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, $Vf=fb3g3/h3n3\xd7[RT/\Delta Ev]3$, and an equation for the entropy of vaporization. $\Delta S=R[ln Vg\u2212lnVl\u2212ln \beta +3ln\beta +3ln(\Delta H/RT\u22121)]$. Here $\beta =\gamma fb3g3/h3n3$, 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 Δ*S* for various pure liquids has a rough linear relationship to the corresponding Δ*H* of vaporization, is shown to imply a general tendency for a liquid to have a smaller β the larger its Δ*H* 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 Δ*H*. 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 CS_{2} 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.

## REFERENCES

*Statistical Thermodynamics*(The Macmillan Company, New York, 1940), 800, p. 319, discuss the commonly accepted distinction between normal and associated liquids. We shall use the words to refer to the substances to which these authors apply them, but shall find it necessary to reject their hypothesis that molecular rotations are unhindered in the liquids they consider typically normal.

*Solubility*(New York, 1936), second edition, p. 99.

*n*, and therefore a smaller one for

*g*and a larger one for $(\u2202d/\u2202l)T.$

*Solubility*(New York, 1936), second edition, p. 102.

*T*is to be 25 °C, $Tc$ cannot be higher than about 533 °K without making ϑ so low $(<0.56)$ that the ideal liquid would freeze. On the other hand, this makes $\Delta H$ only some 5600 cal./mole. The fact that $\Delta H\u2009=\u20095600$ is the highest value for which β can be calculated for an ideal liquid at 25 °C detracts somewhat from the comparison here made. The meaning of the calculation, however, is that β is sensibly independent of temperature for these liquids, which justifies using the value 16.0 as a “norm” for any liquid at any temperature. Incidentally, it appears that most ordinary liquids, with $\Delta H\u2a7e6000\u2009cal./mole,$ would be solids at room temperature if they behaved as ideal substances. The reason that they are liquids at room temperature, then, is that in melting they gain entropy from sources which are not available to the ideal liquid—orientations and bendings. It is very striking that hexamethyl ethane, which is so bunched up and symmetrical as to be of nearly “ideal” shape, melts at about 102 °C (G. Egloff,

*The Physical Constants of Hydrocarbons*(Reinhold Publishing Corporation, New York, 1939), p. 57), compared with melting points well below 0 °C for all the other open chain hydrocarbons of $C8$ or below. The high melting points of benzene and cyclohexane also support this point of view.

*T*in real liquids, we may remark that (14) leads to the relation

*T*in qualitative agreement with our physical picture. Numerically $\u2202\u2009ln\u2009\beta /\u2202\u2009ln\u2009T$ at 25 °C is predicted to be positive for $\Delta CP$ more negative than about $\u22127.0$ at $\Delta H\u2009=\u20097200,$ or about $\u22126.0$ at $\Delta H\u2009=\u200910,800.$