Comparison of the nonlinear and linear forms of the van't Hoff equation for calculation of adsorption thermodynamic parameters (∆S° and ∆H°)

The use of nonlinear fitting of data of isotherm and kinetics is becoming more frequently used in the adsorption literature since the authors are becoming convinced that the use of linear isotherm and kinetics adsorption models could lead to extremally erroneous results. The utilization of nonlinear form of the van't Hoff equation for calculating the changes in enthalpy (∆H°) and changes in entropy (∆S°) of an adsorption process has not been reported in the literature until now. In this study, the values of equilibrium constants obtained from isotherms of adsorption (n = 57) at several temperatures (i.e., Langmuir, Liu, and Sips) were used to calculate the thermodynamic parameters of adsorption by the linear form and nonlinear form of the van't Hoff equation. Results demonstrated that the sign of thermodynamic parameters obtained from the linear and nonlinear forms was the same, whereas the magnitude of the nonlinear method is slightly higher than the linearized method. Two statistical methods—the parametric statistical (paired t-test) and non-parametric statistical (non-parametric Wilcoxon signed-rank paired test)—were applied for the comparison of difference. Although the difference on the magnitude of the thermodynamic parameters (obtained from the linear and nonlinear forms) was not apparently too enormously (n = 57), the statistical result at the 90%, 95% and 99% of probability level indicated that the difference was significant, being the values of the thermodynamic parameters obtained by the nonlinear method statistically higher than the values of these parameters obtained by the linearized method. Therefore, the nonlinear form of the van't Hoff equation should be used for accurately calculating the ∆H° and ∆S° parameters in the study of adsorption thermodynamics.