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144 CHAPTER 2
usually used in the calculation. It is interesting to note that the use of raw solvent
viscosities does, however, give values that agree (±30%) with the mean of the other
five or so nonspectroscopic approaches.
The use of hydration numbers calculated from the effect of ions on the dielectric
constant of ionic solutions was seen (Section 2.12.1) at first to be relatively free of
difficulties. However, the theory has become more sophisticated since the original
conception, and it has been realized that in all but quite dilute solutions, interionic
forces affect a straightforward interpretation of the relaxation time, making it impor-
tant to have sets of data over a wide range of frequencies—1 mHz to 1 GHz. The
methods of Yeager and Zana and Bockris and Saluja (Section 2.8.1), which use
compressibility measurements to obtain the sum, and the ionic vibration potentials to
get the difference, represent an approach to determining hydration number that has the
least number of reservations (although there are questions about the degree of residual
compressibility of the inner sheath).
Finally, there is the troubling matter that the spectroscopic methods of measure-
ment generally gave results as much as 50% lower (Table 2.10) than the values
obtained by the relatively concordant nonspectroscopic methods (compressibility,