Question:
The $\mathrm{pH}$ of $0.1 \mathrm{M}$ solution of cyanic acid (HCNO) is $2.34$. Calculate the ionization constant of the acid and its degree of ionization in the solution.
Solution:
$c=0.1 \mathrm{M}$
$\mathrm{pH}=2.34$
$-\log \left[\mathrm{H}^{+}\right]=\mathrm{pH}$
$-\log \left[\mathrm{H}^{+}\right]=2.34$
$\left[\mathrm{H}^{+}\right]=4.5 \times 10^{-3}$
Also,
$\left[\mathrm{H}^{+}\right]=c \alpha$
$4.5 \times 10^{-3}=0.1 \times \alpha$
$\frac{4.5 \times 10^{-3}}{0.1}=\alpha$
$\alpha=45 \times 10^{-3}=.045$
Then,
$K_{a}=c \alpha^{2}$
$=0.1 \times\left(45 \times 10^{-3}\right)^{2}$
$=202.5 \times 10^{-6}$
$=2.02 \times 10^{-4}$