The Frumkin and Temkin Isotherms

The assumption that the standard Gibbs energy of adsorption is independent of coverage may be viewed as the first-order approximation. A better approximation will then be to assume a linear dependence of AG° jg on 0  

Keeping in mind the relationship between the standard Gibbs energy and the equilibrium constant, it is very easy to modify the Langmuir isotherm, taking into account the variation of AG g with 0. To do this, we replace AGj g in Eq. (11.4) by AG0 and combine with Eq. (11.10), to obtain 

This equation is known as the Frumkin isotherm. It should be clear that the Langmuir isotherm is a special case of the Frumkin isotherm, derived from it by setting r = 0. It 

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If the relative values of the rate constants among the consecutive or parallel steps in reactions such as that of hydrogen evolution have the most decisive influence here, Frumkin-Temkin should be used. If they lead to a situation in which the intermediate radical coverage tends toward zero or one, the matter is decided. As remarked above, for 0 — 0 or 0 — 1, the Frumkin and Temkin isotherms coincide in effect with that of Langmuir. 

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