Simple isotherm equations to fit type I adsorption data

We propose that the Hill model of adsorption can be used to fit type I adsorption isotherms in general. The main assumption that allows us to apply this model empirically 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 adsorption equilibrium constants. A simple recurrence relation for the equilibrium constants is proposed for systems that show an apparent variation in the coverage limit with temperature. This relation avoids overparametrization and improves fitting deviations. We revisit a simplified isotherm derived by Ruthven and show that it can also be applied to heterogeneous systems. We also show how to use the isotherms of Hill and Ruthven, along with the recurrence relation shown in this work, to fit the adsorption data to obtain parameters with statistical significance. Due to their high accuracy, both isotherm equations can be used to estimate thermodynamic properties like isosteric and differential heats of adsorption. 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.