Thermodynamic parameters of liquid–phase adsorption process calculated from different equilibrium constants related to adsorption isotherms: A comparison study

Adsorption thermodynamics is an integral part of the study of adsorption and plays a vital role in estimating adsorption mechanism (i.e., physisorption and chemisorption). For the liquid-phase adsorption, the equilibrium constant of some adsorption isotherm models (Langmuir, modified Langmuir, Langmuir–Freundlich, modified Langmuir–Freundlich, Liu, Khan, Sips, Hill, Toth, Redlich–Peterson, Koble–Corrigan, and Radke–Prausnitz models) and the constant of Henry and Freundlich models have been directly or indirectly applied for calculating the corresponding thermodynamic parameters (∆G°, ∆H°, and ∆S°). This study explored the effects of the selection of (1) the unit of adsorption isotherm (qe vs. C e), (2) the equilibrium constant of adsorption isotherm model, and (3) the linear and nonlinear forms of the van’t Hoff equation on the value (sign and magnitude) of the thermodynamic parameters. A commercial activated carbon was selected as a typical adsorbent to adsorb methylene green dye (target adsorbate) in solution. Results indicated that the constants of the Henry and Freundlich models could not be applied for calculating the thermodynamic parameters. The equilibrium constants of the modified Langmuir and modified Langmuir–Freundlich models were not suitable for calculating the thermodynamic parameters in this study compared to the other equilibrium constants of the Langmuir, Langmuir–Freundlich, Khan, Liu, Sips, Redlich–Peterson, Toth, Hill, Radke–Prausnitz, and Koble–Corrigan models. The thermodynamic parameters were calculated from thermodynamic equilibrium constant derived from the equilibrium constant of the Redlich–Peterson model or the Radke–Prausnitz model (the van’t Hoff equation: adj-R2 = 0.9999).