Concentration of the Ag + ions in a saturated solution of Ag 2 C 2 O 4 is 2 . 2 × 10 - 4 mol L - 1 . Solubility product of Ag 2 C 2 O 4 is [2017]

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Solution

Q.
Concentration of the ${Ag}^{+}$ ions in a saturated solution of ${Ag}_{2} C_{2} O_{4}$ is $2.2 \times 10^{- 4}$ $mol$ $L^{- 1}$ . Solubility product of ${Ag}_{2} C_{2} O_{4}$ is [2017]

1 $2.66 \times 10^{- 12}$

2 $4.5 \times 10^{- 11}$

3 $5.3 \times 10^{- 12}$

4 $2.42 \times 10^{- 8}$

Ans.
(3)

Let solubility of ${Ag}_{2} C_{2} O_{4}$ be $s$ $mol$ $L^{- 1}$

$\underset{s}{{Ag}_{2} C_{2} O_{4 (s)}} ⇌ \underset{2 s}{2 {Ag}_{(aq)}^{+}} + \underset{s}{C_{2} O_{4 (aq)}^{2 -}}$

$K_{sp} = {[{Ag}^{+}]}^{2} [C_{2} O_{4}^{2 -}]$

$K_{sp} = {(2 s)}^{2} (s) = 4 s^{3}$

$K_{sp} = 4 \times {(1.1 \times 10^{- 4})}^{3} (∵ [{Ag}^{+}] = 2 s = 2.2 \times 10^{- 4})$

$K_{sp} = 5.3 \times 10^{- 12}$

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