Page 266 - MODERN ELECTROCHEMISTRY

202 CHAPTER 2

Most of the data that one gets from the experimental point of view of hydration
concerns the net effect of all the ions in the electrolytes, and it is necessary to pull out
the quantities corresponding to each ion separately. This is tricky but possible. For
example, one can couple a certain anion with a series of cations of increasing size and
extrapolate a plot in such a manner that the effect of the cation becomes negligible and
that of the anion is isolated. Then, the individual value for that anion can be used to
obtain individual values for any cations that can form salts with this anion.
Apart from neutron diffraction, what other method distinguishes between the
static or equilibrium coordination number and the dynamic solvation number, the
number of solvent molecules that travel with an ion when it moves? One method is to
obtain the sum of the solvation numbers for both cation and anion by using a
compressibility approach, assuming that the compressibility of the primary solvation
shell is small or negligible, then using the vibration potential approach of Debye to
obtain the difference in mass of the two solvated ions. From these two measurements
it is possible to get the individual ionic solvation numbers with some degree of
reliability.
Another approach that can help in getting hydration numbers is the study of
dielectric constants—both the static dielectric constants and the dielectric constant as
it depends on frequency. Such measurements give a large amount of information about
the surrounds of the ion but a good deal more has to be done before the theoretical
interpretation can bear the weight of clear structural conclusions. Density, mobility,
and entropy measurements may also be informative.
The material so far has all come from discussions of methods of examining
hydration and solvation in solutions. It is now good to turn to a simpler field, the study
of which began much later—hydration of the gas phase. It was not until high-pressure
mass spectroscopy became available that such studies could be easily made. If we had
had these studies 50 years ago, it would have been much easier to interpret the values
obtained in solution. Thus, the numbers we get from the unambiguous gas-phase
results are close to results for the first shell of water around ions in solution, and
knowledge of this, and the energies that go with it, helps us greatly in building models
in solution.
The models assume that the energies are entirely electrostatic and go about
calculation in terms of ion-dipole forces for the first layer, together with correction
for the quadrupole properties of water, and for the extra dipole that the ion induces in
the water. There are two more steps. One is to take into account the interaction of the ion
with distant water molecules, which we do by means of the Born equation, and then finally
we take into account the structure-breaking effects of the ions on the surrounding solvent.
The agreement between theory and experiment is good and this applies (though somewhat
less well) to the corresponding calculation of the entropies of hydration.
A special case, but one of seminal importance, is the heat of hydration of the
proton because so much depends upon it. A rather clever method was set out many
years ago by Halliwell and Nyburg and although their approach has been reexamined