If the concentration of $\mathrm{Ag}^{+}$ions in the saturated solution of $\mathrm{Ag}_2 \mathrm{CO}_3$ is…
If the concentration of $\mathrm{Ag}^{+}$ions in the saturated solution of $\mathrm{Ag}_2 \mathrm{CO}_3$ is $1.20 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$, then find the solubility product of $\mathrm{Ag}_2 \mathrm{CO}_3$.
$5.30 \times 10^{-12}$
$4.50 \times 10^{-11}$
$2.66 \times 10^{-12}$
$6.90 \times 10^{-12}$
Solution
$\mathrm{Ag}_2 \mathrm{CO}_3 \longrightarrow 2 \mathrm{Ag}^{+}+\mathrm{CO}_3^{2-}$
Let solubility be $S$.
The solubility of silver will be $2 S$ as two moles ions are dissociated.
$$
\begin{aligned}
K_{\text {sp }} & =\left[\mathrm{Ag}^{+}ight]^2\left[\mathrm{CO}_3^{2-}ight] \\
K_{\text {sp }} & =(2 S)^2 \times S=4 S^3 \\
S & =1.20 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \text { (given) } \\
K_{\text {sp }} & =4 \times\left(1.20 \times 10^{-4}ight)^3=6.90 \times 10^{-12}
\end{aligned}
$$