(Solid + liquid) solubility of organic compounds in organic solvents - Correlation and extrapolation

A semi-empirical model is developed for the regression of (solid + liquid) solubility data with temperature. The model fulfils the required boundary conditions, allowing for robust extrapolation to higher and lower temperatures. The model combines a representation of the solid-state activity which accommodates a temperature-dependent heat capacity difference contribution with a scaled three-parameter Weibull function representing the temperature dependence of the solution activity coefficient at equilibrium. Evaluation of the model is based on previously published experimental calorimetric and solubility data of four organic compounds, fenoxycarb, fenofibrate, risperidone and butyl paraben, in five common organic solvents, methanol, ethyl acetate, acetone, acetonitrile, and toluene. The temperature dependence of the van't Hoff enthalpy of solution and its components is analysed and discussed. Among the four compounds the influence of temperature on the enthalpy of fusion varies from moderate to substantial. Based on the semi-empirical model, a new equation containing three adjustable parameters is proposed for regression and extrapolation of solubility data for cases when only melting data and solubility data is available. The equation is shown to provide good accuracy and robustness when evaluated against the full semi-empirical model as well as against commonly used, more simple empirical equations. It is shown how such a model can be used to obtain an estimate of the heat capacity difference for cases where accurate solubility data is available in multiple solvents.