Which of the following relations is correct during the hydrolysis of salts of weak acid and strong bases ?

Options

A. `K_(h)=(K_(w))/(K_(a))`
B. `K_(h)=(K_(w))/(K_(a)K_(b))`
C. `K_(h)=(K_(w))/(K_(b))`
D. `K_(h)=(K_(a))/(K_(w))`

Answer

A

Explanation

`A^(-)+H_(2)OhArrHA+OH^(-)`
`K_(b)=([HA][OH^(-)])/([A^(-)])=([HA][OH^(-)])/([A^(-)])xx([H^(+)])/([H^(+)])`
`= ([HA])/([H^(+)][A^(-)])xx[H^(+)][OH^(-)]`
`=(1)/(K_(a))xxK_(w)`
`= (K_(w))/(K_(a))`
Expression `(2)` is valid for the hydrolysis of salts of weak bases and weak acids. Expression `(3)` is valid for the hydrolysis of salts of weak bases and strong acids