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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,
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