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The stoichiometry and solubility product of a salt

Question:

The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :

  1. $\mathrm{X}_{2} \mathrm{Y}, 2 \times 10^{-9} \mathrm{M}^{3}$

  2. $\mathrm{XY}_{2}, 1 \times 10^{-9} \mathrm{M}^{3}$

  3. $\mathrm{XY}_{2}, 4 \times 10^{-9} \mathrm{M}^{3}$

  4. XY, $2 \times 10^{-6} \mathrm{M}^{3}$


Correct Option: , 3

Solution:

From the graph \& dimensions salt is : $\mathrm{XY}_{2}$

${[\mathrm{X}]=1 \times 10^{-3} \mathrm{M} }$

${[\mathrm{Y}]=2 \times 10^{-3} \mathrm{M} }$

$\mathrm{XY}_{2}(\mathrm{~s}) \rightleftharpoons \mathrm{X}_{(\mathrm{aq})}^{2+}+2 \mathrm{Y}_{(\mathrm{aq} .)}^{-}$

$\mathrm{ksp}=\left[\mathrm{X}^{2+}\right]\left[\mathrm{Y}^{-}\right]^{2}$

$=\left(10^{-3}\right)\left(2 \times 10^{-3}\right)^{2}$

$=4 \times 10^{-9} \mathrm{M}^{3}$

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