A saturated solution of which silver salt has the highest concentration of $A g^{+}$ ?

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$A g C l, K_{s p} = 1.8 \times 10^{- 10}$

$A g B r, K_{s p} = 5.0 \times 10^{- 13}$

$A g_{2} S O_{3}, K_{s p} = 1.5 \times 10^{- 14}$

$A g_{2} C r O_{4}, K_{s p} = 1.1 \times 10^{- 12}$

answer is B.

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Detailed Solution

We can solve $[A g^{+}]$ for each choice as follows.
$[A g^{+}]$ in AgCl solution:
$K_{s p} = [A g^{+}] [C l^{-}] = {[A g^{+}]}^{2}$
$[A g^{+}] = \sqrt{K_{s p}} = \sqrt{1.8 \times 10^{- 10}} = 1.3 \times 10^{- 5} M$
$[A g^{+}] i n A g_{2} C r O_{4}$ solution:
$K_{s p} = {[A g^{+}]}^{2} [C r O_{4}^{2 -}] = \frac{1}{2} {[A g^{+}]}^{3}$
$[A g^{+}] = \sqrt[3]{2 \times K_{s p}} = \sqrt[3]{2 \times (1.1 \times 10^{- 12})} = 1.3 \times 10^{- 4} M$
$[A g^{+}]$ in AgBr solution:
$K_{S p} = [A g^{+}] [B r^{-}] = {[A g^{+}]}^{2}$
$[A g^{+}] = \sqrt{K_{s p}} = \sqrt{5.0 \times 10^{- 13}} = 7.1 \times 10^{- 7} M$
$[A g^{+}] i n A g_{2} S O_{3}$ solution:
$K_{s p} = {[A g^{+}]}^{2} [S O_{3}^{2 -}] = \frac{1}{2} {[A g^{+}]}^{3}$
$[A g^{+}] = \sqrt[3]{2 \times K_{s p}} = \sqrt[3]{2 \times (1.5 \times 10^{- 14})} = 3.1 \times 10^{- 5} M$