Abstract
According to the ideas considered in Chap. 1, when electric current passes through the electrolyte containing species of a polyvalent element in highest oxidation state N, the N – 1 low valency intermediates (LVIs) are formed in all possible oxidation states. Assuming the system is at equilibrium conditions, its properties have been determined by thermodynamic stability of the intermediates.
Any data can be generalized in an infinite number of ways. From them, we must choose only one, namely, the simplest one.
H. Poincarè
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Notes
- 1.
No possible set of independent equilibria fulfils these conditions. For example, N – 1 elementary disproportionation reactions of Eq. (1.8) type were used to describe the reversible polarographic wave of N-electron process [1]; however, the mathematics is too cumbersome in this case.
- 2.
For example, three equilibria should be used for the description of the system where Ti metal is at equilibrium with the melt containing Ti(IV) species: \( 3/4\mathrm{ Ti}(0) + 1/4\mathrm{ Ti}(\mathrm{ I}\mathrm{ V})\leftrightarrows \mathrm{ Ti}(\mathrm{ I}) \), \( 1/2\mathrm{ Ti}(0) + 1/2\mathrm{ Ti}(\mathrm{ IV})\leftrightarrows \mathrm{ Ti}\ (\mathrm{ II}) \), and \( 1/4\mathrm{ Ti}(0) + 3/4\mathrm{ Ti}(\mathrm{ IV})\leftrightarrows \mathrm{ Ti}\ (\mathrm{ III}) \).
- 3.
It is worthwhile to remember the “non-system” electrochemistry operating with “αn a-equations” which was mentioned in Chap. 1. Remaining in the framework this misconception, such situation would be dealt with regarding the process as one-step two-electron irreversible one and introducing “transfer coefficient” into the denominator of pre-logarithm coefficient of Eq. (2.76).
- 4.
Of course, it is correct for Nernstian reversible process, which is the only subject of this chapter.
- 5.
In a way, both approaches are true, because nobody can propose an experimentum crusis to distinguish which of them is right and which is wrong—such experiment is impossible in principle. Let us explain this statement. For example, experimental study of a process \( E(\mathrm{ IV})+4{e^{-}}\to E(0) \) by cyclic voltammetry gave following results: (1) only one wave was observed; (2) E(0) was reliably identified as the final product. OK, says a “non-system” electrochemist, the process is one-step four-electron one. We try to prove that he is wrong. For that, we carry out a second experiment investigating the same process by some modern fast technique. We apply very short pulses of current or potential and fix the intermediates by an appropriate spectral method in situ. Finally, we resolve each intermediate identifying it as short-lived compound which decomposes quickly by disproportionation reactions. “You see—we could say to the colleague—you are wrong, the process is stepwise, each step is one-electron, in accordance with our” system “concept, although both thermodynamic and kinetic stability of intermediates are very low and that is why we did not see it in the first experiment.” “You proved nothing”—might be the answer. “The process was the one-step in the first experiment and became multistep in the conditions of the second experiment, that is all”. But the nature of process cannot be dependent on the experimental conditions!—we oppose. Stop! Here we come to the core. The statement in italics is not a fact that can, by any means, be verified experimentally. It is pure convention. A fruitful convention, because it brings many separated facts into one system. That is why our concept is neither true nor wrong—it is just more convenient for any research purpose.
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Andriiko, A.A., Andriyko, Y.O., Nauer, G.E. (2013). Many-Electron Systems at Equilibrium. In: Many-electron Electrochemical Processes. Monographs in Electrochemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35770-1_2
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