Answer to Question #185274 in Organic Chemistry for Amit

Question

b)         Define degree of hydrolysis and hydrolysis constant, and derive a relationship

between them. 

Answer 1

A hydrolysis constant is an equilibrium constant for a hydrolysis reaction.

For example, if a metal salt such as $AlCl_3$

dissolves in an aqueous solution, the metal cation behaves as a Lewis acid and hydrolyzes the water molecules in the solvent.

Al³⁺ + 2H₂O → AlOH²⁺ + H₃O⁺

The hydrolysis constant for this reaction is as shown:

K_hydrolysis = [H₃O⁺] * [AlOH²⁺] / [Al³⁺]

In a more generalized form, the hydrolysis constant can be described as:

K_a = [H₃O⁺] * [A⁻] / [HA]

where A⁻ represents any base, and HA represents any acid.

Relationship

Let us consider the reactions between a strong acid, $HCl$ , and a weak base, $NH_4OH$ , to produce a salt, $NH_4Cl$ , and water.

HCl (aq) + NH4OH (aq) ⇌ NH4Cl (aq) + H2O(I) 

$NH_4Cl(aq) → NH_4^+ + Cl^- (aq)$

$NH_4^+$ is a strong conjugate acid of the weak base $NH_4OH$ and it has a tendency to react with $OH^-$ from water to produce unionised $NH_4OH$ shown below.

$NH_4^+ (aq) + H_2O (l) ⇌ NH_4OH (aq) + H^+(aq)$

There is no such tendency shown by Ct and therefore [H+] > [OH-] the solution is acidic and the pH is less than 7.

As discussed in the salt hydrolysis of strong base and weak acid. In this case also, we can establish a relationship between the Ka and Kb as Kh.Kb = Kw

 

Let us calculate the Kb value in terms of degree of hydrolysis (h) and the concentration of salt Kh = h2C and