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Question

Consider the solubility of AgCN in water. If x is amount of CN that gets hydrolysed by water and s is the solubility of AgCN when two equilibriums are coexisting :
AgCN(s)KspAg+(aq)+CN(aq)
CN(aq)+H2O(l)KhHCN(aq)+OH(aq)

Which of the following relation is correct?

A
KwKa=Kh=s+xx2
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B
KwKa=Kh=sx2+s
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C
KwKa=Kh=sxx2
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D
KwKa=Kh=x2sx
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Solution

The correct option is D KwKa=Kh=x2sx

Theory:
Solubility of salt in water :
Solubility of salt in water containing anion from weak acid . Example - AgCN

AgCN(s)KspAg+(aq)+CN(aq)

CN(aq)+H2O(l)KhHCN(aq)+OH(aq)

Adding the above two reactions the overall reaction is:

AgCN(s)+H2O(l)Ag+(aq)+HCN(aq)+OH(aq)

AgCN(s)Ag+(aq)+CN(aq)
s (sx)
CN(aq)+H2O(l)KhHCN(aq)+OH(aq)
sx x x

Ksp=s(sx)

KwKa=x2sx=Kh

Also, Ksp×Kh=s.x2

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