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

Adsorption processes often include three important components: kinetics, isotherm, and thermodynamics. In the study of solidliquid adsorption, standard thermodynamic equilibrium constant (K-Eq degrees; dimensionless) plays an essential role in accurately calculating three thermodynamic parameters: the standard Gibbs energy change (Delta G degrees; kJ/mol), the standard change in enthalpy (Delta H degrees; kJ/mol), and the standard change in entropy [Delta S degrees; J/(mol x K)] of an adsorption process. Misconception of the derivation of the K-Eq degrees 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 (K-D) and Freundlich constant (K-F) have been intensively applied for calculating the thermodynamic parameters. However, a critical question is whether K-D or K-F is equal to K-Eq degrees. 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 K-D or K-F for calculating the thermodynamic parameters based on the derivation of K-Eq degrees and (3) helpful suggestions for improving the quality of papers published in this field.

Automated summary

This study discusses the important thermodynamic parameters and the errors in their calculation in solid-liquid adsorption processes. The derivation of thermodynamic equilibrium constant and the inconsistent application of distribution coefficient and Freundlich constant for calculating these parameters are addressed. Correcting these misconceptions is crucial for improving the quality of research papers in this field.