Intermolecular Forces and Energies of Vaporization of Liquids

By using a ``smoothed potential'' model for the liquid state and assuming isotropic, homogeneous expansion with temperature which involves no change in coordination, it is shown that it is possible to reduce the expression for the configurational energy of the liquid to a function of a single parameter, the density. If the intermolecular forces can be put into a polynomial form then the expression for the configurational energy can be factored, resulting in an algebraic equation of the form: $$E_c{\mathrm{=-B}}_1{D}^2{\mathrm{-B}}_2{D}^{\text{8/3}}{\mathrm{-B}}_3{D}^{\text{−10/3}}{\mathrm{+B}}_4{D}^4$$ in which D is the molar density and the B's are constants independent of temperature. For the distances occurring in liquids, the last three terms can be either dropped or combined with the first, leaving as an approximation: E<sub>c</sub>=AD<sup>x</sup>/3. The energy of vaporization is given by: E<sub>v</sub>=A(D<sub>1</sub><sup>x/3</sup>—D<sub>g</sub><sup>x</sup>/3 ). Values calculated from this last equation show excellent agreement with experimental values for a large number of both normal and ``abnormal'' liquids. Values of x=5 or 6 both work, the latter being better up to the critical temperature.