Question

In hydrolysis of a salt of weak acid and strong base, $A^{-}+H_{2} O \rightleftharpoons H A+O H^{-}$,the hydrolysis constant $\left(K_{h}\right)$ is equal to

• A. $\frac{K_{w}}{K_{a}}$
• B. $\frac{K_{w}}{K_{b}}$
• C. $\sqrt{\frac{K_{a}}{C}}$
• D. $\frac{K_{w}}{K_{a} \times K_{b}}$

Answer 1

Answer: (A)

In hydrolysis of a salt of weak acid and strong base
$A ^{-}+ H _{2} O \rightleftharpoons HA + OH ^{-}$
the hydrolysis constant $K_{h}$
$K_{h}=\frac{[H A]\left[ OH ^{-}\right]}{\left[A^{-}\right]}$
(According to law of mass action)
( $\because$ conc. of water remains constant)
For the ionisation of weak acid $HA$,
we has $H A \rightleftharpoons H^{+}+A^{-}$
$K_{a}=\frac{\left[H^{+}\right]\left[A^{-}\right]}{[H A]}$
Also we know that
$\frac{K_{w}}{K_{a}}=\frac{\left[H^{+}\right]\left[O H^{-}\right][H A]}{\left[H^{+}\right]\left[A^{-}\right]}$
$\frac{K_{w}}{K_{a}}=\frac{\left[O H^{-}\right][H A]}{\left[A^{-}\right]}=K_{h}$