Is the Free Energy Change of Adsorption Correctly Calculated?

Abstract

In the study of adsorption, changes in free energy (Δ G °), enthalpy (Δ H °), and entropy (Δ S °) have been most frequently calculated from the Langmuir equilibrium constant. In a strict theoretical sense, the Langmuir equilibrium constant with units of liters per mole and the thermodynamic equilibrium constant without units are not the same. Moreover, the equilibrium constants for thermodynamic calculation have also been derived in different ways in the literature, for example, Frumkin isotherm, Flory−Huggins isotherm, distribution constants, and so on. As a result, values of Δ G °, Δ H °, and Δ S ° of adsorption reported in the literature are very confusing. This study shows that for a dilute solution of charged adsorbates or for a solution of uncharged adsorbates at any concentration, the thermodynamic equilibrium constant of adsorption would be reasonably approximated by the Langmuir equilibrium constant, and thus the use of the Langmuir equilibrium constant for calculation of Δ G ° and subsequent determination of Δ H ° and Δ S ° of adsorption would be acceptable. However, special attention should be given if the equilibrium constants derived from other adsorption isotherm equations or distribution constants were used for determination of Δ G °.