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ION–SOLVENT INTERACTIONS 127
The second term in the right-hand side of Eq. (2.86) is the entropy of the ion in the gas
phase and the first term represents the total entropy change caused upon the entry of
the ion into the solution. will be given as
where is the translational entropy of the ion, is the entropy of coordinated
water in the first shell around the ion, is the entropy of water in liquid water,
is Born-charging entropy, and are the entropy of solvationally
coordinated water and nonsolvationally coordinated water, respectively, near the ion,
and is the net entropy contribution of the structure-broken region around the
ion.
The substitution into Eq. (2.86) of the values of from Eqs. (2.87) and (2.88)
gives the entropy of hydration. Relevant terms will be evaluated next.
2.15.13.1. One uses the Sackur–Tetrode equation for the translational
entropy of a monatomic ion in the gas phase and it gives
where is the mass of the ion (Table 2.19).
2.15.13.2. The Born-charging entropy is given by
which at 298 K becomes
where and are in nanometers (Table 2.19).
2.15.13.3. The partition function corresponding to “translation” of a
particle in a liquid can be written as
