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ION–SOLVENT INTERACTIONS 51

A third group involves the spectroscopic approaches. These are discussed in
Section 2.11.
Finally, computational approaches (including the Monte Carlo and molecular
dynamic approaches) are of increasing importance because of the ease with which
computers perform calculations that earlier would have taken impractically long times.

2.5.2. Thermodynamic Approaches: Heats of Solvation

The definition of the heat of solvation of a salt is the change in heat content per
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mole for the imaginary transition of the ions of the salt (sufficiently far apart so that
they have negligible energies of interaction between them) from the gas phase into the
dissolved state in solution. Again, a simplification is made: the values are usually stated
for dilute solutions, those in which the interaction energies between the ions are
negligible. Thus, the ion–solvent interaction is isolated.
The actual calorimetric measurement that is made in determining the heat of
hydration of the ions of a salt is not the heat of hydration itself, but the heat of its
dissolution of the salt in water or another solvent (Fajans and Johnson, 1942). Let this
be Then one can use the first law of thermodynamics to obtain the property
which it is desired to find, the heat of hydration. What kind of thought process could
lead to this quantity? It is imagined that the solid lattice of the ions concerned is broken
up and the ions vaporized to the gaseous state (heat of sublimation). Then one thinks
of the ions as being transferred from their positions far apart in the gas phase to the
dissolved state in dilute solution (heat of hydration). Finally, the cycle is mentally
completed by imagining the dissolved ion reconstituting the salt-lattice
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It is clear that by this roundabout or cyclical route the sum of all the
changes in the cycle should be equal to zero, for the initial state (the crystalline
salt) has been re-formed.
This process is sketched in Fig. 2.13.
Thus,

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It is an imaginary transition because we don’t know any actual way of taking two individual ions from the
gas phase and introducing them into a solution without passing through the potential difference, which
occurs across the surface of the solution. There is always a potential difference across an interphase, and
were ions actually to be transferred from the gas phase to the interior of a solution, the energy,
would add to the work one calculates by the indirect method outlined here. It’s possible to add this energy
of crossing the interphase to the heats of solution of Table 2.4 and the resultant values are consequently
called “real heats of solvation,” because they represent the actual value that would be obtained if one found
an experimental way to go from the vacuum through the interface into the solution.
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When, as here, an imaginary cycle is used to embrace as one of its steps a quantity not directly determinable,
the process used is called a “Born–Haber cycle.” The sum of all the heats in a cycle must be zero.