Thermochemical behavior of dissolved carboxylic acid solutes: Part 4 - Mathematical correlation of 4-nitrobenzoic acid solubilities with the Abraham solvation parameter model

The Abraham general solvation model is used to calculate the numerical values of the solute descriptors for 4-nitrobenzoic acid from experimental solubilities in organic solvents. The mathematical correlations take the form of log(C(S)/C(W)) = c + r.R(2) + s. pi(2)(H) + a.Sigmaalpha(2)(H) + b.Sigmabeta(2)(H) + v.V(x) log(C(S)/C(G)) = c + r.R(2) + s.pi(2)(H) + a.Sigmaalpha(2)H+ b.Sigmaalpha(2)(H) + l.log L((16)) where C(S) and C(W) refer to the solute solubility in the organic solvent and water, respectively, C(G) is a gas phase concentration, R(2) is the solute excess molar refraction, V(x) is the McGowan volume of the solute, Sigmaalpha(2)(H) and Sigmabeta(2)(H) are measures of the solute hydrogen-bond acidity and hydrogen-bond basicity, pi(2)(H) 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 R(2) as 0.9900, set Sigmaalpha(2)(H) = 0.6800 and calculate V(x) as 1.1059, and then solve a total of 51 equations to yield pi(2)(H) = 1.5200, Sigmabeta(2)(H) = 0.4000, and log L((16)) = 5.7699. These descriptors reproduce the observed log(C(S)/C(W)) and log(C(S)/C(G)) values with a standard deviation of only 0.076 log units.