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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 $NY_3$?
A
The molar solubility of MY in water is less than of $NY_3$.
B
The salts MY and $NY_3$ are more soluble in 0.5 M KY than in pure water.
C
The addition of the salt of KY to solution of MY and $NY_3$ will have no effect on their solubilities.
D
The molar solubilities of MY and $NY_3$ in water are identical.
Explanation
Same $K_{sp}$ but different stoichiometry gives different s.
Detailed Solution
For MY: $MY \rightleftharpoons M^+ + Y^-$; $K_{sp} = s^2 \Rightarrow s = \sqrt{6.2\times10^{-13}} = 7.874\times10^{-7}$
For $NY_3$: $NY_3 \rightleftharpoons N^{3+} + 3Y^-$; $K_{sp} = s(3s)^3 = 27s^4 \Rightarrow s = \sqrt[4]{\frac{6.2\times10^{-13}}{27}} = 3.89\times10^{-4}$
Hence the molar solubility of MY in water is less than that of $NY_3$.
For $NY_3$: $NY_3 \rightleftharpoons N^{3+} + 3Y^-$; $K_{sp} = s(3s)^3 = 27s^4 \Rightarrow s = \sqrt[4]{\frac{6.2\times10^{-13}}{27}} = 3.89\times10^{-4}$
Hence the molar solubility of MY in water is less than that of $NY_3$.