Correct statement for $H C N$ weak acid at $25^{o} C$

α = \frac{K_{a}}{[H^{+}]}

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α = \frac{K_{a} \times [O H^{-}]}{K w}

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(1)

(2)

both

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K_{b} = C α^{2}

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Solution

The correct option is A $(1)$ & $(2)$ both
we have,

A.

$H C N ⇌ H^{+} + C N^{-}$

$K_{a} = \frac{[H^{+}] [C N^{-}]}{[H C N]}$

$= \frac{[H^{+}] c α}{c (1 - α)}$

$K_{a} = [H^{+}] α$

$α = \frac{K_{a}}{[H^{+}]}$

B.

$C N^{-} + H_{2} O ⇌ H C N + O H^{-}$

$K_{b} = \frac{[H C N] [O H^{-}]}{[C N^{-}]}$

$= \frac{c α [O H^{-}]}{c (1 - α)}$

$K_{b} = α [O H^{-}]$

$α = \frac{[O H^{-}]}{K_{b}}$

$α = \frac{K_{a} [O H^{-}]}{[K_{b}]}$

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