Page 176 - Modern Analytical Chemistry

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Chapter 6 Equilibrium Chemistry 159

6G.3 Systematic Approach to Solving Equilibrium Problems
Calculating the solubility of Pb(IO 3 ) 2 in a solution of Pb(NO 3 ) 2 was more com-
plicated than calculating its solubility in distilled water. The necessary calcula-
tions, however, were still relatively easy to organize, and the assumption used to
simplify the problem was fairly obvious. This problem was reasonably straight-
forward because it involved only a single equilibrium reaction, the solubility of
Pb(IO 3 ) 2 . Calculating the equilibrium composition of a system with multiple
equilibrium reactions can become quite complicated. In this section we will
learn how to use a systematic approach to setting up and solving equilibrium
problems.
As its name implies, a systematic approach involves a series of steps:

1. Write all relevant equilibrium reactions and their equilibrium constant
expressions.
2. Count the number of species whose concentrations appear in the equilibrium
constant expressions; these are your unknowns. If the number of unknowns
equals the number of equilibrium constant expressions, then you have enough
information to solve the problem. If not, additional equations based on the
conservation of mass and charge must be written. Continue to add equations
until you have the same number of equations as you have unknowns.
3. Decide how accurate your final answer needs to be. This decision will influence
your evaluation of any assumptions you use to simplify the problem.
4. Combine your equations to solve for one unknown (usually the one you are
most interested in knowing). Whenever possible, simplify the algebra by
making appropriate assumptions.
5. When you obtain your final answer, be sure to check your assumptions. If any
of your assumptions prove invalid, then return to the previous step and
continue solving. The problem is complete when you have an answer that does
not violate any of your assumptions.
Besides equilibrium constant equations, two other types of equations are used
in the systematic approach to solving equilibrium problems. The first of these is a
mass balance equation, which is simply a statement of the conservation of matter. mass balance equation
In a solution of a monoprotic weak acid, for example, the combined concentrations An equation stating that matter is
–
of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the conserved, and that the total amount of a
species added to a solution must equal
weak acid’s initial concentration, C HA .*
the sum of the amount of each of its
The second type of equation is a charge balance equation. A charge balance possible forms present in solution.
equation is a statement of solution electroneutrality.
Total positive charge from cations = total negative charge from anions charge balance equation
An equation stating that the total
Mathematically, the charge balance expression is expressed as concentration of positive charge in a
solution must equal the total
n m
–
z
[
å (z + ) ´ [M z+ ] i = å ( ) j ´A z – ] j concentration of negative charge.
i
i= 1 j = 1
z+
z–
where [M ] i and [A ] j are, respectively, the concentrations of the ith cation
+
–
and the jth anion, and (z ) i and (z ) j are the charges of the ith cation and the jth
anion. Note that the concentration terms are multiplied by the absolute values
of each ion’s charge, since electroneutrality is a conservation of charge, not con-
centration. Every ion in solution, even those not involved in any equilibrium
*You may recall that this is the difference between a formal concentration and a molar concentration.