Some notes on the statistical theory of adsorption

A derivation is given for the Langmuir, Brunauer-Emmett-Teller, and Cassie adsorption isotherms with the help of the grand-canonical ensemble. This method justifies the approximations contained in the usual statistical treatments of adsorption. Furthermore, it is possible to reveal the implicit assumptions about the structure of the adsorbed layers contained in the kinetic derivations seemingly based only on the principle of detailed balancing. If one uses these assumptions one may deduce other types of adsorption isotherms probably exhausting the possibilities contained in these simple molecular models.