Page 320 - MODERN ELECTROCHEMISTRY

256 CHAPTER 3

free energy associated with a change in salt concentration: (1) the contribution of the
positive ions and (2) the contribution of the negative ions.
Since neither the positive nor the negative ions can be added separately, the
individual contributions of the ionic species to the free energy of the system are
difficult to determine. Normally, one can only measure the activity coefficient of the
net electrolyte, i.e., of at least two ionic species together. It is necessary therefore to
establish a conceptual link between the activity coefficient of an electrolyte in solution
(thatquantity directly accessible to experiment) and that of only one of its ionic species
[not accessible to experiment, but calculable theoretically from Eq. (3.60)].

3.4.4. The Mean Ionic Activity Coefficient
Consider a uni-univalent electrolyte MA (e.g., NaCl). The chemical potential of
the ions is [Eq. (3.57)]

and the chemical potential of the ions is

Adding the two expressions, one obtains

What has been obtained here is the change in the free energy of the system due to the
addition of 2 moles of ions—1 mole of ions and 1 mole of ions—which are
contained in 1 mole of electroneutral salt MA.
Now, suppose that one is only interested in the average contribution to the free
energy of the system from 1 mole of both and ions. One has to divide Eq. (3.67)
by 2

At this stage, one can define several new quantities