MY and `NY_(3)` two nearly insoluble salts, have the same `K_(sp)` values of `6.2xx10^(-13)` at room temperature. Which statement would be true in rearged to MY and `NY_(3)` ?

Options

A. The molar solubility of MY in water is less than that 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 MU and `NY_(3)` in water are identical.

Explanation

To solve the problem regarding the solubility of the salts MY and NY₃, we will follow these steps:

### Step 1: Understand the dissociation of salts
- MY dissociates into M⁺ and Y⁻ ions.
- NY₃ dissociates into N³⁺ and 3Y⁻ ions.

### Step 2: Write the expression for Ksp for MY
For MY:
- The dissociation can be represented as:
\[ MY (s) \rightleftharpoons M^+ (aq) + Y^- (aq) \]
- The solubility product (Ksp) expression is:
\[ K_{sp} = [M^+][Y^-] = s \cdot s = s^2 \]
where \( s \) is the molar solubility of MY.

### Step 3: Calculate the solubility of MY
Given \( K_{sp} = 6.2 \times 10^{-13} \):
\[ s^2 = 6.2 \times 10^{-13} \]
\[ s = \sqrt{6.2 \times 10^{-13}} \approx 7.87 \times 10^{-7} \, \text{mol/L} \]

### Step 4: Write the expression for Ksp for NY₃
For NY₃:
- The dissociation can be represented as:
\[ NY_3 (s) \rightleftharpoons N^{3+} (aq) + 3Y^- (aq) \]
- The Ksp expression is:
\[ K_{sp} = [N^{3+}][Y^-]^3 = s \cdot (3s)^3 = 27s^4 \]
where \( s \) is the molar solubility of NY₃.

### Step 5: Calculate the solubility of NY₃
Given \( K_{sp} = 6.2 \times 10^{-13} \):
\[ 27s^4 = 6.2 \times 10^{-13} \]
\[ s^4 = \frac{6.2 \times 10^{-13}}{27} \]
\[ s = \left( \frac{6.2 \times 10^{-13}}{27} \right)^{1/4} \approx 3.89 \times 10^{-4} \, \text{mol/L} \]

### Step 6: Compare the solubilities
- Solubility of MY: \( 7.87 \times 10^{-7} \, \text{mol/L} \)
- Solubility of NY₃: \( 3.89 \times 10^{-4} \, \text{mol/L} \)

Since \( 7.87 \times 10^{-7} < 3.89 \times 10^{-4} \), it follows that:
\[ \text{The molar solubility of MY is less than that of NY₃.} \]

### Conclusion
The correct statement regarding MY and NY₃ is that the molar solubility of MY is less than that of NY₃.

### Final Answer
The correct option is: **The molar solubility of MY is less than that of NY₃.**

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