The Equation for a Single-Step Electrode Reaction

The relationship between the Gibbs energy and potential was discussed in Section 4.1.2. For the standard electrochemical Gibbs energy of a reaction, we wrote Eq. (4.6) and for the standard electrochemical Gibbs energy of activation, Eq. (4.7). 

The symmetry factor p in Eq. (4.7) is discussed in Section 5.3 below. The positive and negative signs in Eq. (4.7) are applicable to cathodic and anodic reactions, respectively. When Eq. (4.7) is combined with the rate equation we have, for an anodic process 

There are two ways in which we wish to modify this equation. First, we simplify it by replacing the term o) exp(AG /RT) by a chemical rate constant, fej, which is the value of the heterogeneous rate constant at A( ) = 0, to yield 

Second, we would like to replace the awkward term A( ) which, as we recall, cannot be measured. Now, we have gone to some length to show that, although Acj) cannot be measured, changes in it can be readily determined (cf Section 2.1.2). Bearing this in mind we can write the overpotential as  

Equation (5.23) represents the rate of an anodic oxidation reaction for which the overpotential is, by definition, positive. For a cathodic reduction we write a similar equation with a negative sign in the exponent, and take the overpotential, by definition, to be negative. In either case the current density increases exponentially with increasing absolute value of the overpotential, t].  

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