Measuring the Gibbs free energy of mixing using the concept of an osmotic engine

This manuscript develops a membrane-thermodynamic framework for quantifying the Gibbs free energy of mixing in real binary solutions. Using an osmotic engine representation under pressure retarded osmosis, the method links static and dynamic membrane-based osmometry to the excess Gibbs free energy of mixing, enabling operational estimation of ΔG_E from measurable osmotic and volumetric responses. As an analytical perspective, the van't Hoff limit produces a simple colligative form that connects the Henry-reference activity coefficient at infinite dilution to the dimensionless osmotic pressure, highlighting the role of reference-state regularisation and the sensitivity to volume assumptions. Beyond this limiting case, the framework provides a natural route to multicomponent mixtures with electrolytes and non-electrolytes, predicts solvent-dependent shifts in reaction equilibrium constants, and supports routine estimation of the Flory-Huggins solvent-polymer interaction parameter.