The pH of 0.1M solution of cyanic acid (HCNO) is 2.34.

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,

$K_{a}=c \alpha^{2}$

$=0.1 \times\left(45 \times 10^{-3}\right)^{2}$

$=202.5 \times 10^{-6}$

$=2.02 \times 10^{-4}$