At 25° C, the solubility product values of $AgCI$ and $AgCNS$ are $1.8 x 10^{- 10}$ and $1.6 x 10^{- 11}$ respectively. When a solution is saturated with both solids, calculate the ratio $[{Cl}^{-}] / [{CNS}^{-}]$ and also $[{Ag}^{+}]$ in the solution.

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$11.25, 1.4 \times 10^{- 5} M$

$1.125, 4 \times 10^{- 6} M$

$1.25, 4 \times 10^{- 6} M$

$1.25, 4 \times 10^{- 5} M$

answer is B.

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Detailed Solution

The ratio $[{Cl}^{-}] / [{CNS}^{-}]$ and also $[{Ag}^{+}]$ in the solution.

$\begin{array}{ll} K_{s p_{1}} = [{Ag}^{+}] [{Cl}^{-}]; K_{s p_{2}} = [{Ag}^{+}] [{CNS}^{-}] \\ \frac{K_{s p_{1}}}{K_{s p_{2}}} = \frac{[{Cl}^{-}]}{[CNS]}; [{Ag}^{+}] = \sqrt{K_{s p_{1}} + K_{s p_{2}}} \end{array}$

$11.25, 1.4 \times 10^{- 5} M$

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