A simplified method for enhanced accuracy in calculating adsorption thermodynamic parameters

Abstract

This study investigates the thermodynamic parameters of phosphate adsorption on activated carbon using the Pitzer ion-interaction model. The adsorption data were analyzed using the Langmuir and Sips models, both providing satisfactory fits. Maximum adsorption (plateau) occurred at an equilibrium phosphate concentration of 60.8 mmol⋅ dm⁻³ (pH = 5.1), with an adsorption capacity of 7.03 mmol⋅g⁻¹. The Pitzer model was used to calculate the activity coefficient of phosphates, considering the influence of all ions in the solution on the adsorption plateau. The maximum degree of dissociation of H₂PO₄^-(aq) ions was determined to be x_d(2) = 0.0026, taking hydrolysis into account. The activity coefficient of KH₂PO₄ in the mixed solution {K₂HPO₄ + KH₂PO₄ + H₃PO₄}(aq) was found to be γ_± = 0.7788, while in a pure KH₂PO₄ solution at the same ionic strength corresponding to the plateau, it is γ_± = 0.7790. Given the minor difference in activity coefficient, the mixed solution could be approximated as a pure KH₂PO₄(aq) for thermodynamic analysis, which greatly simplified the calculations. The Gibbs free energy was ΔG_L  = − 8.6200 ± 0.0004 (kJ⋅mol⁻¹) using the Langmuir equilibrium constant shifting to ΔG_a = − 9.240 ± 0.006 (kJ⋅mol⁻¹) when accounting for activity coefficient and the thermodynamic equilibrium constant. With the Sips model, the Gibbs free energy was ΔG_S  = − 9.620 ± 0.004 (kJ⋅mol⁻¹) and further refinement using phosphate activity coefficient gave ΔG_a  = −10.235 ± 0.007 (kJ⋅mol⁻¹). The absolute differences in adsorption energy were approximately 7 % (Langmuir) and 6 % (Sips), highlighting the importance of considering ionic activities.