graphite electrode on various factors obeys the Igolinsky equation.
Literature
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E. M. Roizenblat. Abstracts of papers of the Fourth Polarographic Conference. Alma-Ata, 1969.
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V. A. Igolinsky. Dissertation. Tomsk, 1964.
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W. T. de Vries, “J. Electroanalyt. Chem.,” 9, 448, 1965.