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Question

At 25C, the solubility product values of AgCl and AgCNS are 1.7×1010 and 1.0×1012 respectively. When water is saturated with both solids, calculate the ratio [Cl]/[CNS] and also [Ag+] in the solution.

A
1.3×102, 1.7×105M
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B
1.7×102, 1.308×105M
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C
1.3×104, 1.308×104M
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D
1.7×103, 1.67×106M
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Solution

The correct option is B 1.7×102, 1.308×105M
AgCNSAg++CNS
(1δ1) (δ+δ2) δ1
AgClAg++Cl
(1δ2) (δ+δ2) δ2
(Ksp)AgCNS=(δ1)(δ1+δ2) ................(i)
(Ksp)AgCl=(δ2)(δ1+δ2) ......................(ii)
Adding equation (i) and (ii), we get
(δ1+δ2)2=(Ksp)AgCNS+(Ksp)AgCl
(δ1+δ2)=(Ksp)AgCNS+(Ksp)AgCl=1.0×1012+1.7×1010
(AgT)=(δ1+δ2)=1.3×105
Divide equation (ii) from (i), we get
[Cl][CNS]=δ2δ1=1.7×10101.0×10121.7×102

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