pH calculations and buffers · Year 13
pH measures the concentration of hydrogen ions: pH = −log[H⁺]. A strong acid is fully dissociated, so [H⁺] is the concentration of the acid. A weak acid only partly dissociates, and its acid dissociation constant, Ka, says how far. Water has its own ionic product, Kw, which links [H⁺] and [OH⁻]. A buffer is a mixture that keeps the pH almost the same when a little acid or alkali is added.
Key facts
- pH = −log[H⁺] and [H⁺] = 10^(−pH). Each unit of pH is a factor of 10 in [H⁺].
- Strong acids such as HCl and HNO₃ are fully dissociated: [H⁺] equals the concentration of the acid.
- Kw = [H⁺][OH⁻] = 1.00 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. For a strong base find [OH⁻], then [H⁺] = Kw ÷ [OH⁻]. Kw grows with temperature, so pure water at 50 °C has a pH of 6.63, but it is still neutral.
- For a weak acid, HA ⇌ H⁺ + A⁻: Ka = [H⁺][A⁻] ÷ [HA], and pKa = −log Ka. The larger Ka (the smaller pKa), the stronger the acid.
- pH of a weak acid: take [H⁺] = [A⁻] and assume [HA] stays at its starting value, so [H⁺] = √(Ka × [HA]).
- A buffer resists changes in pH. An acidic buffer is a weak acid with its salt, such as ethanoic acid with sodium ethanoate: [H⁺] = Ka × [HA] ÷ [A⁻].
- At half-neutralisation of a weak acid by a strong base, [HA] = [A⁻], so pH = pKa.