Kinetic Equations for Discharge

For a further analysis of the experimental data, we shall need kinetic equations for an electrode process. It is therefore expedient to give their detailed derivation at this point. For the time being, we shall confine ourselves within the framework of the absolute rate theory. 

In order to illustrate the ideas that form the basis of this discussion, we shall consider the specific example of the cathodic evolution of hydrogen. 

The current density for the discharge reaction of a proton donor HB is given by 

Here and in the following, e is the charge of an electron, k and h are Boltzmann s constant and Planck s constant respectively, is the transmission coefficient, a - the activity, y the activity coefficient, G - the Gibbs free energy, and G - the Gibbs electrochemical free energy. The superscript 7 denotes the transition state, the subscripts i and f indicate the initial and final states, a stands for the adsorbed particles, and the superscript 0 means that the corresponding values refer to standard conditions. 

The effect of the surface coverage with adsorbed hydrogen (0) on the reaction rate is considered only through its effect on the fraction of the free surface. We thus assume that the Langmuir isotherm is valid. This simplification is admissible since we are primarily interested in cathodes which are poor adsorbers of hydrogen, i.e. the cathodes with 6 1. 

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If Eq. (31a) is substituted into the kinetic equation for discharge, the term including y and if/i takes the form... 

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