A procedure to find thermodynamic equilibrium constants for CO₂ and CH₄ adsorption on activated carbon

Thermodynamic equilibrium for adsorption means that the chemical potential of gas and adsorbed phase are equal. A precise knowledge of the chemical potential is, however, often lacking, because the activity coefficient of the adsorbate is not known. Adsorption isotherms are therefore commonly fitted to ideal models such as the Langmuir, Sips or Henry models. We propose here a new procedure to find the activity coefficient and the equilibrium constant for adsorption which uses the thermodynamic factor. Instead of fitting the data to a model, we calculate the thermodynamic factor and use this to find first the activity coefficient. We show, using published molecular simulation data, how this procedure gives the thermodynamic equilibrium constant and enthalpies of adsorption for CO₂(g) on graphite. We also use published experimental data to find similar thermodynamic properties of CO₂(g) and of CH₄(g) adsorbed on activated carbon. The procedure gives a higher accuracy in the determination of enthalpies of adsorption than ideal models do.