The are two types of equilibrium problems, depending upon whether the condition presented is at equilibrium or is about to approach equilibrium. The first (at) with be referred to as a type I problem and the second (approaching) will be referred to as type II.©*
Type I:
example:
In the following reaction reaction:
The HF concentration is 0.010 M and the F^{} concentration is 0.10 M. What is the concentration of the H_{3}O^{+} ions?
This is a type I problem since the conditions are stated as being at equlibrium. Here are the steps to perform for a type I problem:
step 1: Write the equilibrium expression
step 2: Substitute the concentrations given into the equilibrium expression.
step 3: Solve for the unknown.
solution:
Step 1: equilibrium expression:
Steo 2: substitute:
Step 3: solve: [H_{3}O^{+}] = 1.8 x 10^{3}
Type II:
In this type of problem, the conditions presented are not at equilibrium and equilibrium is then approached. For example, it may be that how the solution was created is known but the final equailbrium concentrations are unknown.
Example:
A solution of H_{2}SO_{3} and NaHSO_{3} is made up to be 0.10 M in H_{2}SO_{3} and 0.10 M in NaHSO_{3} . What is the hydronium ion concentration?
The BrønstedLowry reaction is: H_{2}SO_{3} + H_{2}O ⇌ HSO_{3}^{} + H_{3}O^{+}
Step 1) Set up a table for the initial and final concentrations for all dissolved species
Step 2) Write down the initial concentrations for each in the table.
Step 3) Use "x" to represent the concentration of the reaction.
Step 4) Subtract υx (υ is the respective stoichiometric coefficient) from each of the reactants and add υx to each product.
Step 5) Write the equilibrium expression
Step 6) Substitute the concentrations given into the equilibrium expression.
Step 7) Solve for x.
Step 8) Now check to see if x is the answer or if the answer has x in it. It may be υx for one or more species. (I.E. watch out for the "Grandmother Answer"**.)
Execution of the above problem:
Step 1) The table:
[H_{2}SO_{3}]  [HSO_{3}^{}] 
[H_{3}O^{+}] 

Initial 

Final 
Step 2) Fill in initial concentrations:
[H_{2}SO_{3}]  [HSO_{3}^{}] 
[H_{3}O^{+}] 

Initial 
0.10 
0.10 
0 
Final 
Step 3) Use x for concentration of reaction:
Step 4) Fill in the υx s
[H_{2}SO_{3}]  [HSO_{3}^{}] 
[H_{3}O^{+}] 

Initial 
0.10 
0.10 
0 
Final 
0.10  x 
0.10 + x 
x 
Step 5) The equilibrium expression:
Step 6) Substitute:
Step 7) Solve for x: (See the handout on algebra for a handy approximation.)
x = 1.3 x 10^{2}
[H_{3}O^{+}] = 1.3 x 10^{2} is the answer.
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*© copyrighted by J. B. Condon, Roane State Community College, 1994
** What's the Grandmother answer: In answer to
a question such as the example a student could say, "My grandmother (or great
grandmother) is dead." It might be true but is not the answer to the
question. These are sometimes hard to determine. The answer might seem
correct, but check to see if it is answering the question.