Page 153 - MODERN ELECTROCHEMISTRY

ION–SOLVENT INTERACTIONS 93

zero. From this (for details of how to do this, see Conway, 1982), it is possible to find
the of the solution as a function of frequency (and hence the relaxation time of water
as a function of the presence of ions). This quantity clearly depends on how many
water molecules have been withdrawn from the free solvent, where they can relax, and
how many are attached to ions, where they cannot. It therefore leads to primary
hydration numbers
Studies of the dielectric constant of solutions and the relaxation times of water in
the presence of ions have been refined since the 1980’s and indeed difficulties do turn
up if one looks at data from measurements over large frequency ranges. The variation
of the dielectric constant with frequency has been studied particularly by Winsor and
Cole, who used the Fourier transform of time domain reflectometry to obtain dielectric
constants of aqueous solutions and the relaxation times in them. Their frequency
ranges from over 50 MHz to 9 GHz.
The problem of making significant dielectric constant measurements in these
ranges is to separate the relaxation effects of the ionic atmosphere around the ions
(Chapter 3) from effects connected with ion-solvent interactions. At low concentra-
tions the former effects are less important, but at such concentra-
tions the decrements in the dielectric constant are too small for accurate measurement.
Theoretical work makes it clear that a series of measurements over a large range of
frequencies (e.g., 1 Hz to 1 GHz) are needed to separate dielectric effects from those
due to relaxation of the ionic atmosphere.
Nevertheless, in spite of these warnings, values of dielectric decrements have a
sufficiently clear basis to allow their use in discussing the elusive solvation numbers.

2.12.3. Conclusion
Measurements of dielectric constants of solutions allow the deduction of not only
how many waters are taken up and held irrotationally by ions, but also how the ions
affect the frequency of the movements of molecules near them. This will help a person
interested in electrostatic effects calculate the local pressure near an ion (Section
2.22.1).

Further Reading

Seminal
1. J. J. Webb, “Electric Field near an Ion in Solution,” J. Am. Chem. Soc. 48: 2589 (1926).
2. J. B. Hasted, D. M. Ritson, and C. H. Collie, “The Dielectric Constants of Ionic Solutions,”
J. Chem. Phys. 16: 1 (1948).
3. F. Booth, “Dielectric Constant As a Function of the Applied Field,” J. Chem. Phys. 19:
1451 (1951).
4. D. C. Grahame, “Electric Field and Dielectric Constant near an Ion,” J. Phys. Chem. 11:
1054(1951).