Handbook of Solvents - George Wypych - ChemTech - Ventech!

13.1 Solvent effects on chemical reactivity 757
Summed up, it appears that any concept to be used in a realistic study of water should
have as a fundamental ingredient the competition between expanded, less dense structures,
and compressed, more dense ones. Thus, the outer structure in the total potential of water
should be characterized by a double minimum: open tetrahedral structure with a second-neighbor
O�O distance of 4.5 Å and a bent H-bond structure with an O�O
non-H-bonded distance of about 3.4 Å. Actually, according to a quite recent theoretical
study, all of the anomalous properties of water are qualitatively explainable by the existence
of two competing equilibrium values for the interparticle distance. 78 Along these lines the
traditional point of view as to the structure of water is dramatically upset. Beyond that, also
the classical description of the hydrogen bond needs revision. In contrast to a purely electrostatic
bonding, quite recent Compton X-ray scattering studies have demonstrated that the
hydrogen bonds in ice have substantial covalent character, 79 as already suggested by
Pauling in the 1930s. 80 In overall terms, a hydrogen bond is comprised of electrostatic, dispersion,
charge-transfer, and steric repulsion interactions. Similarly, there are charge-transfer
interactions between biological complexes and water 81 that could have a significant
impact on the understanding of biomolecules in aqueous solution.
Finally, we return to the physical meaning of the large difference, for the protic solvents,
between the cohesive energy density ε c and the internal pressure P i, quoted in section
13.1.3. For water this difference is highest with the factor ε c/P i equal to 15.3. At first glance
this would seem explainable in the framework of the mixture model if H bonding is insensitive
to a small volume expansion. However, one should have in mind the whole pattern of
the relationship between the two quantities. Thus, ε c -P iis negative for nonpolar liquids, relatively
small (positive or negative) for polar non-associated liquids, and strongly positive
for H-bonded liquids. A more rigorous treatment 41 using the relations, P i =(∂U/∂V) T =T(∂P/
∂T) V - P and the thermodynamic identity (∂S/∂V) T =(∂P/∂T) V reveals that the relationship is
not as simple and may be represented by the following equation with dispersion detached
from the other types of association,
disp
εc Pi P ρ ass ρ ( ∂ ass ∂ρ)
T
RT
V Z
⎡ U ⎤
2
− = − ⎢ 0 + ⎥ − U + T S / [13.1.14]
⎣ RT ⎦
where:
P external pressure
V liquid volume
Z0 compressibility factor due to intermolecular repulsion
Udisp potential of dispersion
Uass potential of association excluding dispersion
ρ liquid number density
Sass entropy of association excluding dispersion
With the aid of this equation we readily understand the different ranges of εc -Pifound for the different solvent classes. Thus, for the nonpolar liquids, the last two terms are negligible,
and for the usual values, Zo ≈10, -Udisp/RT ≈8, and V ≈150 cm 3 , we obtain the typical
order of εc -Pi≈-(300 - 400) atm (equal to -(30 - 40) J cm -3 , since1Jcm -3 ≡9.875 atm). For
moderately polar liquids, only the last term remains small, while the internal energy of
dipolar forces is already appreciable -ρUpolar ≈(200-500) atm giving the usual magnitude of
εc -Pi. For H-bonded liquids, ultimately, the last term turns out to dominate reflecting the
large increase in entropy of a net of H-bonds upon a small decrease in liquid density.