At room temperature, MY and $NY_3$, two nearly insoluble salts, have the same $K_{sp}$ values of $6.2 imes 1

Question

At room temperature, MY and $NY_3$, two nearly insoluble salts, have the same $K_{sp}$ values of $6.2 	imes 10^{-13}$. The true statement regarding MY and $NY_3$ is:

Accepted Answer

Let the molar solubility of MY be $S_1$.
$MY ightleftharpoons M^+ + Y^-$
$K_{sp} = S_1 	imes S_1 = S_1^2$
$S_1 = \sqrt{6.2 	imes 10^{-13}} = \sqrt{62 	imes 10^{-14}} \approx 7.87 	imes 10^{-7} 	ext{ M}$

Let the molar solubility of $NY_3$ be $S_2$.
$NY_3 ightleftharpoons N^{3+} + 3Y^-$
$K_{sp} = S_2 	imes (3S_2)^3 = 27S_2^4$
$S_2 = \left(\frac{6.2 	imes 10^{-13}}{27}ight)^{1/4} = \left(\frac{6200 	imes 10^{-16}}{27}ight)^{1/4} \approx (229.6 	imes 10^{-16})^{1/4} \approx 3.89 	imes 10^{-4} 	ext{ M}$

Comparing $S_1$ and $S_2$, we find that $S_1 < S_2$. Therefore, the molar solubility of MY in water is less than that of $NY_3$.
Furthermore, the addition of KY will decrease the solubility of both salts due to the common ion ($Y^-$) effect. Thus, the other statements are false.

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