Question

Calculate the degree of ionisation and $pH$ of $0.05$M solution of a weak base having the ionization constant $\left(K_c\right)$ is $1.77\times {10}^{-5}$. Also calculate the ionisation constant of the conjugate acid of this base.

Answer 1

$BOH\rightleftharpoons B^{+}+O{H}^{-}$

$C(1-\alpha )$ $C\alpha$ $C\alpha$

$K_C=\frac{C^2{\alpha }^2}{C(1-\alpha )}......C$= concentration of the acid

$\because \alpha <<1,K_C=C{\alpha }^2$

$\therefore \alpha =\sqrt{\frac{K_C}{C}}=\sqrt{\frac{1.77\times {10}^{-5}}{5\times {10}^{-2}}}=1.881\times {10}^{-2}$

$\Rightarrow pOH=\frac{1}{2}[p{K}_C-\log C]=\frac{1}{2}[4.752+1.301]$

$=3.0265$

$\therefore pH=14-3.0265=10.97$

Ionization constant of conjugate acid= $\frac{K_W}{K_C}=\frac{{10}^{-14}}{1.77\times {10}^{-5}}=5.65\times {10}^{-10}$ .