Determination, Correlation, and Thermodynamic Analysis of Solid-Liquid Phase Equilibrium of 3-Methoxycinnamic Acid in Pure and Mixed Solvents at Different Temperatures

The solubility of 3-methoxycinnamic acid was determined in nine pure solvents (methanol to ethyl acetate) and ethanol–ethyl acetate binary mixtures (293.15–333.15 K). Results demonstrate positive temperature dependence in all systems, with maximum solubility in binary solvent at ethanol volume fraction of 0.3, while benzene exhibited the lowest solubility. Solid–liquid equilibrium (SLE) data were correlated using five thermodynamic models (modified Apelblat, Van’t Hoff, Wilson, NRTL, UNIQUAC). The modified Apelblat equation showed superior accuracy for both solvent systems. KAT-LSER analysis revealed solvent hydrogen-bond acidity (α), basicity (β), and cohesive energy density (CED) (δH) as dominant molecular descriptors. Thermodynamic parameters (ΔGmix < 0) confirmed spontaneous dissolution, with enthalpy–entropy compensation revealed by Gibbs energy deconvolution. The obtained solubility and thermodynamic data may be useful for the design and optimization of crystallization processes of 3-methoxycinnamic acid.