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174 Modern Analytical Chemistry

back to zero ionic strength to give the thermodynamic equilibrium constant. Sec-
ond, activity coefficients are smaller, and thus activity effects are more important,
for ions with higher charges and smaller effective diameters. Finally, the extended
Debye–Hückel equation provides reasonable activity coefficients for ionic
strengths of less than 0.1. Modifications to the extended Debye–Hückel equation,
which extend the calculation of activity coefficients to higher ionic strength, have
been proposed. 6

EXAMPLE 6.15

Calculate the solubility of Pb(IO 3 ) 2 in a matrix of 0.020 M Mg(NO 3 ) 2 .
SOLUTION

We begin by calculating the ionic strength of the solution. Since Pb(IO 3) 2 is
only sparingly soluble, we will assume that its contribution to the ionic strength
can be ignored; thus
1 2 2
0
.
m= [( 0 20 M )( +) +0 040 M )(– 1) ] =060 M
2
.
.
(
2
2+
–
Activity coefficients for Pb and I are calculated using equation 6.50
. 051 ´+ 2 ´ . 0060
( ) 2
– log g Pb 2+ = = . 0 366
1 + . 3 3 ´ . 0 45 ´ . 0 060
giving an activity coefficient for Pb 2+ of 0.43. A similar calculation for IO 3 –
gives its activity coefficient as 0.81. The equilibrium constant expression for the
solubility of PbI 2 is
+
2
– 2

K sp =[ Pb ][ IO ] g Pb 2 + g - = .25 ´10 –13
IO
3 3
Letting
2+
–
[Pb ]= x and [IO 3 ]=2x
we have
2
2
(x)(2x) (0.45)(0.81) = 2.5 ´10 –13
–5
–5
Solving for x gives a value of 6.0 ´10 or a solubility of 6.0 ´10 mol/L. This
compares to a value of 4.0 ´10 –5 mol/L when activity is ignored. Failing to
correct for activity effects underestimates the solubility of PbI 2 in this case by
33%.
As this example shows, failing to correct for the effect of ionic strength can lead
to significant differences between calculated and actual concentrations. Neverthe-
less, it is not unusual to ignore activities and assume that the equilibrium constant
Colorplate 3 provides a visual
demonstration of the effect of ionic is expressed in terms of concentrations. There is a practical reason for this—in an
strength on the equilibrium reaction analysis one rarely knows the composition, much less the ionic strength of a sample
3+
2+
–
Fe (aq) + SCN (aq) t Fe(SCN) (aq) solution. Equilibrium calculations are often used as a guide when developing an an-
alytical method. Only by conducting the analysis and evaluating the results can we
judge whether our theory matches reality.