Introduction

A buffer is a solution that can maintain a nearly constant pH when diluted, or when strong acids or bases are added. A buffer solution consists of a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid).

Example: Consider a solution containing both acetic acid, CH₃COOH, and acetate ions, CH₃COO^-.

Any strong base that is added to the solution is neutralized by acetic acid:
CH₃COOH _(aq) + OH^-_(aq) CH₃COO^-_(aq) + H₂O _(aq)

Any strong acid that is added to the solution is neutralized by acetate:
CH₃COO^-_(aq) + H⁺_(aq) CH₃COOH _(aq)

The amount of strong acid or base that a buffer can neutralize is called the buffer capacity. After the strong base or acid is neutralized, equilibrium will be reestablished.

Since the concentrations of the conjugate acid-base pair in a buffer are usually high, there is very little change in the acid-base pair concentrations as the system establishes equilibrium. Therefore, the [H⁺] concentration can be calculated from the equilibrium expression using the pre-equilibrium concentrations of the conjugate acid-base pair. For our problem-solving method, step 4 can be omitted.

In the example above how could we produce the solution containing CH₃COOH and CH₃COO^-? In general a buffer can be prepared by:

1. Mixing a weak acid and a salt of its conjugate base in solution.
2. Mixing a weak acid and enough strong base to neutralize a portion of the weak acid.
3. Mixing a weak base and enough strong acid to neutralize a portion of the weak base.

Sample Problem

What is the pH of a buffer solution containing 0.100 moles of both CH₃COOH and CH₃COO^- in 0.100 L of water?

1. The only species present in solution that take part in the equilibrium are acetic acid and acetate ion. The pre-equilibrium concentrations of acetic acid and acetate ion are given as 1.00 M (0.100 moles/0.100 L). In buffers, the concentrations of the weak acid and conjugate base are high, so the [H⁺] of water (1.0x10^-7 M) can always be neglected.

2. The balanced equilibrium reaction is: CH₃COOH_(aq) H⁺_(aq) + CH₃COO^-_(aq)

and the equilibrium constant expression is:

     [H+][CH3COO-]
Ka = -------------
      [CH3COOH]

3. It is seldom necessary to calculate Q in buffer problems. See explanation in step 4.

4. As stated in the introduction above, this step is not necessary in buffer problems. The concentrations of CH₃COOH and CH₃COO^- do not change appreciably as equilibrium is established.

5. We can now calculate the equilibrium concentrations using the equilibrium constant expression:

     [H+][CH3COO-]
Ka = -------------
      [CH3COOH]

     (x)(1.00 M)
Ka = -----------
      (1.00 M)

x = 1.8x10^-5

This problem asked for the pH of the solution.

[H⁺] = x = 1.8x10^-5 M

pH = -log[H⁺] = -log(1.8x10^-5)

pH = 4.74

Notice that when the concentrations of the weak acid and conjugate base are equal, the pH of the buffer solution equals pK_a.