Coupled homogeneous electrode reactions following reaction

The EC mechanism (Scheme 2.1) associates an electrode electron transfer with a first-order (or pseudo-first-order) follow-up homogeneous reaction. It is one of the simplest reaction schemes where a heterogeneous electron transfer is coupled with a reaction that takes place in the adjacent solution. This is the reason that it is worth discussing in some detail as a prelude to more complicated mechanisms involving more steps and/or reactions with higher reaction orders. As before, the cyclic voltammetric response to this reaction scheme will be taken as an example of the way it can be characterized qualitatively and quantitatively. 

We consider three simple schemes, shown in Fig. 6.11, and examine the effect of homogeneous coupled reactions on the current at the electrode they are CE, EC, and EC, where E represents an electrochemical step (at the electrode) and C a chemical step (in solution). The equations to calculate the rate constants from experimental measurements for the various types of electrode can be found in the specialized literature. In most studies the electrochemical step has been considered reversible—thus, in the following, the rate constant for the electrode reaction is not indicated. 

The form of the response is a succession of points following the same profile as a conventional voltammogram. However, since a pulse causes greater mass transport than a steady-state technique (hydrodynamic electrode), a reaction that appears reversible in the steady state can appear quasi-reversible with this technique. On the other hand, given the short timescale, effects due to coupled homogeneous reactions may not be observed. 

It is important to obtain experimental information on the thermodynamics of electrode processes to ascertain the tendency of a particular reaction to occur under a given set of experimental conditions namely temperature, pressure, system com H)sition and electrode potential. Such information is provided by the standard- or formal-electrode potentials for the redox couple under consideration. Appropriate combinations of these potentials enable the thermodynamics of homogeneous redox processes to be determined accurately. However, such quantities often are subject to confusion and misinterpretation. It is, therefore, worthwhile to outline their significance for simple electrochemical reactions. This discussion provides background to the sections on electrochemical kinetics which follow. The evaluation of formal potentials for various types of electrode-reaction mechanisms is dealt with in 12.3.2.2. 

Consequently, a complete experimental separation of intrinsic and thermodynamic contributions to the electrochemical reactivity is restricted chiefly to one-electron processes where both halves of the redox couple are stable in solution. Nevertheless, the formalism embodied in Eq. (n) provides a useful basis for treating electrochemical reactivity in terms of fundamental physical models and is utilized for homogeneous redox reactions. It therefore will be employed in the following discussion of the structural and environmental factors that can influence the kinetics of simple inorganic electrode reactions. 

Let us first consider briefly how the use of mass transport as a variable can provide a guide to the reaction mechanism and give quantitative kinetic detail. As an illustration, we consider the behaviour of CE and EC processes (where E signifies electron transfer and C represents a chemical step) at a rotating disc electrode (RDE). This hydrodynamic system has already been discussed by Albery et al. and the reader is referred to Chap. 4 for details. CE and EC processes represent the simplest conceivable electrode reactions involving coupled homogeneous kinetics mechanistic examples of both types are shown in Table 1. In the discussion which follows, the electron-transfer reaction in the two mechanisms is considered to be a cathodic process the extension to the anodic case is trivial. 

This section concerns heterogeneous electron transfer reactions coupled with homogeneous chemical reactions in which either the electroactive species A or the product of the electron transfer B participate as reactants. Perturbations of electrochemical responses of different techniques evoked by these reactions enable the elucidation of the mechaism and the evaluation of the kinetic parameters of the chemical steps. Chemical reactions that are indicated in the electrochemical way occur in the thin layer reaction layer) adjacent to the electrode surface only. This is illustrated in Fig. 1 where the concentration dependence of the product B on the distance from the electrode plane (with and without follow-up chemical reaction) is plotted. It must be stressed that the kinetics and the electrode mechanism are affected not only by the nature of the electroactive as well as electroinactive species including the type of the solvent, but also by the electrode material and substances adsorbed on the electrode surface. 

Flow coulometry experiments were performed to study the reduction of U02 in nitric, perchloric, and sulfuric acid solutions [56]. The results of these studies show a single two-electron reduction wave attributed to the U02 /U + couple. The direct two-electron process is observed without evidence for the intermediate U02" " species because of the relatively long residence time of the uranium ion solution at the electrode surface in comparison to the residence time typically experienced at a dropping mercury working electrode. The implication here is that as the UO2 is produced at the electrode surface, it is immediately reduced to the ion. As the authors note a simplified equation for this process can be written, Eq. (7), but the process is more complicated. Once the U02" species is produced it experiences homogeneous reactions comprising Eqns (8) and (9) or (8) and (10) followed by chemical decomposition of UOOH+ or UO + to [49]. 

The current density controls the concentration of radicals at the electrode surface. This concentration, depending on the rate constants of the follow-up reactions of the radicals, is 10 to 10 times higher than in homogeneous reactions. A low current density favors the monomolecular cyclization against the bimolecular coupling to an acyclic product. A decrease in the current density by a factor of 30 increased the proportion of cyclized product tenfold (Eq. 15) [133]. 

Since the 1960s, cyclic voltanunetry has been the most widely used technique for studies of electrode processes with coupled chentical reactions. The theory was developed for numerous mechanisms involving different combinations of reversible, quasi-reversible, and irreversible heterogeneous ET and homogeneous steps. Because of space limitations, we will only consider two well-studied examples—(i.e., first-order reversible reaction preceding reversible ET) and E Ci (i.e., reversible ET followed by a first-order irreversible reaction)—to illnstrate general principles of the coupled kinetics measurement. A detailed discussion of other mechanisms can be found in Chapter 12 of reference (1) and references cited therein, including a seminal publication by Nicholson and Shain (19). 

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