Predicting Proton Activity and Acid Dissociation Equilibria in Mixed-Solvent Systems, and Their Impact on Esterification Kinetics of Levulinic Acid

This study presents a novel thermodynamic modeling approach for predicting the reaction kinetics of esterification reactions. The system studied in detail was levulinic acid esterification by various alcohols, using sulfuric acid as a homogeneous catalyst at reaction temperatures between 323 and 353 K at atmospheric pressure. The effects of temperature, solvent, and cosolvent on the kinetics and equilibrium of LA esterification were found to be significant. The novel modeling approach developed in this work introduces absolute proton activity into reaction formalism by focusing on a thermodynamic description of the catalyst effects on reaction kinetics. That required accurate modeling of proton activities, Gibbs energies of solvation, and acid dissociation equilibria in the mixed aqueous–organic reaction system that changes composition with reaction progress. In this work, the electrolyte equation of state ePC-SAFT was applied to predict absolute proton activities in mixed solvent systems. The ePC-SAFT parameters were adjusted by literature-based data on proton Gibbs energies of solvation and on acid dissociation equilibria. The new approach allowed very good accuracy in calculating proton Gibbs energies of solvation, acid dissociation equilibria, and absolute proton activity in mixed-solvent systems. It could quantitatively explain the disadvantageous effect of water on kinetics, despite acid dissociation in water solvent is strong while proton activity is very low. Ultimately, this allowed predicting the influence of catalyst, solvent and of cosolvent addition on the kinetics and the equilibrium of the esterification, demonstrating that the cosolvent γ-valerolactone had minimal effect on the kinetics while water significantly decreased the reaction rate and sulfuric acid addition accelerated the reaction depending on sulfuric acid concentration. To conclude, this approach allows for a reduction in experimental effort by reliably predicting the influence of the key reaction conditions on kinetics and equilibria of chemical reactions.