Derive the relationship between K_h, K_w, K_a.

Let us consider the concentration of water remains constant, the equilibrium constant for hydrolysis reaction called hydrolysis constant may be written as:
K_h = [HX] [OH^–] / [X^–] ………………………………. (1)
The following equilibrium also exists in solution.
For weak acid HX,
HX <---------> H⁺ + X^–
So that K_a = [H⁺] [X^–] / [HX] ……………………….. (2)
Also, K_w = [H⁺] [OH^–] ……………………………… (3)
Multiplying the numerator and denominator of the right hand equation (1) by [H⁺], we get:
K_h = [HX] [OH^–] [H⁺] / [X^–] H⁺]
= [HX] [OH^–] [H⁺] / [X^–] H⁺]
= K_w / K_a
K_h = K_w / K_a
Hence, the hydrolysis constant, K_h of the salt is inversely proportional to the dissociation constant, K_a of the weak acid. Therefore, the weaker the acid, the greater is the hydrolysis constant of the salt.