Note on the energy density in the solvent induced by a solute.

The question of how far the effect of the presence of a solute molecule propagates into the solvent is studied in a lattice model that had been used earlier to describe hydrophobic interactions. The local energy density in the model solvent is obtained as an explicit function of distance from the solute and is found to decay to its bulk-phase value with the same decay length as that of the solvent-mediated part of the potential of mean force between a pair of solute molecules. The integrated deviation of the energy density from its bulk-phase value is evaluated in Bethe-Guggenheim approximation and shown to be identical to the energy change accompanying the dissolution of the solute as obtained from the temperature dependence of its solubility.