Cosphere Overlap Model and Hydration Dynamics in Aqueous Potassium Sorbate–Glucose Systems: A Volumetric and Acoustic Perspective

Understanding solute–solvent interactions in multicomponent aqueous systems is crucial for applications in food preservation, pharmaceuticals, and biochemical formulations. This study investigates the hydration dynamics and molecular interactions in aqueous potassium sorbate–glucose systems using density and acoustic measurements as functions of temperature and ambient pressure. Several thermodynamic and acoustic parameters have been derived from experimentally measured density and sound velocity, including the apparent molar volume (V_2,ϕ), apparent molar isentropic compressibility (Ks_2,ϕ); limiting apparent molar volume $\left(V_{2,\varphi }^{\infty }\right)$ and limiting apparent molar isentropic compression $\left(K{s}_{2,\varphi }^{\infty }\right)$. Additionally, limiting apparent molar volume of transfer $\left({\Delta }^{\mathrm{tr}}{V}_{2,\varphi }^{\infty }\right))$ and isentropic compression of transfer $\left({\Delta }^{\mathrm{tr}}K{s}_{2,\varphi }^{\infty }\right)$, were calculated. Further derived properties include partial molar expansibility $\left(E_{\varphi }^0\right)$, its temperature derivative $(\partial E_{\varphi }^0/\partial T)p$, and interaction coefficients for pairs and (V_AB, K_AB, V_ABB, K_ABB), as well as hydration number (n_H) and some empirical parameters. The cosphere overlap model was applied to explain the values of $({\Delta }^{\mathrm{tr}}{V}_{2,\varphi }^{\infty })$ and $\left({\Delta }^{\mathrm{tr}}K{s}_{2,\varphi }^{\infty }\right)$. Positive values of $(\partial E_{\varphi }^0/\partial T)p$ indicate that potassium sorbate acts as a structure-maker in aqueous glucose solutions. The partial molar properties further suggest hydrogen bond formation in the system. Collectively, these properties indicate strong solute–solvent interactions in the examined ternary system across the studied temperature and composition ranges.