Cohesion Energies of Ideal Solutions

If the forces between molecules are of the van der Waals type, it can be shown that the internal pressure, Pi, is given by the change in energy with volume at constant temperature. 

Although the terms cohesion energy density and internal pressure refer to the same characteristic of a liquid, they are not identical. The cohesion energy density (Ec/V) is equivalent to the energy of vaporization per mole of hquid and it is calculated in that way. The internal pressure, P , is given by 

For a mixture of components 1 and 2, the cohesion energy for the mixture, Ecm, wiU be given by 

This relationship is often referred to as the Bertholet geometric mean. If no change in volume occurs when the mixture is formed. 

The cohesion energy of the mixture, Ecm, is given in terms of the mole fractions (X) and cohesion energies of the two components by 

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