The solubility product of a sparingly soluble salt $\mathrm{AX}_2$ is $3.2 \times 10^{-8}$. What is it's…

The solubility product of a sparingly soluble salt $\mathrm{AX}_2$ is $3.2 \times 10^{-8}$. What is it's solubility in $\mathrm{mol} \mathrm{dm}^{-3}$
  1. $2.8 \times 10^{-4}$
  2. $1.6 \times 10^{-5}$
  3. $2.0 \times 10^{-3}$
  4. $4.0 \times 10^{-4}$

Solution

\(\underset{\large \mathrm{t}_{eq}}{\mathrm{AX}_{2(\mathrm{s})}} \rightleftharpoons \underset{\large \mathrm{S}}{\mathrm{A}_{(\mathrm{aq})}^{2+}}+\underset{\large 2\mathrm{S}}{2 \mathrm{X}_{(\mathrm{aq})}^{-}}\) $\begin{aligned} & \mathrm{Ksp}=\left[\mathrm{A}^{2+}\right]\left[\mathrm{X}^{-}\right]^2 \\ & =\mathrm{S}(2 \mathrm{~S})^2 \\ & =4 \mathrm{~S}^3 \\ & 3.2 \times 10^{-8} 4 \mathrm{~S}^3 \\ & \mathrm{~S}^3=\frac{32}{4} \times 10^{-9}=8 \times 10^{-9} \\ & \mathrm{~S}=2 \times 10^{-3} \mathrm{~mol} . \mathrm{dm}^{-3} \text {. } \\ & \end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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