Solubility of crystalline nonelectrolyte solutes in organic solvents: mathematical correlation of 3-nitrobenzoic acid solubilities with the Abraham general solvation model

The Abraham general solvation model is used to calculate the numerical values of the solute descriptors for 3-nitrobenzoic acid from experimental solubilities in organic solvents. The mathematical correlations take the form oflog(CS/CW)=c+rR2+sπ2H+aΣα2H+bΣβ2H+vVxlog(CS/CG)=c+rR2+sπ2H+aΣα2H+bΣβ2H+l⁢logL(16)where CS and CW refer to the solute solubility in the organic solvent and water, respectively; CG is a gas-phase concentration; R2 is the solute excess molar refraction; Vx is McGowan volume of the solute; Σα2H and Σβ2H are measures of the solute hydrogen-bond acidity and hydrogen-bond basicity; π2H denotes the solute dipolarity/polarizability descriptor; and L(16) is the solute gas-phase dimensionless Ostwald partition coefficient into hexadecane at 298 K. The remaining symbols in the above expressions are known solvent coefficients, which have been determined previously for a large number of gas/solvent and water/solvent systems. We estimate R2 as 0.9900 and calculate Vx as 1.1059, and then solve a total of 48 equations to yield π2H=1.1800, Σα2H=0.7300, Σβ2H=0.5200 and log L(16)=5.6011. These descriptors reproduce the experimental data with a standard deviation of only 0.082 log units.