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ION–SOLVENT INTERACTIONS 83

molecules in a first shell was 5.85 and the lifetime of these waters was relatively long,
about Thus, because this time is much greater than that needed for a diffusive
movement the waters in the first shell are certainly a part of the hydration
number. By analogy with it seems likely that the total hydration number is greater
than this coordination number because of a second shell containing water with a
lifetime greater than s, which would then also qualify (because its lifetime greatly
exceeds a jump time) as contributing to a hydration number. Similar remarks apply to
but the lifetime of the inner shell is greater (about 6 × s) than that for ferrous
ions because of the stronger binding to water with ferric rather than ferrous ions.
The ion has a special place in the history of solvation because it was the first
ion for which the lifetime of the water in its hydration shell was measured. This work
was done by Hunt and Taube in 1957. The exchange of water between the hydration
shell and the surroundings was slow, so the change in the concentration of the isotope
could be measured. The lifetime found is 1.6 × s (about 6 months). There is
evidence of outer-sphere water, so the value for the total hydration water that travels
with the ion is much higher than the value of about 6 found for the first shell in
transition-metal ions.
The hydration number of the ion has been measured by a number of nonspec-
troscopic methods and a value of 5 ±1 represents the range of results. The difference
method of neutron diffraction gives 6 with reasonable consistency. The lifetime is 3
× s, so the value is clearly a hydration number (i.e., it is much greater than
s, so water travels with the ion).
An interesting result is obtained for Neutron diffraction work shows the value
to be 6, which is in strong disagreement with nonspectroscopic methods, which give
the much lower value of 1 or 2. However, light is at once thrown on what seems a
breach difficult to mend when the lifetime of the 6 waters around the is found to
be only 10 × s; this is on the borderline as viable for a dynamic hydration number.
It seems likely, then, that the moves on average without its hydration water,
because its lifetime is barely enough for the time needed for wares to travel
one jump distance. Thus, the 1 or 2 hydration numbers of other measurements is
understandable. It is possible to regard the 6 value as coordination water, but few of
the waters manage to stay with the ion when it moves from site to site.

2.11.4. To What Extent Do Raman Spectra Contribute to Knowledge of
the Solvation Shell?
Raman spectra have a more involved origin than do IR absorption spectra. They
concern the scattering of light. This is a subject that was studied in the nineteenth
century when Rayleigh showed that the elastic scattering of light (no absorption) was
proportional in intensity to where is the wavelength of the scattered light. In
conditions that pertain to the application of this formula, the photon is assumed to
“bounce” off the molecules it strikes with the same energy latterly as it had initially.