Verification of the Theory Under Equilibrium Conditions

2 Verification of the Theory Under Equilibrium Conditions. It has already been remarked that the ultimate test of any kinetic theory is that, under equilibrium conditions, the kinetic equations must coincide with the thermodynamic equations. 

The fundamental relationship for a heterogeneous charge transfer (Butler-Volmer equation) is  

when the electrode, depending upon the concentrations of Ox and Red, assumes an equilibrium potential, Eeq, (keep in mind that E° is the particular equilibrium potential set up when the concentrations of Ox and Red at the electrode surface are identical) it will reach the zero current condition (i = 0), so that  

However, if there is an equilibrium between the two species at the electrode surface, such an equilibrium must also exist in the bulk of the solution. Hence  

In reality such an expression is nothing more than the exponential form of the Nernst equation seen previously (Sections 3 and 4.1)  

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