Isotherms Derived from the Equation of State

The use of an equation of state to derive isotherms is based on the assumption that the adsorbed layer can be treated as a two-dimensional phase. In this case, the fimdamental equations in classical thermodynamics can be applied. Thus, at constant temperature, the Gibbs adsorption isotherm becomes 

Equation (3.15) forms the basis for the derivation of adsorption isotherms from equations of state. Alternatively, it can also be used to obtain equations of state from adsorption isotherms. For example, for a linear isotherm, n/p is constant and the integration of Eq. (3.15) gives 

A simple modification of Eq. (3.16) is to include a co-volume term to give 

A large number of equations of state has been used to derive adsorption isotherms. Some of the isotherms and their corresponding equations of state have been presented by Adamson [7]. 

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