Your TA asks you to make 100 mL of a benzoic acidbenzoate bu

Your TA asks you to make 100 mL of a benzoic acid/benzoate buffer solution of pH = 3.84. The Ka of benzoic acid is 6.5 × 10–5 .

a) Determine the volumes of 0.50 M benzoic acid and 0.50 M sodium benzoate required to make 100.0 mL of a pH 3.84 buffer solution.

b) Determine the volumes of 0.50 M benzoic acid and 0.50 M sodium hydroxide required to make 100.0 mL of a pH 3.84 buffer solution.

Solution

pH = 3.84

pKa = 4.187

pH = pKa + log [salt / acid]

3.84 = 4.187 + log [salt / acid]

[salt / acid] = 0.4498

total volume of buffer = 100.0 mL = 0.10 L

(0.5 (100-x) / 0.5 x = 0.4498

50 - 0.5 x / 0.5 x = 0.4498

50 - 0.5x = 0.2249 x

x = 68.975

volume of sodium benzoate = 68.98 mL

volume of benzoic acid = 31.02 mL