$20.0 mL$ of a monoprotic weak acid HA of unknown concentration is titrated with a standard NaOH solution. The pH is $4.28$ after $10.0 mL$ of titrant and $4.76$ after $20.0 mL$ . Both points are in the buffer region (use Henderson's equation, $p K_{a}$ unknown). The volume of titrant needed to reach the equivalence point, to the nearest integer in mL, is

Numerical answer type, answer in mL, tolerance 1.

Answer: 40 mL

Let

V_{e}

be the equivalence volume.

pH = p K_{a} + lo g [V / (V_{e} - V)]

. Subtracting:

4.76 - 4.28 = 0.48 = lo g \frac{20 ( V _{e} - 10 )}{10 ( V _{e} - 20 )}

, so

2 (V_{e} - 10) / (V_{e} - 20) = 3.020

. Solving,

V_{e} = 39.6 \approx 40 mL

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