The $pH$ of $0.1 \, M$ solution of cyanic acid $(HCNO)$ is $2.34$. Calculate the ionization constant of the acid and its degree of ionization in the solution.

(N/A) $c = 0.1 \, M$
$pH = 2.34$
$-\log [H^{+}] = pH$
$-\log [H^{+}] = 2.34$
$[H^{+}] = 10^{-2.34} \approx 4.57 \times 10^{-3} \, M$
Also,$[H^{+}] = c \alpha$
$4.57 \times 10^{-3} = 0.1 \times \alpha$
$\alpha = \frac{4.57 \times 10^{-3}}{0.1} = 0.0457$
Then,$K_{a} = c \alpha^{2}$
$K_{a} = 0.1 \times (0.0457)^{2}$
$K_{a} = 0.1 \times 2.088 \times 10^{-3} \approx 2.09 \times 10^{-4}$