Page 348 - Physical chemistry understanding our chemical world

ACTIVITY 315

The extent of ionic screening depends on the extent of associa-
Infinite dilution (extra-
tion. The only time that association is absent, and we can treat ions
polation to zero con-
as though free and visible (‘unscreened’), is at infinite dilution.
centration) means so
small a concentration
that the possibility of
Why does MgCl cause a greater decrease two ions meeting, and
2
in perceived concentration than KCl? thence associating, is
tiny to non-existent.

The mean ionic activity coefficient γ ±
The value of γ depends
The extent of ionic association depends on the ions we add to on the solute employed.
the solution. And the extent of association will effect the extent of
screening, itself dictating how extreme the difference is between
perceived and real concentration. For these reasons, the value of
γ(= a ÷ c) depends on the choice of solute as well as its concentration, so we ought
to cite the solute whenever we cite an activity coefficient.
The value of γ is even more difficult to predict because solutes
contain both anions and cations. In fact, it is impossible to dif- We cannot know either
ferentiate between the effects of each, so we measure a weighted γ + or γ − ;we can only
average. Consider a simple electrolyte such as KCl, which has know the value of their
one anion per cation. (We call it a ‘1:1 electrolyte’.) In KCl, the geometric mean γ ± .
− and the activity
activity coefficient of the anions is called γ (Cl )
coefficient of the cations is γ (K ) . We cannot know either γ + or
+
γ − ; we can only know the value of γ ± . Accordingly, we modify We call KCl a 1:1 elec-
Equation (7.25) slightly by writing
trolyte, since the ratio
of anions to cations is
c
a = γ ± (7.28) 1:1.
c O

where the only change is the incorporation of the mean ionic activity coefficient γ ± .
The mean ionic activity coefficient is obtained as a geometric mean via

γ ± = γ (K ) × γ (Cl ) (7.29)
−
+
By analogy, the expression for the mean ionic activity coefficient γ ± for a 2:1
electrolyte such as K 2 SO 4 is given by

3 2
γ ± = γ × γ − (7.30)
+
where the cube root results from the stoichiometry, since K 2 SO 4 contains three ions
√
(we could have written the root term alternatively as 3 γ + × γ + × γ − , with one γ
term per ion). Again, a 1:3 electrolyte such as FeCl 3 dissolves to form four ions, so
an expression for its mean ionic activity coefficient γ ± will include a fourth root, etc.