Question

The $pH$ at the equivalence point of the titration of $10\text{mL}$, $0.1\text{M}$ weak base $BOH$ with $0.1\text{M}HCl$ is $6$. Find the $p{K}_b$ of $BOH$:
(Given : log 2 =0.3 )

• A. $-3.3$
• B. $3.3$
• C. $6.66$
• D. $-6.66$

Answer 1

The correct option is B $3.3$

$\begin{array}{ccccccc}BOH& +& HCl& \to & BCl& +& H_{2}O\\ 1\text{mmole}& & & & 1\text{mmole}& & 0\end{array}$
Hence, volume of $HCl$ used $10\text{mL}$
$\left[B^{+}\right]=\frac{1}{20}\Rightarrow pH=\frac{1}{2}=(p{K}_w-p{K}_b-\log C)$
$6=\frac{1}{2}(14-p{K}_b-\log \frac{1}{20})$
$12=14-p{K}_b-\log \frac{1}{20}$
$\Rightarrow -2=log{K}_b+log20$
$\Rightarrow -2=log{K}_b+log2+log10$
$\Rightarrow -3.3=log{K}_b$
$\Rightarrow p{K}_b=3.3$