Page 189 - Modern Analytical Chemistry

1400-CH06 9/9/99 7:41 AM Page 172

172 Modern Analytical Chemistry

depends on the composition of the solution. When the solubility product for AgIO 3
+ –
is calculated using the equilibrium concentrations of Ag and IO 3
+
–
K sp = [Ag ][IO 3 ]
its apparent value increases when an inert electrolyte such as KNO 3 is added.
Why should adding an inert electrolyte affect the equilibrium position of a
chemical reaction? We can explain the effect of KNO 3 on the solubility of AgIO 3 by
considering the reaction on a microscopic scale. The solution in which equilibrium
+ + + – –
is established contains a variety of cations and anions—K , Ag , H 3 O , NO 3 , IO 3
–
and OH . Although the solution is homogeneous, on the average, there are more
+
–
anions in regions near Ag ions, and more cations in regions near IO 3 ions. Thus,
+
–
Ag and IO 3 are surrounded by charged ionic atmospheres that partially screen the
ions from each other. The formation of AgIO 3 requires the disruption of the ionic
+
–
atmospheres surrounding the Ag and IO 3 ions. Increasing the concentrations of
ions in solution, by adding KNO 3 , increases the size of these ionic atmospheres.
Since more energy is now required to disrupt the ionic atmospheres, there is a
decrease in the formation of AgIO 3 , and an apparent increase in the equilibrium
constant.
ionic strength The ionic composition of a solution frequently is expressed by its ionic
A quantitative method for reporting the strength, m
ionic composition of a solution that 1
takes into account the greater effect of m= å cz 2
i i
more highly charged ions (m). 2 i
where c i and z i are the concentration and charge of the ith ion.
EXAMPLE 6.1 4

Calculate the ionic strength of 0.10 M NaCl. Repeat the calculation for a
solution of 0.10 M Na 2 SO 4 .

SOLUTION
The ionic strength for 0.10 M NaCl is
1 1
2
2
[
m= ([Na + ]( + 1) 2 +Cl – ](– 1) ) = 010)( 1) + 2 ( . 1) ] 01 . =0 M
+ 010)(–
[( .
2 2
For 0.10 M Na 2 SO 4 , the ionic strength is
1 2– 1
2
2
2
=0M
.
.
[(
m= ([Na + ]( +) 2 +SO 4 ](– 2) ) = 020)( 1) + ( + 010)(– 2) ] 03
1
.
[
2 2
Note that the unit for ionic strength is molarity, but that the molar ionic strength
need not match the molar concentration of the electrolyte. For a 1:1 electrolyte,
activity such as NaCl, ionic strength and molar concentration are identical. The ionic
True thermodynamic constants use a strength of a 2:1 electrolyte, such as Na 2 SO 4 , is three times larger than the elec-
species activity in place of its molar trolyte’s molar concentration.
concentration (a).
The true thermodynamic equilibrium constant is a function of activity
rather than concentration. The activity of a species, a A , is defined as the prod-
activity coefficient uct of its molar concentration, [A], and a solution-dependent activity coeffi-
The number that when multiplied by a cient, g A .
species’ concentration gives that species’
activity (g). a A = [A]g A