The objective minimization function for the mathematical representation of solubility data for solutes dissolved in binary solvent mixtures

Two minimization objective functions are used in calculating the curve-fit parameters of the Simplified Combined Nearly Ideal Binary Solvent (NIBS)/Redlich-Kister model for describing the experimental solubility of both linonin in binary aqueous-acetone solvent mixtures and betulinic acid in binary aqueous-tetrahydrofuran solvent mixtures. Curve-fit parameters based on the minimization of the summed squared differences between the experimental mole fraction solubilities and back-calculated values were found to provide a very good mathematical description of the observed solubility behavior in the organic solvent-rich portions of the binary solvent system. The back-calculated values, however, differed significantly from the observed values at low organic solvent compositions. Curve-fit parameters obtained using the summed squared difference between the natural logarithms of the experimental and back-calculated mole fraction solubilities provided the better mathematical description over the entire range of solvent composition.