A tenfold dilution of a weak monoprotic acid can raise its pH by about 0.50 when the usual weak-acid approximation holds. Hydrogen ion concentration falls by about √10 rather than 10, because a greater fraction of the acid dissociates.
The 2027 H2 Chemistry 9476 syllabus covers pH calculations for weak monoprotic acids. This example uses the same acid before and after dilution, at constant temperature.
- Keep Kₐ fixed at the stated temperature.
- Calculate the new acid concentration.
- Use the weak-acid approximation when justified.
- Check the dissociated fraction at each concentration.
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Set up the equilibrium
For HA ⇌ H⁺ + A⁻, start with acid concentration c. Let x be the equilibrium hydrogen ion concentration due to the acid. When x is small compared with c and water’s contribution is negligible, Kₐ ≈ x²/c. This gives x ≈ √(Kₐc).
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Worked example | Dilute from 0.100 to 0.0100 mol dm⁻³
Use Kₐ = 1.80 × 10⁻⁵ mol dm⁻³. Before dilution, [H⁺] ≈ √(1.80 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol dm⁻³ and pH ≈ 2.87. After tenfold dilution, [H⁺] ≈ 4.24 × 10⁻⁴ mol dm⁻³ and pH ≈ 3.37. The approximate increase is 0.50.
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Check the fraction that dissociates
The approximate percentage dissociation is 100x/c. It is 1.34% before dilution and 4.24% after dilution. The diluted solution has a higher fraction of its acid dissociated, while its hydrogen ion concentration is lower. These fractions are small enough for a useful approximation in this example.
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Frequently asked questions
Does dilution change Kₐ?
At the same temperature, Kₐ stays fixed. Dilution changes the concentrations at equilibrium.
Does the half-unit increase apply to every dilution?
It applies to a tenfold dilution under the approximation used here. Recheck the assumptions for a much more dilute solution or a more strongly dissociated acid.