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Question

Simultaneous solubility of AgCNS (a) and AgBr (b) in a solution of water will be

Ksp(AgBr)=5×1013 and Ksp(AgCNS)=1012

A
a=4.08×107mol litre1; b=8.16×107 mol litre1
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B
a=4.08×107mol litre1; b=4.08×107 mol litre1
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C
a=8.16×107mol litre1; b=4.08×107 mol litre1
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D
None of these
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Solution

The correct option is B a=8.16×107mol litre1; b=4.08×107 mol litre1
Suppose solubility of AgCNS and AgBr in a solution are a and b respectively.
AgCNS(s)Ag+(aq)a+b+CNS(aq)a
AgBr(s)Ag+a+b+Brb
[Ag2+]=(a+b);[CNS]=a and [Br]=b
For AgCNS:KspAgCNS=[Ag+][CNS]
or 1×1012=(a+b)(a)......(i)
For AgBr:KspAgBr=[Ag+][Br]
or 5×1013=(a+b)(b)........(ii)

By Eqs (i) and (ii), we get
ab=10125×1013=2 (a=2b)
By Eq (i)
(2b+b)(2b)=1×1012
6b2=1×1012
or b=4.08×107 mol litre1
Similarly by Eq (ii)
[a+(a/2)]a=1×1012
a=8.16×107 mol litre1

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