Calculating the solubility of Pb(IO3)2 in distilled water is a straightforward prob- lem since the dissolution of the solid is the only source of Pb2+ or IO3–.

**A More Complex Problem: The Common Ion Effect**

Calculating the solubility of Pb(IO_{3})_{2} in distilled water
is a straightforward prob-
lem since the dissolution of the solid
is the only
source of Pb2+ or IO_{3}–. How is the solubility of Pb(IO_{3})_{2} affected if we add Pb(IO_{3})_{2} to a solution
of 0.10 M Pb(NO_{3})_{2}? Before
we set up and solve
the problem algebraically, think about the chemistry occurring in this system, and decide whether
the solubility of Pb(IO_{3})_{2}
will
increase, decrease, or remain the same. This is a good habit to develop. Knowing what answers are reasonable will help you spot errors
in your calcula- tions and give you
more confidence that
your solution to a problem
is correct.

We begin by setting up a table
to help us keep track
of the concentrations of P b2+ and IO_{3}– in this system.

Substituting the equilibrium concentrations into the solubility product
expression (equation 6.33)

(0.10 + *x*)(2*x*)2 = 2.5 x 10–13

and multiplying out the terms on the left leaves us with

4*x*3 +
0.40*x*2 = 2.5
x 10–13

This is a more difficult equation to solve
than that for the solubility of Pb(IO_{3})_{2} in dis-
tilled water, and its solution
is not immediately obvious. A rigorous solution
to equa- tion 6.34 can be found using
available computer software
packages and spreadsheets.

How
might
we solve equation
6.34 if we do not have access to a computer?
One possibility is that we can apply our understanding of chemistry
to simplify the algebra. From Le Châtelier’s principle, we expect that the large initial concentration of Pb2+ will
significantly decrease
the solubility of Pb(IO_{3})_{2}. In this case we can reasonably expect the
equilibrium concentration of Pb2+ to be very close to its initial
concentration; thus, the
following approximation for the equilibrium concentration of Pb2+ seems reasonable

[Pb2+] = 0.10 + *x *= 0.10 M

Substituting into equation 6.34

Before accepting this answer, we check to see if our approximation was reasonable. In this
case the approximation 0.10 + *x *= 0.10 seems
reasonable since the
difference between the two values is negligible. The equilibrium concentrations of Pb2+ and IO_{3}–, therefore, are

The solubility of Pb(IO_{3})_{2} is equal to the additional concentration of Pb2+ in solu- tion, or 7.9 x 10–7 mol/L. As expected, the solubility of Pb(IO_{3})_{2} decreases in the presence of a solution that already contains one of its
ions. This is known as the
**common ion effect.**

As outlined in the following example, the process
of making and evaluating ap- proximations can be extended if the
first approximation leads to an unacceptably
large error.

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