Deducing solute differential heat capacity from experimental solubilities. An exemplified treatment of ascorbic acid to improve solubility prediction

Context

Solubility prediction based on the general solubility equation (GSE) rests on reliable values for the isobaric heat capacity difference ΔC_p,1 of the solid solute. Usually, this value is estimated with either zero or the melting entropy ΔS₁(T_m,1) or, in few cases, is extrapolated from data of thermally stable melts of the solute. This causes uncertainties in the prediction.

Objective

To improve prediction accuracy a simple regression method is proposed that determines ΔC_p,1 from measured solubilities.

Materials and methods

Published experimental solubilities in neat organic solvents at 298 K of a model compound (L-(+)-ascorbic acid (LAA)) have been regressed using the GSE together with the Hansen parameter model for the activity coefficient.

Results and discussion

Regression yielded ΔC_p,1 = 238 J∙mol⁻¹∙K⁻¹ which agrees well with cross-validation results and is consistent with estimates from various group contribution methods. It was found that prediction accuracy improved in the order of increasing ΔC_p,1, that is, from 0, via 91 (=ΔS₁(T_m,1)) to 238 J∙mol⁻¹∙K⁻¹. It could be shown that mole fraction solubility of LAA can be forecast this way with an accuracy within current inter-laboratory variation.

Conclusion

The proposed method shows a general way to improve prediction accuracy of activity coefficient based solubility models by determining ΔC_p,1 without resorting to common assumptions. The method is universally applicable and easy to implement.