Derive the relationship between Kh, Kw, Ka.

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

Category: Ionic Equilibria

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