E18 PERCENTAGE IONISATION OF A WEAK ACID
While strong acids are considered to be 100% ionised in a water solution, weak acids are only slightly
ionised to H3O+ and their conjugate base.
The [H3O+] present in a solution of strong acid is therefore directly related to the original concentration of
the acid.
Consider the reaction:
HNO3(aq) + H2O(l) Æ H3O+(aq) + NO3-(aq)
Since this reaction is irreversible, [H3O+] can be found using the stoichometric ratio. If the concentration of
the nitric acid is 0.10 M, then [H3O+] = [HNO3]initial = 0.10 M.
However, to calculate the concentration of H3O+ present in a given solution of a weak acid, it is necessary
to know not only the concentration of the acid but also the equilibrium constant for the acid's ionisation.
Weak acids
For a weak acid HA, the equilibrium is
H3O+(aq) + A-(aq)
HA(aq) + H2O(l)
or
HA(aq)
H+(aq) + A-(aq)
and the equilibrium constant is
Ka = [H3O+][A-] / [HA]
or
Ka = [H+][A-] / [HA]
If the solution is prepared by dissolving HA into water, or by diluting an existing HA solution, then the
only possible source of A- is HA. In such a case, [H3O+] = [A-]. As a result, Ka can be calculated from a
measurement of the pH of a solution of a weak acid of known concentration.
For example, suppose that the pH of a 0.10 M solution of acetic acid is measured to be 3.50. This means:
[H3O+] = 10-3.50 = [A-].
Substituting in the expression for Ka,
Ka = (10-3.50)(10-3.50)/(0.10 - 10-3.50) = 1.0 x 10-6 (2 significant figures).
Examples of weak acids
•
Hydrofluoric acid (HF) Ka = 6.8 x 10-4 M
•
Benzoic acid (C6H5COOH) Ka = 6.3 x 10-5 M
•
Acetic acid (CH3COOH) Ka = 1.8 x 10-5 M
The larger Ka, the stronger the acid.
Weak bases
Similarly, for a general weak base B, the equilibrium is
B(aq) + H2O(l) Æ HB+(aq) + OH- (aq)
Many weak bases carry a negative charge and for a weak base B-, the equilibrium is
B-(aq) + H2O(l) Æ HB(aq) + OH- (aq)
For example, B = NH3 or B- = CN-. Thus, the equilibrium constant for the above equations are
Kb = [HB+][OH- ] / [B] or Kb = [HB][OH- ] / [B-]
where Kb is the base ionisation constant.
Examples of weak bases
•
Ammonia (NH3) Kb = 1.8 x 10-5 M
•
Cyanide ion (CN-) Kb = 1.7 x 10-5 M
•
Pyridine (C5H5N) Kb = 1.7 x 10-9 M
The larger Kb, the stronger the base.
Percentage ionisation of a weak acid
The % ionisation of a weak acid changes with the concentration of the weak acid. However, Ka is
independent of the concentration of the weak acid.
% ionisation = {[H3O+]/[HA]initial} x 100%
For example, suppose that the pH of a 0.10 M solution of nitrous acid (HNO2) is measured to be 2.19.
% ionisation = {[H3O+] / [HA]initial} x 100 = {(10-2.19) / 0.10 } x 100 = 6.6%
If the same acid was more dilute with a concentration of 0.010 M, the pH changes to 2.72.
% ionisation = {[H3O+] / [HA]initial } x 100 = {(10-2.72) / 0.010 } x 100 = 19%
These calculations illustrate that the % ionisation increases as a solution is diluted, even though the actual
number of moles which ionizes decreases.
In the laboratory work, the pH of acetic acid solutions ranging in concentration from 1 x 10-3 M to 1 M are
measured. From this the Ka and % ionisation for acetic acid can be deduced.