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Question

Calculate the simultaneous solubility of AgSCN and AgBr.

(Ksp(AgSCN)=1.1×1012, Ksp(AgBr)=5×1013)

A
4×107 mol/L AgBr; 9×107 mol/L AgSCN
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B
9×107 mol/L AgBr; 4×107 mol/L AgSCN
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C
8×107 mol/L AgBr; 18×107 mol/L AgSCN
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D
18×107 mol/L AgBr; 8×107 mol/L AgSCN
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Solution

The correct option is A 4×107 mol/L AgBr; 9×107 mol/L AgSCN
Let a M be the solubility of AgSCN and b M be the solubility of AgBr.
AgSCNAg+a+CNSb
AgBrAg+b+Brb
[Ag+]=(a+b)
[CNS]=a
[Br]=b

Ksp(AgCNS)=[Ag+][CNS]
1×1012=(a+b)a......(i)

Ksp(AgBr)=[Ag+][Br]
5×1013=(a+b)b.....(ii)

Dividing equation (i) by equation (ii), we get
ab=1×10125×1013=2
a=2b or b=a2
Substittue the value of (a) in (i),
(a+b)a=1012
(2a+b)2b=1012
4b2+2b2=1012
b=4.08×107
This is the solubility of AgBr.
Substitute the value b=a2 in equation (i),
(a+b)a=1012
(a+a2)a=1012
3a2=2×1012
a=8.16×107M
This is the solubility of AgSCN.

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