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ION–SOLVENT INTERACTIONS 141

However, the term primary salvation number, although it has apparently a clear
definition (see above), is open to further discussion. Thus it may be that a water
molecule loses its degree of translational freedom and travels with a given ion as it
moves from site to site. The question is, how long does it have to remain the ion’s
consort to count in the definition? There is no difficulty in accepting “travels with the
ion in its movements” when the lifetime of the complex is clearly greater than that
needed for registration in some experimental method. Thus, a relatively long lifetime,
–6
more than 10 s, say, would find a strong positive vote on the question of whether
such an ion counts primarily as a hydrated molecule. However, it seems better to accept
the limit of one jump as the necessary qualification. Thus, if the lifetime of water
molecules in contact with an ion is only enough for one jump, it still means that the
ion always has water molecules with it on jumping, and the number of these is
reasonably taken as the primary hydration (solvation) number.
Another matter concerns the time of “reaction” between a set of water molecules
after an ion has just pushed its way into the middle of them. Thus, if the lifetime of
molecules in the primary solvation shell is sufficiently short, there must be some jumps
in which the ion is bare or at least only minimally clothed. How is the hydration number
affected by the time needed for the solvent molecules buried in the solvent layer to
break out of that attachment and rotate so that their dipoles are oriented toward the ion
to maximize the energy of interaction

2.16.2. Dynamic Properties of Water and Their Effect on Hydration
Numbers
A critical question one might ask in obtaining a closer concept of the primary
hydration number pertains to the average time during which a water molecule stays
with an ion during its movements (cf. Fig. 2.23). One can begin by repeating yet again
the distinction between coordination number and primary hydration water. The
coordination number is the number of particles in contact with the ion (independently
of whether any of the molecules concerned move with the ion and independently of
how they orient in respect to it). It is a matter of geometry, space filling, etc. Now,
when an ion moves from one site to the next, not all of the water molecules coordinating
it at the beginning of the movement cling to it.
One can see at once that the free volume for coordinating waters is

If water molecules fill this space without regard to directed valences and without
accounting for repulsion between head-to-head dipoles, the coordination number
could be obtained by dividing the above number by the volume of one water molecule.
For = 70, 100, 150, and 200 pm, the calculated coordination numbers obtained
on such a basis are shown in Tables 2.21 and 2.22. Real values should be less, because
of lateral repulsion of molecules.