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134 CHAPTER 2

(Table 2.19).
2.15.13.7. (Model C). In this model, the molecules in the SB region,
which are not H bonded to the first shell, are taken as unbonded, i.e., freely rotating
monomers. These molecules are assigned three translational and three rotational
degrees of freedom. The intramolecular bond stretching and bending modes are of
high frequencies and do not contribute to the entropy of an unbonded molecule.
One has to know the free volume available to the unbonded molecule, and
its temperature dependence, so that the translational entropy may be calculated. The
term may be found from sound velocity measurements [Eq. (2.96)]. If one takes
a number of unassociated liquids and plots their free volumes obtained from the
velocity of sound against their molar weights, an extrapolation through a molar weight
33
of 18 will give for a freely rotating monomer of water. A value of 0.2
for is obtained. The temperature dependence of is obtained from the
integration of the heat capacity

which gives

where is the heat capacity of the freely rotating monomers in the SB region,
is the number of degrees of freedom, and the term –1.2 is the integration constant.
has a value of (6/2)R arising from three translational and three rotational degrees
of freedom. Thus, from Eq. (2.126)

Using of 0.20 of –1.2 in the general equation
relating entropy to partition function,

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This is to be distinguished from the entropy of water in water for which, of course, free-volume values
are available directly from measurements of sound velocity.