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ION–ION INTERACTIONS 255

3.4.3. The Activity Coefficient of a Single Ionic Species Cannot Be
Measured

Before the activity coefficients calculated on the basis of the Debye–Hückel
model can be compared with experiment, there arises a problem similar to one faced
in the discussion of ion–solvent interactions (Chapter 2). There, it was realized the
heat of hydration of an individual ionic species could not be measured because such
a measurement would involve the transfer of ions of only one species into a solvent
instead of ions of two species with equal and opposite charges. Even if such a transfer
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were physically possible, it would result in a charged solution and therefore an extra,
undesired interaction between the ions and the electrified solution. The only way out
was to transfer a neutral electrolyte (an equal number of positive and negative ions)
into the solvent, but this meant that one could only measure the heat of interactions of
a salt with the solvent and this experimental quantity could not be separated into the
individual ionic heats of hydration.
Here, in the case of ion–ion interactions, the desired quantity is the activity
coefficient which depends through Eq. (3.57) on This means that one seeks
the free-energy change of an ionic solution per mole of ions of a single species i. To
measure this quantity, one would have a problem similar to that experienced with
ion–solvent interactions, namely, the measurement of the change in free energy of a
solution resulting from a change in the concentration of one ionic species only.
This change in free energy associated with the addition of one ionic species only
would include an undesired work term representing the electrical work of interaction
between the ionic species being added and the charged solution. To avoid free-energy
changes associated with interacting with a solution, it is necessary that after a change
in the concentration of the ionic species, the electrolytic solution should end up
uncharged and electroneutral. This aim is easily accomplished by adding an elec-
troneutral electrolyte containing the ionic species i. Thus, the concentration of sodium
ions can be altered by adding sodium chloride. The solvent, water, maintains its
electroneutrality when the uncharged ionic lattice (containing two ionic species of
opposite charge) is dissolved in it.
When ionic lattices, i.e., salts, are dissolved instead of individual ionic species,
one eliminates the problem of ending up with charged solutions but another problem
emerges. If one increases the concentration of sodium ions by adding the salt sodium
chloride, one has perforce to produce a simultaneous increase in the concentration of
chloride ions. This means, however, that there are two contributions to the change in

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The solution may not be initially charged but will become so once an ionic species is added to it.
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The use of the symbol for the activity coefficients when the concentration is expressed in molarities and
molalities should be noted. When the concentration is expressed as a mole fraction, has been used here.
For dilute solutions, the numerical values of activity coefficients for these different systems of units are
almost the same.