Correlation of the solubility of isoniazid in some aqueous cosolvent mixtures using different mathematical models

Solubility is one of the most important physicochemical properties, because it is related to some industrial processes such as: formulation, preformulation, purification and quantification. The experimental determination of solubility requires rigorous processes that involve a significant amount of resources. In this context, mathematical models allow estimating solubility under conditions different from the experimental ones from a limited number of data. The objective of this research was to evaluate the pertinence of 10 mathematical models (Extended Hildebrand, van’t Hoff, Two-parameter Weibull, Buchowski–Ksiazczak \(\lambda h\) $\lambda h$ , van’t Hoff-Yaws, Apelblat, Wilson, NRTL, Modified Wilson and van’t Hoff-Modified Wilson) in the calculation of the solubility of isoniazid in PEG 200 (1) + Water (2) cosolvent mixtures, the parameters of each model were calculated using Python, Pandas and the NumPy and SciPy library. Once each model was evaluated, two models were defined as the best alternatives based on their predictive power and mathematical simplicity. Thus, the van’t Hoff and Modified Wilson models were combined to obtain an equation that allows the calculation of solubility as a function of temperature and cosolvent composition, obtaining MRD% less than 3.0. In conclusion, mathematical models represent a good prediction tool being a potential alternative in relation to the optimization of some industrial processes related to solubility.