The influence of heat capacity assumptions on the estimation of solubility parameters from solubility data

Regular solution theory indicates that solubility parameters of crystalline organic compounds can be estimated from solubilities in London solvents. The equation for this purpose is: IN X₂ - ΔH_f RT_f (T_f-T) T + ΔC_p R (T_f - T) T - ln T_f T - V₂θ²₁ RT (δ₁ - δ₂)² where X₂ is the mole fraction solubility of a compound in a solvent with a solubility parameter of δ₁. With the exception of ΔC_p, all parameters in the equation necessary to estimate the solute parameter, δ₂, can either be suitably approximated or readily determined experimentally. In order to use the equation, simplifying assumptions have been made concerning ΔC_p, namely: ΔC_p = 0 or ΔC_p = ΔS_f, the entropy of fusion. In the present work, we have considered the extent to which these assumptions influence the magnitude of solubility parameters estimated from solubilities in n-hexane, n-heptane, n-dodecane, cyclohexane, carbon tetrachloride, toluene and benzene. Using n-alkyl p-aminobenzoates as test compounds, it is shown that solubility-based solubility parameters are relatively insensitive to the form of the equation used to calculate δ₂. Specifically, solubility parameter estimations based on the two simplifying assumptions differ by no more than 0.2 (cal/ml) ^{1 2}, an increment of the order of the presumed inherent error of estimation.