Question

A solution of $0.1 \,M$ weak base $(B)$ is titrated with $0.1\, M$ of a strong acid $(HA)$. The variation of $pH$ of the solution with the volume of $HA$ added is shown in the figure below. What is the $p K_{ b }$ of the base? The neutralization reaction is given by $B + HA \rightarrow BH ^{+}+ A ^{-}$.

Answer 1

$\underset{\text { (weak base) }}{ B }+\underset{\text { (strong acid) }}{ HA } \longrightarrow BH ^{+}+ A ^{-}$
From the graph, it is clear, that the equivalence point is reached at a titre value of $6 \,mL$
i.e. when $6 \,mL$ of HA are added base (B) is completely neutralized.
So it will be half neutralized at titre value of $3 \,mL$;
when $3\, mL$ of HA is added, 'B' is half-neutralized.
So at this stage it will form a best buffer.
i.e. $pOH = pK _{ b }=3$
So, $pK _{ b }$ of weak base $=3$