Buffers, titration curves and indicators

What you’ll learn

• Explain buffer action using a conjugate pair.
• Calculate buffer pH after establishing the amounts present.
• Choose indicators from titration curves.

Understand the idea

An acidic buffer contains appreciable amounts of a weak acid and its conjugate base. Added hydrogen ions are removed mainly by the base, while added hydroxide ions react with the acid. These changes alter the ratio only slightly for a small addition, so pH changes little. Buffer capacity is finite and increases with the amounts of both components present.

For a weak-acid–strong-base titration, the half-equivalence point has equal acid and conjugate-base amounts, so pH equals $\mathrm{p}K_a$. The equivalence solution is alkaline because the conjugate base hydrolyses. An indicator must change colour within the steep part of the curve; a weak-acid–weak-base titration has no sufficiently sharp jump for an ordinary visual endpoint. Diprotic acids may show two equivalence stages when their dissociations are sufficiently separated.

Key formulae

$$\mathrm{HA+OH^-\longrightarrow A^-+H_2O}$$

$$\mathrm{A^-+H^+\longrightarrow HA}$$

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

$$\mathrm{pH}=\mathrm{p}K_a\quad\text{at half-equivalence (weak acid/strong base)}$$

Worked example

A buffer has $\mathrm{p}K_a=4.76$ and concentrations $[\mathrm{A^-}]=0.20$, $[\mathrm{HA}]=0.10\,\mathrm{mol\,dm^{-3}}$. Calculate its pH.

1. Identify the ratio of conjugate base to acid: $0.20/0.10=2$.
2. Use $\mathrm{pH}=4.76+\log_{10}2$.
3. Evaluate $4.76+0.30103=5.06103$.

Answer: $\mathrm{pH}=5.06$ (2 d.p.).