Intermolecular Forces in Liquids

The volume energy of liquids, $E_v$, is formulated, as in the Born and Landé theory of the lattice energy of crystals, in terms of attractive and repulsive forces varying with inverse powers of the distance, or volume, giving $E_v=\frac{-a}{V^m}\left[1-\frac{n}{m}{\left(\frac{V_0}{V}\right)}^{n^{-}m}\right],$ where $m$ and $n$ are, respectively, the exponents of attraction and repulsion, $a$ the attraction constant and $V$ the volume and $V_0$ the volume at absolute zero, or when the external pressure just balances the thermal pressure, $T{\left(\frac{\partial P}{\partial T}\right)}_v$. The theory is tested by the use of values of ${\left(\frac{\partial E}{\partial V}\right)}_T$ calculated by the aid of the thermodynamic equation of state from experimental values of ${\left(\frac{\partial P}{\partial T}\right)}_v$, also by use of the energy of vaporization. It is found, (1) that values of $V_0$ derived from highly compressed ether and mercury agree well with those derived from density at low temperatures; (2) that $m$ varies from 1 for non-polar molecules, $m=1\mathrm{}$ corresponding to the attraction between quadrupoles, to much less than 1 as polarity increases, $m=\frac{1}{3}$ corresponding to dipole attraction; (3) that at ordinary temperatures and pressures the repulsive term is small for the liquids studied, except mercury, indicating a large value of $n$ and that the attractive pressure is balanced by the thermal pressure; (4) that taking $a={3180.10}^4$, $m=1\mathrm{}$, $n=9\mathrm{}$ and $V_0=79\mathrm{}$ it is possible to calculate ${\left(\frac{\partial E}{\partial V}\right)}_T$ for ether from a molal volume of 79 cc, in the liquid at 12,000 atmospheres, to a volume of 4000 cc in the vapor. It is suggested that the thermal pressure should be introduced into the calculation of lattice energies by the methods of Born and Landé and Pauling.