Calculating pH for a solution of a weak acid
For solutions where only the acid of a conjugate pair is dissolved, the reaction to reach equilibrium is the only source of the conjugate base and the major source of H3O+.
acid + H2O
conjugate base + H3O+
For strong acids, the extent of reaction is high.
For weak acids (Ka < 10–2) the extent of reaction with water is small.
To calculate pH using Ka, both [acid] and [conjugate base] must be related to [H3O+].
A second approach uses mass balance: The initial concentration of a species equals the sum of the equilibrium concentrations of that species and any species arising from it by reaction.
acid + H2O
conjugate base + H3O+For strong acids, the extent of reaction is high.
[H3O+] is equal to the initial concentration of the acid
[H3O+] is the same for different acids provided they are present in the same concentration.
[H3O+] is the same for different acids provided they are present in the same concentration.
| Ka = | [conjugate base][H3O+] |
| [acid] | |
| reaction quotient |
[H3O+] is much less than [acid]
[H3O+] depends on Ka and the initial concentration of the acid
[H3O+] depends on Ka and the initial concentration of the acid
To calculate pH using Ka, both [acid] and [conjugate base] must be related to [H3O+].
If only the acid is dissolved, the reaction above is the only source of the conjugate base.
Thus for a solution of this type: [conjugate base] = [H3O+]
Thus for a solution of this type: [conjugate base] = [H3O+]
One approach to deducing the relationship between [acid] and [H3O+] is shown in the table below.
| concentrations | H3O+ | conj base | acid |
| initial (before reaction) | 0 | 0 | c(acid) |
| change (due to reaction) | +[H3O+] | +[H3O+] | -[H3O+] |
| at equilibrium (after reaction) | [H3O+] | [H3O+] | c(acid) - [H3O+] ≈ c(acid) if the extent of reaction is small |
A second approach uses mass balance: The initial concentration of a species equals the sum of the equilibrium concentrations of that species and any species arising from it by reaction.
Thus: cinitial(acid) = [acid] + [conjugate base]
Where [conjugate base] << [acid], the approximation cinitial(acid) = [acid] is valid.
Where [conjugate base] << [acid], the approximation cinitial(acid) = [acid] is valid.
Substituting the above for [acid] and [conjugate base] into the reaction quotient expression allows, for a solution of this type, calculation of Ka from known [H3O+] or [H3O+] from known Ka .