Advanced thermodynamic approach to adsorption of charged adsorbates from aqueous electrolyte solutions

Abstract

This study present estimation of the thermodynamic parameters and the influence of ionic activity coefficient on the thermodynamic equilibrium constant of adsorption of phosphates on fly ash. The adsorption was conducted over a wide range of initial phosphate concentrations at different pH values pH = (3; 7; 10). The adsorption results were treated using the Langmuir, Freundlich and Sips adsorption isotherms, which provide information about the maximum adsorption capacity. The Langmuir and Sips isotherms were a satisfactory fit to the adsorption data, especially at pH = 3, with an acceptable regression coefficient over the entire concentration range, Langmuir (r2 = 0.9737) and Sips (r2 = 0.9969). The estimated maximum phosphate sorption capacity of fly ash was 6.21 ± 0.68 (mmol·g−1) according to Langmuir and 4.19 ± 0.16 (mmol·g−1) according to the Sips model, at pH = 3.0. However, there is no data in the published literature for estimating the thermodynamic parameters of the phosphate adsorption process using thermodynamic models for activity coefficients. Novel approach of this paper was determination of the thermodynamic equilibrium constant and Gibbs free energy, using the Pitzer ion-interaction model to predict the nature of adsorption. The Pitzer-ion interaction model was used for the mixed ionic systems, taking into consideration the effect of other present ions besides phosphates in the equilibrium solution resulting from fly ash desorption. The procedure for comprehensive estimation of the ion activity coefficient at maximum adsorption capacity and the dimensionless thermodynamic equilibrium constant using Langmuir's and Sips’s constants was presented. The calculated value of the phosphate activity coefficient in the equilibrium solution was γH2PO4,e = 0.7003 ± 0.0027 and the converted molar activity coefficient was γH2PO4,e = 0.6903 ± 0.0027. The estimated values of Gibbs free energy were: ΔGL = −6.788 ± 0.521 kJ·mol−1 based on Langmuir equilibrium constant and ΔGa = −7.707 ± 0.527 kJ·mol−1 based on activity and thermodynamic equilibrium constant. According to Sips model, the adsorption process is even more spontaneous, with the Gibbs free energy calculated using the phosphate activity coefficient and the thermodynamic equilibrium constant, ΔGa = −9.707 ± 0.617 kJ·mol−1. Consideration of the ionic activity coefficient is particularly important for large, charged adsorbates at higher concentrations, as the absolute difference in free energy for adsorption is app. 12 %. The scientific contribution is reflected in obtaining the necessary and more accurate information for the improvement of adsorption processes and possibly for the upgrading of fly ash in overall wastewater treatment technology.