How Do You Calculate the pH of a Buffer Solution? (HL)

For an acidic buffer, calculate pH from the acid dissociation constant and the ratio of conjugate base to weak acid: $\mathrm{pH}=\mathrm{p}K_a+\log_{10}\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right)$. This is additional higher level (AHL) content in Reactivity 3.1.

The Reasoning

A buffer solution resists changes in pH when small amounts of acid or alkali are added. An acidic buffer contains appreciable concentrations of a weak acid, $\mathrm{HA}$, and its conjugate base, $\mathrm{A^-}$.

When a small amount of strong acid is added, $\mathrm{A^-}$ consumes $\mathrm{H^+}$ to form $\mathrm{HA}$. When strong alkali is added, $\mathrm{HA}$ reacts with to form and water. Because these reactions prevent a large change in free concentration, the pH changes only slightly.

For the equilibrium

$\mathrm{HA(aq)} \rightleftharpoons \mathrm{H^+(aq)}+\mathrm{A^-(aq)}$

$K_a=\frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$

Rearranging gives

$[\mathrm{H^+}]=K_a\frac{[\mathrm{HA}]}{[\mathrm{A^-}]}$

Taking negative logarithms produces the HendersontoHasselbalch form:

$\mathrm{pH}=\mathrm{p}K_a+\log_{10}\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right)$

This relationship assumes both buffer components are present in much larger amounts than the small quantity ionized, so their equilibrium concentrations are approximated by their analytical concentrations. If the acid and salt solutions have different volumes, calculate moles and divide by the common final volume, or use the final mole ratio directly.

Worked Example

A buffer contains $0.20\ \mathrm{mol\,dm^{-3}}$ ethanoic acid and $0.30\ \mathrm{mol\,dm^{-3}}$ ethanoate ions. Given :

$\mathrm{p}K_a=-\log_{10}(1.8\times10^{-5})=4.74$

$\mathrm{pH}=4.74+\log_{10}\left(\frac{0.30}{0.20}\right)=4.92$

Diluting a buffer by adding water does not significantly change its pH, provided both buffer components are diluted equally, because their concentration ratio remains approximately constant. However, dilution decreases the buffer's capacity to resist changes in pH

Exam Technique

For a calculate question, show $\mathrm{p}K_a$, the correct base-to-acid ratio, substitution, and the final pH. After added acid or alkali, never substitute the original amounts before completing the reaction stoichiometry.