30.0 mL of a 0.10 M weak monoprotic acid HA ( $K_{a} = 2.0 \times 1 0^{- 5}$ ) is titrated with 0.10 M NaOH. At what volume of NaOH added (in mL) will the pH be exactly $p K_{a} + 0.50$ ? Treat the mixture as a simple buffer. Give the answer to one decimal place.

Numerical answer type, answer in mL, tolerance 0.1.

Answer: 22.8 mL

pH - p K_{a} = 0.50

, so

[A X^{-}] / [HA] = 1 0^{0.50} = 3.162

. With NaOH volume

V

(same molarity as the acid),

V / (30 - V) = 3.162

, so

V = 30 \times 3.162/ (1 + 3.162) = 22.8

mL.