Question

For the hydrolysis of a salt of a weak acid and a weak base, show that
Kh=Kw/KaKb

Answer 1

salt hydrolysis of weak acid and weak base

$CH_3COOH+NH_4OH\to CH_3COO^-NH_4^++H_2O$

hydrolysis of salt

$CH_3COO^-NH_4^++H_2O\to CH_3COOH+NH_4OH$

$K_h=\frac{CH_3COOH][NH_4OH]}{[CH_3COO^-NH_4^+]}$

$CH_3COOH\to CH_3COO^-+H^+$

$K_a=\frac{[CH_3COO^-][H^+]}{[CH_3COOH]}$

$NH_4OH\to NH_4^++OH^-$

$K_b=\frac{[NH_4^+][OH^-]}{[NH_4OH]}$

$H_2O\to H^++OH^-$

$K_w=[H^+][OH^-]$

Hence,

$K_h=\frac{K_w}{K_aK_b}$