Handbook of Solvents - George Wypych - ChemTech - Ventech!

762 Roland Schmid
very recent paper, a unified physical picture of hydrophobicity based on both the hydrogen
bonding of water and the hard-core effect has been put forward. 120 Hydrophobicity features
an interplay of several factors.
The structure of liquids
A topic of abiding interest is the issue of characterizing the order in liquids which may be
defined as the entropy deficit due to preferential orientations of molecular multipoles relative
to random orientations (orientational order) and nonuniformly directed intermolecular
forces (positional order). Phenomenologically, two criteria are often claimed to be relevant
for deciding whether or not a liquid is to be viewed as ordered: the Trouton entropy of vaporization
or Trouton quotient and the Kirkwood correlation factor gK. 121 Strictly speaking,
however, both are of limited relevance to the issue.
The Trouton quotient is related to structure of the liquids only at their respective boiling
points, of course, which may markedly differ from their structures at room temperature.
This should be realized especially for the high-boiling liquids. As these include the highly
dipolar liquids such as HMPA, DMSO, and PC, the effect of dipole orientation to produce
order in the neat liquids remains obscure. All that can be gleaned from the approximate constancy
of the Trouton quotient for all sorts of aprotic solvents is that at the boiling point the
entropy of attractions becomes unimportant relative to the entropy of unpacking liquid molecules,
that is repulsions. 122 In terms of the general concept of separating the interaction potential
into additive contributions of repulsion and attraction, the vaporization entropy can
be expressed by
Δ H / T = Δ S = ΔS
− S
[13.1.20]
v b v o att
where:
ΔvH vaporization enthalpy at the boiling point Tb ΔSo entropy of depacking hard spheres = entropy of repulsion
Satt entropy of attraction
ΔSo can be separated into the entropy fo(η) of depacking hard spheres to an ideal gas at the
liquid volume V, and the entropy of volume expansion to Vg = RT/P,
() ( )
ΔS / R = f η + ln V / V
[13.1.21]
o o g
Further, f o(η) can be derived from the famous Charnahan-Starling equation as 43
2 () = ( 4 −3 ) ( 1−
)
2
fo η η η / η
[13.1.22]
It can in fact be shown that, for the nonpolar liquids, Δ vS/R is approximately equal to
f o(η). 122 Along these lines, Trouton’s rule is traced to two facts: (i) The entropy of depacking
is essentially constant, a typical value being ΔS o/R ≈9.65, due to the small range of packing
densities encompassed. In addition, the entropies of HS depacking and of volume change
vary in a roughly compensatory manner. (ii) The entropy of attraction is insignificant for all
the aprotics. Only for the protics the contributions of S att may not be neglected. Actually the
differences between Δ vS and ΔS o reflect largely the entropy of hydrogen bonding. However,
the application of the eqns [13.1.20] to [13.1.22] to room temperature data reveals, in con-