Page 198 - Modern physical chemistry

190 Equilibria in Condensed Phases

Then a is chosen to yield the best weighted average fit to the preceding series. In place
of (8.81), we would then get
ifJatm = __ 1_ Z jeb . [8.86J
l+baj 4m,
And formula (8.83) would be replaced with

2 2
~Gatm = ___ l_Zj e b. [8.87J
l+baj 8m,

Parameter a is interpreted as the average distance of approach of the center of an
oppositely charged ion to the center of the given ion. Parameter a j may then be called
the effective diameter of the jth ion.

8.10 Debye-Hiickel Equations
From the energy needed to form an ionic atmosphere, a person can calculate the cor-
responding ionic activity coefficient.
The general form for the chemical potential of a constituent,

[8.88J
leads to the usual expression,

[8.89J

governing the equilibrium

aA+bB ( ) lL+mM, [8.90J

as we saw in equation (7.57). When concentrations of the solutes are expressed in molal-
ities, we have
[8.91 J

Then equation (8.88) becomes

Pj = pJ +RTlnmj +RTlny j. [8.92J
Dividing by Avogadro's number gives the Gibbs energy for a single ion:
o
Pj = Pj +kTlnmj +kTlny j. [8.93J
NA NA
In dilute solutions, the principal deviation from the ideal value is caused by the elec-
tric interaction. The effect on the Gibbs energy when the ionic strength is small is given
by formula (8.83). So we obtain
z.2e 2 b [ J
kTlny j = ~Gatm = __ J __ 8.94
,
8m,
whence

[8.95J