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 addition of the salt of KY to solution of MY and `NY_3` will have no effect on their solubilities
B. The molar solubilities of MY and `NY_3` in water are identical
C. The molar solubility of MY in water is less than that of `NY_3`
D. The salts MY and `NY_3` are more soluble in 0.5 M KY than in pure water

Answer

To solve the problem regarding the two nearly insoluble salts MY and NY₃ with the same Ksp values of \(6.2 \times 10^{-13}\), we will analyze their solubility and the implications of their dissociation in water.

### Step-by-Step Solution:

1. **Understanding Ksp**:
The solubility product constant (Ksp) is a measure of the solubility of a salt in water. For a salt that dissociates into ions, Ksp can be expressed in terms of the molar solubility (S) of the salt.

2. **Dissociation of MY**:
For the salt MY, we can write the dissociation equation as:
\[ MY \rightleftharpoons M^+ + Y^- \]
If the solubility of MY is \(S\), then:
\[ Ksp = [M^+][Y^-] = S \cdot S = S^2 \]
Therefore,
\[ S = \sqrt{Ksp} = \sqrt{6.2 \times 10^{-13}} \approx 7.88 \times 10^{-7} \text{ M} \]

3. **Dissociation of NY₃**:
For the salt NY₃, the dissociation can be represented as:
\[ NY_3 \rightleftharpoons N^{3+} + 3Y^- \]
If the solubility of NY₃ is \(S\), then:
\[ Ksp = [N^{3+}][Y^-]^3 = S \cdot (3S)^3 = S \cdot 27S^3 = 27S^4 \]
Thus,
\[ S = \left(\frac{Ksp}{27}\right)^{1/4} = \left(\frac{6.2 \times 10^{-13}}{27}\right)^{1/4} \]
Calculating this gives:
\[ S \approx 3.9 \times 10^{-4} \text{ M} \]

4. **Comparison of Solubilities**:
Now we can compare the solubilities:
- Solubility of MY: \(7.88 \times 10^{-7} \text{ M}\)
- Solubility of NY₃: \(3.9 \times 10^{-4} \text{ M}\)

Since \(3.9 \times 10^{-4} > 7.88 \times 10^{-7}\), we conclude that the molar solubility of NY₃ is greater than that of MY.

5. **Analyzing the Options**:
- **Option 1**: The addition of the salt of KY₂ solution of MY and NY₃ will have no effect on their solubilities. (Incorrect due to common ion effect)
- **Option 2**: The molar solubilities of MY and NY₃ in water are identical. (Incorrect, they are different)
- **Option 3**: The molar solubility of MY in water is less than that of NY₃. (Correct)
- **Option 4**: The salts MY and NY₃ are more soluble in 0.5 M KY than in pure water. (Incorrect due to common ion effect)

### Conclusion:
The correct statement is that the molar solubility of MY in water is less than that of NY₃.