Suppose the simultaneous solubilities of AgSCN and AgBr are x and y moles L−1. Then as
AgSCN→Ag++SCN−
and AgBr→Ag++Br−
∴ Total [Ag+]=x+y moles L−1
[SCN−]=x moles L−1
[Br−]=y moles L−1
Ksp for AgSCN=[Ag+][SCB−]
=(x+y)x=1.0×10−12 (Given) ...................(i)
Ksp for AgBr=[Ag+][Br−]
=(x+y)y=5.0×10−13 (Given) ....................(ii)
Dividing (ii) by (i)
yx=0.5 or y=0.5 x
Putting in (i)
(x+0.5 x)x=10−12 or 1.5 x2=10−12
or x2=0.667×10−12
or x=0.82×10−6 mol L−1
∴ y=0.5 x=0.41×10−6 mol L−1
Solubility of AgSCN=0.82×10−6 mol L−1
Solubility of AgBr=0.41×10−6 mol L−1M