Mathematical correlation of naproxen solubilities in organic solvents with the Abraham solvation parameter model

The Abraham solvation parameter model is used to calculate the numerical values of the solute descriptors for naproxen from experimental solubilities in organic solvents. The solute descriptors are denoted as follows: E is the solute excess molar refraction, V is McGowan volume of the solute, A and B are measures of the solute hydrogen-bond acidity and hydrogen-bond basicity, respectively, S is the solute dipolarity/polarizability descriptor and L is the logarithm of solute gas phase dimensionless Ostwald partition coefficient into hexadecane at 298 K. We estimate E as 1.510 and calculate V as 1.7821, and then solve a total of 40 equations to yield S = 2.022, A = 0.600, B = 0.673 and L = 9.207. These descriptors reproduce the observed log solubility ratios to within a standard deviation of only 0.073 log units.