A weak base BOH is titrated with a strong acid HA. When 10 mL of HA is added, pH is found to be 9.00 and when 25 mL is added, pH is 8.00. The volume of the acid required to reach the equivalence point is

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55 mL

40 mL

30 mL

50 mL

answer is C.

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Detailed Solution

$pH = 14 - {pK}_{b} - \log \frac{[B^{+}]}{[BOH]}$

V = volume of acid required for the equivalence point

$(i) ({pH}_{1}) = 9 = 14 - {pK}_{b} - \log \frac{10}{V - 10}$

$(ii) ({pH}_{2}) = 8 = 14 - {pK}_{b} - \log \frac{25}{V - 25}$

Eq. (i) - Eq. (ii)

$1 = \log \frac{25}{V - 25} - \log \frac{10}{V - 10} = \log \frac{25 (V - 10)}{10 (V - 25)}$

$\Rightarrow$ V = 30mL

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