Measuring the Gibbs Free Energy of Mixing Using the Concept of an Osmotic Engine - Solute Activity Coefficient as a Colligative Property

Abstract

This manuscript presents a theoretical framework for quantifying the Gibbs free energy of mixing in real binary solutions. Grounded in the concept of an osmotic engine under pressure retarded osmosis, our approach combines static and dynamic membrane based osmometry to determine with high precision the excess free energy arising when two pure components are mixed. By then imagining this osmotic engine to consist of an infinite number of cylinders, a remarkably simple closed-form expression for the activity coefficient of a single solute molecule in a van’t Hoff ideal binary mixture emerges — one based purely on colligative considerations and free of semi-empirical parameters. This result can readily be extended to multicomponent systems containing both electrolytes and non-electrolytes. Finally, the same framework naturally captures solvent-dependent shifts in reaction equilibrium constants and enables routine determination of the Flory–Huggins interaction parameter between solvent and polymer.