Page 318 - MODERN ELECTROCHEMISTRY

254 CHAPTER 3

Thus, the activity coefficient is a measure of the chemical-potential change arising
from ion–ion interactions. There are several well-established methods of experimen-
tally determining activity coefficients, and these methods are treated in adequate detail
in standard treatises (see Further Reading at the end of this section).
Now, according to the Debye–Hückel theory, the chemical-potential change
arising from ion–ion interactions has been shown to be given by

Hence, by combining Eqs. (3.51) and (3.58), the result is

Thus, the Debye–Hückel ionic-cloud model for ion–ion interactions has permitted a
theoretical calculation of activity coefficients resulting in Eq. (3.60).
The activity coefficient in Eq. (3.59) arises from the formula (3.57) for the
chemical potential, in which the concentration of the species i is expressed in mole
fraction units One can also express the concentration in moles per liter (1 liter = 1
of solution (molarity) or in moles per kilogram of solvent (molality). Thus,
alternative formulas for the chemical potential of a species i in an ideal solution read

and

where and are the molarity and molality of the species i, respectively, and
and are the corresponding standard chemical potentials.
When the concentration of the ionic species in a real solution is expressed as a
molarity or a molality there are corresponding activity coefficients and and
corresponding expressions for

and