  A simple model to fit experimental data of adsorption of gases and vapours on
microporous adsorbents (type I isotherms) is proposed. The main assumption is
that the adsorbate phase can be divided into identical and non-interacting
effective subsystems. This gives rise to a simple multiparametric isotherm
based on the grand canonical ensemble statistics, whose functional form is a
ratio of two polynomial functions. The parameters are interpreted as effective
equilibrium constants. A simplified isotherm that reduces the number of
adjustable parameters with respect to the general isotherm is also proposed. We
show how to use these isotherms to fit the adsorption data in such way that the
parameters have statistical significance. Due to their high accuracy, both
isotherms can be used to estimate thermodynamic properties like isosteric and
differential heats of adsorption. A simple method is presented for systems that
show an apparent variation in the coverage limit with temperature. This method
avoids overparametrization and improves fitting deviations. Finally, several
applications to fitting data, taken from literature, of adsorption of some
gases on activated carbon, molecular sieving carbon, silica gel, and pillared
clays are presented.

Chemical Physics;Mesoscale and Nanoscale Physics;Statistical Mechanics