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ION–SOLVENT INTERACTIONS 75

From an interpretation of peaks in the far IR spectral region, one can obtain
knowledge of hindered translations among water molecules in ionic solutions. Some-
what surprisingly, the force constants associated with such movements are lowered by
the presence of ions because ions free some water molecules from the surrounding
solvent structures. Thus, force constants are given by where U is the potential
energy of particle–particle interaction. The librative frequencies (Section 2.4) of water
also show up in this region and decrease in the order KF > KC1 > KBr > KI. Thus, ions
of smaller radii (higher field and force) give higher librative frequencies, as expected
because of the equation

where k is the force constant (a function of the energy of ion–water interaction) and
is the reduced mass of the vibrating entities.
James and Armitage have analyzed the far IR spectra of some ionic solutions and
attempted to distinguish waters in the primary hydration shell (those waters that stay
with the ion as it moves) from waters (“secondary hydration”) which, although affected
by the ion, are not attracted by it enough to move with it.
Studies that provide more illumination arise from IR measurements in the work
of Bergstrom and Lindgren (Table 2.10). They have made IR studies of solutions
containing and which are transition-metal ions, and also certain
lanthanides, and at a concentration of 0.2–0.3 mol They
find that the O–D stretching vibrations in HOD (2427 in the absence of ions) are
affected by the presence of these substances (Fig. 2.20). Both the transition-metal ions
and the lanthanide elements perturb the HOD molecule in a similar way. However,
even the trivalent lanthanide ions (for which stronger effects are expected because of
the higher ionic charge) only perturb the nearest-neighbor water molecules (the first