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Buffer capacity and range; sodium benzoate concentration

Short answer

Buffer capacity is the moles of strong acid or base needed to change the pH of 1 L buffer by one unit. Buffer range is pH ≈ pKa ± 1 for an acidic buffer. Using pH = pKa + log([salt]/[acid]), [sodium benzoate] = 0.090 M.

Define buffer capacity and buffer range. Calculate the concentration of sodium benzoate that must be present in 0.1 M benzoic acid to make a buffer solution of pH 3.7 (Ka for benzoic acid is 1.8×10⁻⁴).

Buffer capacity

The number of moles of strong acid or base needed to change the pH of 1 L of buffer by one unit. It is highest when [salt] = [acid] and when the concentrations are large.

Buffer range

The pH range over which a buffer works effectively. It is about pKa ± 1 for an acidic buffer (i.e. when [salt]/[acid] lies between 0.1 and 10), and pOH = pKb ± 1 for a basic buffer.

Calculation

pH = 3.7  →  [H⁺] = 10⁻³·⁷ = 2.0×10⁻⁴ M
[H⁺] = Ka [acid]/[salt]
[salt] = Ka [acid]/[H⁺]
       = 1.8×10⁻⁴ × 0.1 / 2.0×10⁻⁴
       = 0.090 M

Check with Henderson: pKa = 3.745; log([salt]/[acid]) = 3.7 − 3.745 = −0.045, so ratio = 0.90 and [salt] = 0.090 M.

Answer: [sodium benzoate] ≈ 0.09 M.

✓ Answer checked by Claude Opus 5.5 (high effort)

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