Question

Derive an expression for relationship of hydrolysis constant and degree of hydrolysis for salt of weak acid and weak base

Answer 1

Maximum hydrolysis occurs in the case of such a salt as both the cation and anion are reactive and react with water to produce H+ and OFT ions. The solution is generally neutral but it can be either slightly acidic or slightly alkaline if both the reactions take place with slightly different rates. Consider, for example, the salt CH3COONH4. It gives CH3COO- and  ions in solution. Both react with water.



Other equilibria which exist in solution are:

CH3COOH  CH3COO- + H+,

Ka =  [CH3COO-][H+]/[CH3COOH]    ..... (i)

NH4OH NH+4 + OH-,

Kb = [NH+4] [OH-]/[NH4OH]           ..... (ii)

H2O H+ + OH-

Kw = [H+][OH-]                                    ..... (iii)

From Eqs. (i), (ii) and (iii),

Kh =  Kw/Ka.Kb = [CH3COOH][NH4OH]/[CH3COO-][NH+4]                     .... (iv)

Let C be the concentration and h be the degree of hydrolysis

Kh = h2/(1-h)2

When h is small, (1-h) → 1.

Kh = h2

h = √Kh = √Kw/Ka*Kb

[H+] Ka × h

= Ka × √Kw/Ka*Kb

= √Kw Ka/Kb

-log [H+] = -1/2log Ka - 1/2log Kw + 1/2log Kb

pH = 1/2pKa +  1/2pKw - 1/2pKb

= 7 +  1/2pKa - 1/2pKb