How to Solve Simple Equilibrium Problems

 

In this document we will consider the chemical reaction that converts reactants (on the left side) to products (on the right side).  We will define K as large if it is greater than 1x103 and K as small when it is less than 1x10-3. Table 1 shows common situations and the approximate methods that can be used.  These are applicable to all equilibrium problems of the type: Reactants  Products.

Type Starting Situation At Equilibrium Solution
1 Given reactants with large K mostly products present, very little reactants Let reaction go all the way to products and assume that the amount of products that return to reactants is negligible .
2 Given reactants with small K mostly reactants, very little products Assume amount of reactants that reacts is negligible compared to total.
3 Given products with large K mostly products present, very little reactants Assume amount of products that return to reactants is negligible compared to total.
4 Given products with small K mostly reactants present, very little products Let reaction go all the way to reactants and then assume that the amount of reactants that return to products is negligible.
5 Any combination of reactants and products with 1x10-3 < K < 1x103 almost equal mixture of products and reactants Solve full problem using method of successive approximations or  computer.

Table 1.  Types of equilibrium problems and methods of solution.

 

When solving equilibrium problems in solution, the above approximations can generally be used. Some additional approximate methods are given below. If you need an exact answer, want the general solution (applicable everywhere), or are dealing with dilute solutions, you will need to take into account mass and charge balance and the solvent autoionization. Follow these steps to obtain approximate solutions for solution equilibrium problems.

 

1. Solve any stoichiometry problem first. We can use a chemical reaction to change the equilibrium conditions by changing the initial concentrations of the species in equilibrium (as during the course of a titration). Common reactions that are used in this way are: 1) acid + base, 2) oxidant + reductant and 3) soluble salt + soluble salt to give an insoluble salt.

 

2. Identify species in solution and their properties and determine their concentrations. Decide on what calculations must be done. Table 2 summarizes some of the common situations encountered with acids and bases and the approximate methods that can be used to solve the problem.

Situation What Happens What to Do
Only strong acid or base present Strong acid or base dissociates completely. Calculate [H+] or [OH-] directly from the concentration of the strong acid or base.
Only weak acid or base present Weak acid or base dissociates incompletely. Solve like type 2 problem in Table 1 using Ka (for weak acid) or Kb (for weak base).
Only conjugate base of a weak acid present Conjugate base reacts with H2O to give OH- and the weak acid. Use Kb for the conjugate base and solve like type 2 problem in Table 1
Only conjugate acid of a weak base present Conjugate acid dissociates to give H+ and the weak base. Use Ka for the conjugate acid and solve like type 2 problem in Table 1
Only conjugate acid/base of a strong base/acid present Nothing. Use Kw to calculate [H+] and [OH-]
Weak acid/base and its conjugate are present Both weak acid/base and its conjugate are present and affect equilibrium. May be a buffer. Use Ka or Kb and initial concentrations to solve for new [H+] or [OH-]. Usually a type 2 problem. If ratio of the species and its conjugate are between 1:10 and 10:1, you can use the Henderson-Hasselbalch equation.
Weak acid/base is present and there is an excess of strong acid/base Equilibrium for weak acid/base is shifted completely to one side by presence of excess strong acid/base. Assume that the weak acid/base equilibrium is inconsequential and calculate [H+] or [OH-] from amount of excess strong acid or strong base present.

Table 2. Common situations encountered in solution acid-base chemistry.