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Question

Which of the following describes the correct relation for hydrolysis constant (Kh) for a salt of weak acid and weak base at 25C ?

A
Kh=KwKa×Kb
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B
Kh=KaKw×Kb
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C
Kh=Ka×KbKw
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D
Kb=KhKa×Kw
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Solution

The correct option is A Kh=KwKa×Kb
Salt of weak acid and weak base (WA) and (WB) :
CH3COOH weak acid + NH4OH weak base CH3COONH4
Partial dissociation (Close to 100% but not exact)
CH3COONH4(aq)NH+4(aq)+CH3COO(aq)
Hydrolysis :
NH+4(aq)+CH3COO(aq)+H2O(l)CH3COOH(aq)+NH4OH(aq)
C C 0 0
CCh CCh Ch Ch
Since both the acid and the base are weak, they will exist in dissociated form.
Kh=[NH4OH][CH3COOH][NH+4][CH3COO]

Finding KwKaKb

KwKaKb=[H3O+][OH][CH3COO][H3O+][CH3COOH]×[NH+4][OH][NH4OH]KwKaKb=[NH4OH][CH3COOH][NH+4][CH3COO]
so, KwKaKb=Kh

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