On the size dependence of hydrophobic hydration

The solubility in water of noble gases, at room temperature, increases with their size, whereas that of gaseous aliphatic hydrocarbons decreases on increasing their size. This puzzling experimental observation is a unique feature of water as solvent. No real explanation of the phenomenon exists, even though it has been suggested that it is evidence of clathrate-type structure formation around nonpolar molecules. In this paper, we show that the experimental data can be reproduced well by means of Lee's theory of hydrophobic hydration. A fundamental ingredient of this theory is the demonstration that the purely structural reorganization of H-bonds in the hydration shell of a nonpolar solute is a compensating process. The solubility is determined by the balance of two contrasting factors: the excluded volume entropy change due to cavity creation in the solvent, and the direct solute-solvent van der Waals interactions. The work of cavity creation is dominant, determining the poor solubility of nonpolar compounds in water. However, for noble gases, on increasing the hard-sphere diameter, the van der Waals interactions increase, in absolute value, more rapidly than the work of cavity creation, enhancing the solubility. On the contrary, for aliphatic hydrocarbons, on increasing the hard-sphere diameter the van der Waals interactions increase, in absolute value, less rapidly than the work of cavity creation, lowering the solubility. The experimental data of hydration Gibbs energies, therefore, can be accounted for without invoking an enhancement of water structure in the hydration shell of a nonpolar solute.