$MY and {NY}_{3}$ , two nearly insoluble salts, have the same $K_{sp}$ values of $6.2 \times 10^{- 13}$ at room temperature. Which statement would be true in regard to $MY and {NY}_{3}$ ?

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$The molar solubilities of MY and {NY}_{3} in water are identical .$

$The addition of the salt of KY to solution of MYand {NY}_{3} will have no effect on their solubilities .$

$The molar solubility of MY in water is less than that of {NY}_{3}$

$The salts MY and {NY}_{3} are more soluble in 0.5 M KY than in pure water .$

answer is D.

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Detailed Solution

For MY: $K_{sp} = s_{1}^{2}$

$\Rightarrow s_{1} = \sqrt{K_{sp}} = \sqrt{6.2 \times 10^{- 13}} = 7.87 \times 10^{- 7} mol L^{- 1}$

For ${NY}_{3}$ : $K_{sp} = 27 s_{2}^{4} \Rightarrow s_{2} = \sqrt[4]{\frac{6.2 \times 10^{- 13}}{27}}$

$\Rightarrow s_{2} = 3.89 \times 10^{- 4} mol L^{- 1}$

$Hence, molar solubility of MY in water is less than that of {NY}_{3}$ .

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