The expression of degree of hydrolysis of strong conjugate base such as acetate ion is given by the expressionwhere Ka is the ionization constant of conjugate acid of the base.

The expression of degree of hydrolysis of strong conjugate base such as acetate ion is given by the expressionwhere K_a is the ionization constant of conjugate acid of the base.

A
$α = \sqrt{K_{w} K_{a} / c}$
B
$α = \sqrt{K_{w} / K_{a} c}$
C
$α = \sqrt{K_{w} c / K_{a}}$
D
$α = \sqrt{K_{a} c / K_{w}}$

Solution:

${Ac}^{-} + H_{2} O ⇌ HAc + {OH}^{-} c (1 - α) cα cα$

$K_{b} = \frac{[HAc] [{OH}^{-}]}{[{Ac}^{-}]} = \frac{(c α) (c α)}{c (1 - α)} = \frac{c α^{2}}{1 - α}$

Assuming $α ≪ 1, K_{b} = c α^{2} or α = \sqrt{K_{b} / c} .$ But $K_{b} = K_{w} / K_{a}$ where $K_{a}$ is the ionization constant of acetic acid .Hence $α = \sqrt{K_{w} / K_{a} c}$ .

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