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.

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$c=0.1 \,M$

$pH =2.34$

$-\log \left[ H ^{+}\right]= pH$

$-\log \left[ H ^{+}\right]=2.34$

$\left[ H ^{+}\right]=4.5 \times 10^{-3}$

Also.

$\left[ H ^{+}\right]=c \alpha$

$4.5 \times 10^{-3}=0.1 \times \alpha$

$\frac{4.5 \times 10^{-3}}{0.1}=\alpha$

$\alpha=45 \times 10^{-3}=.045$

Then

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

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

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

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

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  • [AIPMT 1999]