Hydration entropy change from the hard sphere model

Abstract

The gas to liquid transfer entropy change for a pure non-polar liquid can be calculated quite accurately using a hard sphere model that obeys the Carnahan–Starling equation of state. The same procedure fails to produce a reasonable value for hydrogen bonding liquids such as water, methanol and ethanol. However, the size of the molecules increases when the hydrogen bonds are turned off to produce the hard sphere system and the volume packing density rises. We show here that the hard sphere system that has this increased packing density reproduces the experimental transfer entropy values rather well. The gas to water transfer entropy values for small non-polar hydrocarbons is also not reproduced by a hard sphere model, whether one uses the normal (2.8 Å diameter) or the increased (3.2 Å) size for water. At least part of the reason that the hard sphere model with 2.8 Å size water produces too small entropy change is that the size of water is too small for a system without hydrogen bonds. The reason that the 3.2 Å model also produces too small entropy values is that this is an overly crowded system and that the free volume introduced in the system by the addition of a solute molecule produces too much of a relief to this crowding. A hard sphere model, in which the free volume increase is limited by requiring that the average surface-to-surface distance between the solute and water molecules is the same as that between the increased-size water molecules, does approximately reproduce the experimental hydration entropy values.