Solubility product constant `K_(sp)` of salts of types MX, `MX_(2)` and `M_(3)X` at temperature ‘T’ are `4.0xx10^(-8), 3.2xx10^(-14)`, and `2.7xx10^(-15)` respectively. Which salt has maximum solubility.

Options

A. MX
B. `M_(3)X`
C. `MX_(2)`
D. can’t be predicted

Explanation

To determine which salt has the maximum solubility among the salts MX, MX₂, and M₃X, we will calculate the solubility (S) of each salt using their respective solubility product constants (Ksp).

### Step 1: Calculate solubility for MX
For the salt MX, it dissociates in water as follows:
\[ \text{MX} \rightleftharpoons \text{M}^+ + \text{X}^- \]

Let the solubility of MX be \( S \). Therefore, at equilibrium:
- Concentration of \( \text{M}^+ = S \)
- Concentration of \( \text{X}^- = S \)

The expression for the solubility product \( K_{sp} \) is given by:
\[ K_{sp} = [\text{M}^+][\text{X}^-] = S \cdot S = S^2 \]

Given \( K_{sp} = 4.0 \times 10^{-8} \):
\[ S^2 = 4.0 \times 10^{-8} \]
\[ S = \sqrt{4.0 \times 10^{-8}} = 2.0 \times 10^{-4} \]

### Step 2: Calculate solubility for MX₂
For the salt MX₂, it dissociates as follows:
\[ \text{MX}_2 \rightleftharpoons \text{M}^+ + 2\text{X}^- \]

Let the solubility of MX₂ be \( S \). Therefore, at equilibrium:
- Concentration of \( \text{M}^+ = S \)
- Concentration of \( \text{X}^- = 2S \)

The expression for the solubility product \( K_{sp} \) is:
\[ K_{sp} = [\text{M}^+][\text{X}^-]^2 = S \cdot (2S)^2 = S \cdot 4S^2 = 4S^3 \]

Given \( K_{sp} = 3.2 \times 10^{-14} \):
\[ 4S^3 = 3.2 \times 10^{-14} \]
\[ S^3 = \frac{3.2 \times 10^{-14}}{4} = 8.0 \times 10^{-15} \]
\[ S = \sqrt[3]{8.0 \times 10^{-15}} \approx 2.0 \times 10^{-5} \]

### Step 3: Calculate solubility for M₃X
For the salt M₃X, it dissociates as follows:
\[ \text{M}_3\text{X} \rightleftharpoons 3\text{M}^+ + \text{X}^{3-} \]

Let the solubility of M₃X be \( S \). Therefore, at equilibrium:
- Concentration of \( \text{M}^+ = 3S \)
- Concentration of \( \text{X}^{3-} = S \)

The expression for the solubility product \( K_{sp} \) is:
\[ K_{sp} = [\text{M}^+]^3[\text{X}^{3-}] = (3S)^3 \cdot S = 27S^4 \]

Given \( K_{sp} = 2.7 \times 10^{-15} \):
\[ 27S^4 = 2.7 \times 10^{-15} \]
\[ S^4 = \frac{2.7 \times 10^{-15}}{27} = 1.0 \times 10^{-16} \]
\[ S = \sqrt[4]{1.0 \times 10^{-16}} = 10^{-4} \]

### Step 4: Compare solubilities
Now, we have the solubility values for each salt:
- For MX: \( S = 2.0 \times 10^{-4} \)
- For MX₂: \( S \approx 2.0 \times 10^{-5} \)
- For M₃X: \( S = 10^{-4} \)

### Conclusion
The maximum solubility is for the salt MX, which has a solubility of \( 2.0 \times 10^{-4} \).