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ION–SOLVENT INTERACTIONS 55

where a is activity of the ion in solution and is the mean ionic activity of the
solution defined as
Thus, if one knows the mean activity (see Section 2.9.1) of the electrolyte for the
condition at which the solution is saturated and in equilibrium with the salt, one has
the standard free energy change of solution. To obtain the standard free energy of
solvation (hydration) from this, one has also to know the free energy of the salt lattice
at 298 K. This is easily obtainable (see any physicochemical text) if there are data on
the specific heat of the given salt as a function of temperature, so that the entropy of
the salt in its standard state can be determined in the usual way of integrating the
relation (where is specific heat) to obtain entropies. Knowing then the
standard free energy of solution and that of the salt lattice, one applies reasoning similar
to that used earlier for the heats [Eq. (2.3)]. One can thus obtain free energies of
hydration of salts. Knowing the and for the hydration process, one may
calculate the standard entropy of solvation of the salt from the well-known thermody-
namic equation Values of will be discussed further in Section
2.15.12, which covers the process of splitting up into its component parts for the
individual ions concerned.
Why should one bother with these thermodynamic quantities when the overall
aim of this chapter is to determine the structure of liquids near ions? The answer is the
same as it would be to the generalized question: What is the utility of thermodynamic
quantities? They are the quantities at the base of most physicochemical investigations.
They are fully real, no speculations or “estimates” are made on the way (at least as far
as the quantities for salts are concerned). Their numerical modeling is the challenge
that the theoretical approaches must face. However, such theoretical approaches must
assume some kind of structure in the solution and only a correct assumption is going
to lead to a theoretical result that agrees with experimental results. Thus, such
agreement indirectly indicates the structure of the molecules.
Finally, this section ends with a reminder that heats, entropies, and free energies
of hydration depend on concentration (Fig. 2.14) and that there are significant changes
in values at very low concentrations. It is the latter values that are the desired quantities
because at high concentrations the heats and free energies are influenced not only by
ion–solvent interactions (which is the objective of the venture) but also by interionic
forces, which are much in evidence (Chapter 3) at finite concentrations.

2.6. PARTIAL MOLAR VOLUMES OF IONS IN SOLUTION

2.6.1. Definition
The molar volume of a pure substance can be obtained from density measure-
ments, i.e., (molecular weight)/(molar volume). The volume contributed to a
solution by the addition of 1 mole of an ion is, however, more difficult to determine.
In fact, it has to be measured indirectly. This is because, upon entry into a solvent, the