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The solubility of ${Ag}_{2} {CO}_{3}$ in water at 25° C is $1 x 10^{- 4} mole / litre$ . What is its solubility in $0.01 M {Na}_{2} {CO}_{3}$ solution? Assume no hydrolysis of ${CO}_{3}^{2 -}$ ion.

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$6 \times 10^{- 6} mole/itre$

$2 \times 10^{- 5} mole/litre$

$10^{- 5} mole/litre$

$4 \times 10^{- 5} mole/itre$

answer is C.

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Detailed Solution

$K_{sp} = 4 \times {(10^{- 4})}^{3} = 4 \times 10^{- 12}$

${Ag}_{2} {CO}_{3} ⟶ \underset{2 s}{2 {Ag}^{+}} + \underset{0.01}{{CO}_{3}^{2 -}}$

$\begin{array}{l} 4 s^{2} \times 0.01 = 4 \times 10^{- 12} \\ \Rightarrow s = 10^{- 5} M \end{array}$

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