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Question

Calculate the simultaneous solubility of AgSCN and AgBr. Ksp for AgSCN and AgBr are 1.0×1012 and 5.0×1013 respectively.

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Solution

Suppose the simultaneous solubilities of AgSCN and AgBr are x and y moles L1. Then as
AgSCNAg++SCN
and AgBrAg++Br
Total [Ag+]=x+y moles L1
[SCN]=x moles L1
[Br]=y moles L1
Ksp for AgSCN=[Ag+][SCB]
=(x+y)x=1.0×1012 (Given) ...................(i)
Ksp for AgBr=[Ag+][Br]
=(x+y)y=5.0×1013 (Given) ....................(ii)
Dividing (ii) by (i)
yx=0.5 or y=0.5 x
Putting in (i)
(x+0.5 x)x=1012 or 1.5 x2=1012
or x2=0.667×1012
or x=0.82×106 mol L1
y=0.5 x=0.41×106 mol L1
Solubility of AgSCN=0.82×106 mol L1
Solubility of AgBr=0.41×106 mol L1M

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