Page 140 - MODERN ELECTROCHEMISTRY

80 CHAPTER 2

lifetime of water molecules is short, perhaps only s. For multicomponent systems
it is possible to have several internuclear distances and, correspondingly, a number of
distribution functions. By applying Eq. (2.26) to the data for such as that shown
in the diagram, one can find out how many water molecules are in the first shell, as in
the case of concentrated solutions (Fig. 2.22).
There are always water molecules located around a stationary ion and the structure
of these waters will be dominated by the field of the ion (rather than the pull back into
the structure of the water). This dominance is stronger the smaller the ion because the
ion–solvent interaction is inversely proportional to As the schematics of a typical
distribution function suggest, there may be a second layer in addition to the first shell
of solvent associated with the ion. In this layer the structure is not yet that of bulk
water, though such second solvation layers are usually more prominent with divalent
ions (they are even more so with 3+ and 4+ ions) and are not seen for univalent ions,
in the company of which hydration waters stay for very short times.
Now, the question is how to get information on the more subtle quantity, the
hydration numbers. Some confusion arises here, for in some research papers the
coordination number (the average number of ions in the first layer around the ion) is
also called the hydration number! However, in the physicochemical literature, this
latter term is restricted to those water molecules that spend at least one jump time with
the ion, so that when its dynamic properties are treated, the effective ionic radius seems
to be that of the ion plus one or more waters. A startling difference between co-ordi-
nation number and solvation number occurs when the ionic radius exceeds about 0.2
nm (Fig. 2.23a).
It is important, then, to find out the time that waters stay with the ion. Thus, one
can make an order-of-magnitude calculation for the jump time, by a method shown in
Section 4.2.17. It comes to approximately
One could conclude that if a water molecule stays with its ion for more than about
it has accompanied the ion in a jump. That is, during the time the water is
associated with the ion, it is likely to have made one move with the ion in its sporadic
random movements (and therefore counts as a hydration number rather than a static
21
or equilibrium coordination number). Figure shows the ratio of the solvation number
to the coordination number. The ratio is an important quantity

21
In the case of ions for which the ion–water binding is very strong (the transition-metal ions particularly),
the hydration number may be greater than the coordination number, because more than one shell of waters
moves with the ion and the hydration number will encompass all the water molecules that move with it,
while the coordination number refers to the ions in just the first shell.
However, with larger ions, which have weaker peripheral fields, there is less likelihood that a water
–10
molecule will stay for the time necessary to accomplish an ion movement (e.g., > 10 s). Thus, for larger
– +
ions like CI and large cations such as N(C 2H 5) 4 , the coordination number will be 6 or more, but the
hydration number may tend to be 0. The hydration number is a dynamic concept; the coordination number
is one of equilibrium: it does not depend on the lifetime of the water molecules in the shell but measures
their time-averaged value.