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ION–ION INTERACTIONS 257

and

What is the significance of these quantities and It is obvious they are all
average quantities—the mean chemical potential the mean standard chemical
potential the mean ionic mole fraction and the mean ionic-activity coefficient
In the case of and the arithmetic mean (half the sum) is taken because free
energies are additive, but in the case of and the geometric mean (the square root
of the product) is taken because the effects of mole fraction and activity coefficient on
free energy are multiplicative.
In this notation, Eq. (3.68) for the average contribution of a mole of ions to the
free energy of the system becomes

since a mole of ions is produced by the dissolution of half a mole of salt. In other words,
is half the chemical potential of the salt. 9

Thus, a clear connection has been set up between observed free-energy changes
consequent upon the change from a state in which the two ionic species of a salt
are infinitely far apart to a state corresponding to the given concentration and its mean
ionic-activitycoefficient Hence the value of is experimentally measurable. What
can be obtained from is the product of the individual ionic-activity coefficients [Eq.
(3.72)]. The theoretical approach must be to calculate the activity coefficients and
for the positive and negative ions [Eq. (3.60)] and combine them through Eq. (3.72)
into a mean ionic-activity coefficient which can be compared with the easily
experimentally derived mean ionic-activity coefficient.

3.4.5. Conversion of Theoretical Activity-Coefficient Expressions into
a Testable Form
Individual ionic-activity coefficients are experimentally inaccessible (Section
3.4.3); hence, it is necessary to relate the theoretical individual activity coefficient

9
The symbol should not be taken to mean that molecules of MA exist in the solution; is the observed
free-energy change of the system resulting from the dissolution of a mole of electrolyte.