Free Volume and Entropy in Condensed Systems II. Entropy of Vaporization in Liquids and the Pictorial Theory of the Liquid State

The results of the first paper of this series, and a generalization of a method due to Eyring, are used to obtain an expression for the free volume of a liquid, $V_f{\mathrm{=fb}}^3{g}^3{\mathrm{/h}}^3{n}^3{\mathrm{\times [RT/\Delta E}}_v{]}^3$ , and an equation for the entropy of vaporization. $\mathrm{\Delta S=R[}\ln V_g-\ln V_l-\ln \text{β+3}\ln \text{β+3}\ln \text{(ΔH/RT−1)]}$ . Here ${\mathrm{\beta =\gamma fb}}^3{g}^3{\mathrm{/h}}^3{n}^3$ , where γ measures the interference in the liquid with the internal motions (rotations, vibrations) of the molecule, and f, b, g, h, n are quantities which depend on the geometry of the liquid and the energetic and dynamic interaction of the molecules. The rule of Barclay and Butler, that the 25°C value of ΔS for various pure liquids has a rough linear relationship to the corresponding ΔH of vaporization, is shown to imply a general tendency for a liquid to have a smaller β the larger its ΔH of vaporization. In many cases this means a smaller γ, resulting from increased interference with rotation of the molecules in the liquid. Pitzer's perfect liquid has a value β = 16, sensibly independent of ΔH. This is taken to mean that in such a liquid as benzene or carbon tetrachloride (β≈6) the interference with free rotation is considerable. For CS₂ there is evidence that the intermolecular force field differs from ``normal,'' and the difference in potential function between liquid metals and normal liquids shows up strongly. Accepting the value β = 16 found for the ideal liquid as a norm, it is proposed to call R ln (16/β) for any liquid the hypothetical entropy defect (HED) and interpret it as the amount by which the entropy of the liquid (referred to the same substance as a perfect gas) is less than that of the ideal liquid in the ``corresponding'' state.