Differential Molar Heat Capacities to Test Ideal Solubility Estimations

Purpose. Calculation of the ideal solubility of a crystalline solute in a liquid solvent requires knowledge of the difference in the molar heat capacity at constant pressure of the solid and the supercooled liquid forms of the solute, C_p. Since this parameter is not usually known, two assumptions have been used to simplify the expression. The first is that C_p can be considered equal to zero; the alternate assumption is that the molar entropy of fusion, S_f, is an estimate of C_p. Reports claiming the superiority of one assumption over the other, on the basis of calculations done using experimentally determined parameters, have appeared in the literature. The validity of the assumptions in predicting the ideal solubility of five structurally unrelated compounds of pharmaceutical interest, with melting points in the range 420 to 470K, was evaluated in this study. Methods. Solid and liquid heat capacities of each compound near its melting point were determined using differential scanning calorimetry. Linear equations describing the heat capacities were extrapolated to the melting point to generate the differential molar heat capacity. Results. Linear data were obtained for both crystal and liquid heat capacities of sample and test compounds. For each sample, ideal solubility at 298K was calculated and compared to the two estimates generated using literature equations based on the differential molar heat capacity assumptions. Conclusions. For the compounds studied, C_p was not negligible and was closer to S_f than to zero. However, neither of the two assumptions was valid for accurately estimating the ideal solubility as given by the full equation.