A model to describe adsorbent heterogeneity has been developed by assuming that the adsorbent consists of a distribution of energetically different sites, the local isotherm on a site is of the Langmuir type and the energy distribution on the surface has a gamma probability density form. An analytic isotherm equation is derived. The parameters of the equation are m, the saturation adsorption capacity, and two energy distribution parameters, n and α. These parameters are found to be related to the Henry's-law constant, K. Thus there are only two adjustable parameters in the model when K is known from experimental data.

The model has been used to describe isotherms for adsorption of N₂, CH₄, CO₂ and C₂H₄ on the Calgon BPL activated carbon over large ranges of pressure and temperature. The carbon is found to be very heterogenous for the adsorption of these gases. Calculation of the probability density and the cumulative energy distribution functions indicates that the carbon exhibits a similar variance of surface energies for the adsorption of N₂, CH₄ and C₂H₄, although the isosteric heats of adsorption in the Henry's-law region for these gases are very different, decreasing in the order C₂H₄ > CH₄ > N₂. The isosteric heat of adsorption for CO₂ is comparable to that of C₂H₄ but the carbon is more homogeneous for the adsorption of CO₂ than for the other gases.