Q. If $p K_{b}$ for $C N^{-}$ at $25^{o}C$ is $4.7$ , the $pH$ of $0.5\,M$ aqueous $NaCN$ solution is
NTA AbhyasNTA Abhyas 2022
Solution:
$pk_{b}$ $of \, CN^{-}=4.7$
$pk_{a}$ $of$ $HCN=14-4.7=9.3$
$NaCN$ is salt of weak acid $\left(H C N\right)$ and strong base $\left(N a O H\right)$ So
$pH=7+\frac{1}{2}pk_{a}+\frac{1}{2}logC$
$=7+\frac{1}{2}\times 9.3+\frac{1}{2}log \left(0.5\right)$
$\therefore pH=11.5$
$pk_{a}$ $of$ $HCN=14-4.7=9.3$
$NaCN$ is salt of weak acid $\left(H C N\right)$ and strong base $\left(N a O H\right)$ So
$pH=7+\frac{1}{2}pk_{a}+\frac{1}{2}logC$
$=7+\frac{1}{2}\times 9.3+\frac{1}{2}log \left(0.5\right)$
$\therefore pH=11.5$