In the titration of a solution of a weak base BOH with HCI the pH is 8.2 after 10 ml of $HCl$ solution has been added and 7.6 after 20 ml of $HCl$ solution has been added. Calculate the value of $p k_{b}$ of the base and express your answer as $a b . c d$ [For example if your answer is 3.8 then write answer as 0380]
$[Given : \log 2 = 0.3]$

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answer is 610.

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Detailed Solution

$\begin{array}{l} BOH + HCl ⟶ BCl + H_{2} O \\ C = 10 M - \bar{C} + \frac{10 M}{C - 10 M}; 6.4 = p K_{b} + \log [\frac{20 M}{C - 20 M}] \\ 5.8 = p K_{b} + \log \frac{10 M}{C - 10 M}] \log (\frac{20 M}{C - 20 M}) - \log (\frac{10 M}{C - 10 M}) = 0.6 \\ \Rightarrow \frac{20 M}{(C - 20 M)} \times \frac{(C - 10 M)}{10 M} = 4 \\ \Rightarrow C = 30 M \\ \Rightarrow p K_{b} = 6.1 \end{array}$