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:

HF  +  H2O  ⇌   H3O+  +  F-

The HF concentration is 0.010 M and the F- concentration is 0.10 M.  What is the concentration of the H3O+ 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: HF equilibrium expression

Steo 2:  substitute:   

Step 3: solve:    [H3O+] = 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 H2SO3 and NaHSO3 is made up to be 0.10 M in H2SO3 and 0.10 M in NaHSO3 .  What is the hydronium ion concentration? 

The Brønsted-Lowry reaction is:   H2SO3 +  H2O ⇌   HSO3-  + H3O+

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:


 [H2SO3] [HSO3-]
 [H3O+]
Initial


Final


Step 2)  Fill in initial concentrations:


[H2SO3] [HSO3-]
 [H3O+]
Initial
 0.10
 0.10
 0
Final


Step 3)  Use x for concentration of reaction:

                 Equilibrium expression for H2SO3

Step 4)  Fill in the υx s


[H2SO3] [HSO3-]
 [H3O+]
Initial
 0.10
 0.10
 0
Final
 0.10 - x
 0.10 + x
 x

Step 5)  The equilibrium expression:

    H2SO3 equilibrium expression

Step 6)  Substitute:

    calculation of H2SO3

Step 7)  Solve for x:  (See the handout on algebra for a handy approximation.)

    x = 1.3 x 10-2

Step 8)  In this case [H3O+] = x  thus:

    [H3O+] = 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.