Analytic expressions for the isosteric heat of adsorption from adsorption isotherm models and two-dimensional SAFT-VR equation of state

The isosteric heat of adsorption is an important thermodynamic property used to characterize and optimize adsorption processes. In this work, analytic expressions for isosteric heats of adsorption are derived for a collection of commonly used isotherm models and a two-dimensional molecular equation of state based on the SAFT-VR approach. The use of these expressions is presented with an example of adsorption of nitrous oxide, N₂O, on biochar, which is a waste biomass charcoal that exhibits high adsorption potential. The results show that accurate fitting of the adsorption isotherms leads to consistent results obtained with different approaches; however, the predicted isosteric heat of adsorption exhibits strong variations in the regions where experimental data is insufficient such in the region of low pressure/low coverage. Convergence on the prediction of the isosteric heat of adsorption by the different models is only observed in the region where no extrapolation of experimental data is needed.