Experimental measurement, thermodynamic analysis and mathematical modelling for paracetamol solubility in N -methyl-2-pyrrolidone + water mixtures at T = (293.2 to 313.2) K

The present study investigated the solubility of paracetamol (PARA) in mixtures of N-methyl-2-pyrrolidone (NMP) and water over the temperature range of 293.2–313.2 K using the shaking flask method. The experimental data were employed to determine thermodynamic parameters governing PARA dissolution. To assess the predictive capability, several mathematical models, including van’t Hoff, Yalkowsky, CNIBS/R–K, Jouyban–Acree and Jouyban–Acree–van’t Hoff models, were applied. Results showed that PARA exhibited the highest solubility in pure NMP at all studied temperatures. Thermodynamic analysis indicated that the dissolution process was endothermic and driven by entropy across in all solvent compositions. Evaluation of predictive accuracy using mean relative deviations (MRDs%) demonstrated that the van’t Hoff model provided the highest accuracy (1.5%), while the Yalkowsky model showed the least accuracy (45.0%). The CNIBS/R–K, λh, Jouyban–Acree, and Jouyban–Acree–van’t Hoff models yielded MRDs of 2.5%, 3.0, 3.5%, and 2.9%, respectively, confirming the suitability of multi-parameter approaches.