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ION–SOLVENT INTERACTIONS 217

between the dipole moment of the central molecule and that of its bonded
neighbors as 1/3. (Contractor)
33. Water often comes underextremely strong electric fields as, e.g., in the solvation
of ions. By considering the total H-bond energy of water, calculate the electric
field strength that will break up H-bonded water. At what field strength would
liquid water dissociate, and to what?

34. An IR spectrum has a band at a wavenumber of What are the
wavelength and frequency of the corresponding bond? If the spectrum originates
from water, calculate the force constant between O and H.
35. From the data in the text, the self-diffusion coefficients of certain ions (e.g.,
and are known. The diffusion coefficient is related to the rate constant for
diffusion by the equation What kind of value for l (jump distance) would
you think reasonable? With the known values for D (see text), calculate the time
the anion resides in one place.

36. The effect of electrolytes on the solubility of nonelectrolytes is generally to
decrease the solubility of the nonelectrolyte (salting-out). Taking as the
nonelectrolyte and the relevant solubility data from the text, obtain Setchenow’s
constant for HC1 and Comment on the great difference.

PROBLEMS

1. Use the data of Table 2.8 to calculate the mean activity coefficient of a 5 M NaCI
solution, assuming the total hydration number at this high concentration is <3.
Values for A and B of the Debye–Hückel equation can be recovered from the
text.

2. Define wavenumber and explain why ions of a small radius tend to give higher
librative frequencies in their IR spectra in solution. Why do hydration numbers
obtained from spectroscopic data tend to be lower than those from nonspectro-
scopic methods? Write down the expression for the coordination number of an
ion in terms of the distribution function for the O in the first shell with respect
to an ion. Draw typical plots of as a function of distance from an ion for
(a) a strongly hydrated and (b) a weakly hydrated ion, respectively.
3. Explain what is meant by the statement: “The relative heat of hydration of is
Halliwell and Nyburg’s value for the heat of hydration of
protons was Use this value to establish the absolute heat of
hydration of
4. Calculate the librative and vibrational contributions for the entropy of an
ion in dilute solutions assuming 6 water molecules in the first shell. Why is it