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NEET CHEMISTRYMedium

At room temperature, MY and NY3NY_3, two nearly insoluble salts, have the same KspK_{sp} values of 6.2×10136.2 \times 10^{-13}. The true statement regarding MY and NY3NY_3 is:

A

The molar solubility of MY in water is less than that of NY3NY_3.

B

The salts MY and NY3NY_3 are more soluble in 0.5 M KY than in pure water.

C

The addition of the salt of KY to a solution of MY and NY3NY_3 will have no effect on their solubilities.

D

The molar solubilities of MY and NY3NY_3 in water are identical.

Step-by-Step Solution

Let the molar solubility of MY be S1S_1. MYM++YMY \rightleftharpoons M^+ + Y^- Ksp=S1×S1=S12K_{sp} = S_1 \times S_1 = S_1^2 S1=6.2×1013=62×10147.87×107 MS_1 = \sqrt{6.2 \times 10^{-13}} = \sqrt{62 \times 10^{-14}} \approx 7.87 \times 10^{-7} \text{ M}

Let the molar solubility of NY3NY_3 be S2S_2. NY3N3++3YNY_3 \rightleftharpoons N^{3+} + 3Y^- Ksp=S2×(3S2)3=27S24K_{sp} = S_2 \times (3S_2)^3 = 27S_2^4 S2=(6.2×101327)1/4=(6200×101627)1/4(229.6×1016)1/43.89×104 MS_2 = \left(\frac{6.2 \times 10^{-13}}{27}\right)^{1/4} = \left(\frac{6200 \times 10^{-16}}{27}\right)^{1/4} \approx (229.6 \times 10^{-16})^{1/4} \approx 3.89 \times 10^{-4} \text{ M}

Comparing S1S_1 and S2S_2, we find that S1<S2S_1 < S_2. Therefore, the molar solubility of MY in water is less than that of NY3NY_3. Furthermore, the addition of KY will decrease the solubility of both salts due to the common ion (YY^-) effect. Thus, the other statements are false.

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