Improper Estimation of Thermodynamic Parameters in Adsorption Studies with Distribution Coefficient KD (qe/Ce) or Freundlich Constant (KF): Considerations from the Derivation of Dimensionless Thermodynamic Equilibrium Constant and Suggestions

Abstract

Adsorption processes often include three important components: kinetics, isotherm, and thermodynamics. In the study of solid–liquid adsorption, “standard” thermodynamic equilibrium constant $\left(K_{\text{Eq}}^{\text{o}}\right.$ ; dimensionless) plays an essential role in accurately calculating three thermodynamic parameters: the standard Gibbs energy change (∆G°; kJ/mol), the standard change in enthalpy (∆H°; kJ/mol), and the standard change in entropy [∆S°; J/(mol × K)] of an adsorption process. Misconception of the derivation of the $K_{\text{Eq}}^{\text{o}}$ constant that can cause calculative errors in values (magnitude and sign) of the thermodynamic parameters has been intensively reflected through certain kinds of papers (i.e., letters to editor, discussions, short communications, and correspondence like comment/rebuttal). The distribution coefficient (KD) and Freundlich constant (KF) have been intensively applied for calculating the thermodynamic parameters. However, a critical question is whether KD or KF is equal to $K_{\text{Eq}}^{\text{o}}$ . This paper gives (1) thorough discussion on the derivation of thermodynamic equilibrium constant of solid–liquid adsorption process, (2) reasonable explanation on the inconsistency of (direct and indirect) application of KD or KF for calculating the thermodynamic parameters based on the derivation of $K_{\text{Eq}}^{\text{o}}$ , and (3) helpful suggestions for improving the quality of papers published in this field.