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ION–SOLVENT INTERACTIONS 49

value is too high because it includes the free space in liquid water. The lower value is
too low, because it neglects the volume needed to cover some water movements in the
liquid. The mean, 181 ± 13 pm, is a regrettably imprecise figure for such an important
quantity, but, as can be understood, it all depends upon what one takes into account.
The dipole moment of water in the gas phase is well known as 1.87 D but is 2.42
D in water at 298 K. The reason for the difference is that in liquid water there is
electrostatic pull on a given water molecule from the surrounding ones, and this
lengthens the distance in the dipoles (Fig. 2.7).

2.4.3. The lon–Dipole Model for Ion–Solvent Interactions

The preceding description of the solvent surrounding an ion was used as the basis
of a structural treatment of ion–solvent interactions initiated by Bernal and Fowler
(1933). Their paper is a seminal one for much else in the structural picture of hydration
(Section 2.4).
Bernal and Fowler thought of the changes of free energy during solvation as being
largely electrostatic in nature. In their picture, the passage of an ion began in the gas
phase, and here they took (for most of their calculations) the ions to have a zero
potential energy of interaction. Transferring an ion mentally to the interior of the
solvent, they thought this to be associated with three energy changes:

1. The ion–dipole interaction caused by the ion’s attracting water dipoles in the
first layer around the ion (ion–dipole interaction). (cf. Appendix 2.2)
2. Then there would be the energy needed to break up the water structure, which
occurs when ions enter it.
3. There would be a further allowance for the ion–water interactions “further out”
from the first layer to the rest of the solvent surrounding the ion. Such an
interaction might be thought to be relatively small, not only because of the
increasing distance but because of the increasing dielectric constant; small
(near to 6) near the ion but rapidly attaining the value of about 80 (at 25 °C),
as near as 1000 pm from the ion. Both these factors would diminish the
individual ion–dipole interaction energy.

Bernal and Fowler’s calculation remains famous because it grappled for the first
time with the structure of water and with ion–solvent interactions on a molecular basis.
Better theories have been developed, but most have their roots in the Bernal and Fowler
work of 1933.
The modern developments of solvation theory will not be discussed at this point
because nearly all the tools for investigating the ion–solvent interaction have become
available since 1933. One has to see some of the information they have provided before
ion–solvent interactions can be worked out in a more quantitative way.