Systems involving coupled homogeneous reactions

Cyclic voltammetry is a powerful tool for investigating electrode processes involving coupled homogeneous reactions. We exemplify with the EC mechanism  

An alternative strategy consists in analysing the variation of peak 

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The preceding approach applies to all linear systems that is, those involving mechanisms in which only first-order or pseudo-first-order homogeneous reactions are coupled with the heterogeneous electron transfer steps. As seen, for example, in Section 2.2.5, it also applies to higher-order systems, involving second-order reactions, when they obey pure kinetic conditions (i.e., when the kinetic dimensionless parameters are large). If this is not the case, nonlinear partial derivative equations of the type... 

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. 

More complicated systems, involving slow heterogeneous kinetics, coupled homogeneous reactions or equilibria (e.g., as in Chapter 12), or more complex forms of mass transfer (e.g., at a UME, Section 5.3), are most easily treated by digital simulation. Osteryoung and O Dea (50) discuss the application of SWV to a wide range of such phenomena. 

As will now be clear from the first Chapter, electrochemical processes can be rather complex. In addition to the electron transfer step, coupled homogeneous chemical reactions are frequently involved and surface processes such as adsorption must often be considered. Also, since electrode reactions are heterogeneous by nature, mass transport always plays an important and frequently dominant role. A complete analysis of any electrochemical process therefore requires the identification of all the individual steps and, where possible, their quantification. Such a description requires at least the determination of the standard rate constant, k, and the transfer coefficients, and ac, for the electron transfer step, or steps, the determination of the number of electrons involved and of the diffusion coefficients of the oxidised and reduced species (if they are soluble in either the solution or the electrode). It may also require the determination of the rate constants of coupled chemical reactions and of nucleation and growth processes, as well as the elucidation of adsorption isotherms. A complete description of this type is, however, only ever achieved for very simple systems, as it is generally only possible to obtain reliable quantitative data about the slowest step in the overall reaction scheme (or of two such steps if their rates are comparable). 

Oxidation-reduction processes involving the Fe -Fe couple have been intensively studied, and the elementary electron exchange, taking place either in solution or at an electrode interface, has served for a long time as a test case for theoretical interpretations of electron transfer kinetics. For reactions involving ground-state ions, the mechanisms of the reactions are now well understood for the homogeneous systems, for example, electron transfer can occur, as demonstrated by Taube, via either a simple outer-sphere electron... 

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