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48 CHAPTER 2

water is disturbed to varying degrees. The in-between water molecules, however, do
not partake of the translational motion of the ion. Finally, at a sufficient distance from
the ion, the water structure is unaffected by the ion and again displays the tetrahedrally
bonded networks characteristic of bulk water.
The three regions just described differ in their degree of sharpness. The primary
region (discussed in greater detail later), in which there are (at least for the smaller
cations) water molecules that share the translational motion of the ion, is a sharply
defined region.
In contrast, the secondary region, which stretches from the termination of the
primary region to the resumption of the normal bulk structure, cannot be sharply
defined; the bulk properties and structure are asymptotically approached.
These structural changes in the primary and secondary regions are generally
referred to as solvation (or as hydration when, as is usual, water is the solvent). Since
they result from interactions between the ion and the surrounding solvent, one often
uses the term “solvation” and “ion–solvent interactions” synonymously; the former is
the structural result of the latter.

2.4.2. Size and Dipole Moment of Water Molecules in Solution
In discussions of the radius of a molecule, the only well-defined, exact part of the
answer lies in the internuclear distances (e.g., between H and O for water), but this
distance comprises only part of the radius, albeit the main part. All other measures of
the radius of a molecule are affected by some aspect of the occupancy of space that is
connected with the packing of the molecule, which varies with circumstances.
In ice (where X-ray measurements of internuclear distances, d, are more exact
than those in the liquid), the O–O internuclear distance is accurately known: 280 pm.
The distance between the nucleus of oxygen and that of hydrogen (see a space-fitting
picture of water, Fig. 2.9) is 138 pm.
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The so-called van der Waals radius of H can be taken to be 52.8 pm (this is the
Bohr radius for the ground state of H). The van der Waals radius of O is ~115 pm and
from these values 168 pm is obtained for the radius of water.
Now, several other radii between ca. 140 and 193 pm can be obtained by equating
to certain volumes (e.g., the close-packed volume of water, or a volume based
on the molecular dimensions). Each of these radii is “applicable” as the circumstances
dictate.
Thus, the “radius of water” varies, according to the method used to estimate it,
between 168 (the model shown in Fig. 2.9) and 193 pm, which arises from measure-
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ments on the density of water (and the resulting molar volume of 18 cm ). The larger
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The phrase “van der Waals radius” arises as a distinction from “internuclear distance radii.” Thus, from
the van der Waals equation for the P-V relation in gases (an improvement on the simple gas law PV=nRT),
a quantity b can be found which refers to the space taken up out of the whole gas volume V by the molecules
themselves.