For a `MX_2` type salt if `K_(sp)` is solubility product, then solubility will be

Options

A. `S=sqrt(K_(sp)/(2))`
B. `S=3sqrt(K_(sp)/(4))`
C. `S=3sqrt(K_(sp)/(6))`
D. `S=3sqrt(K_(sp)/(8))`

Answer

To find the solubility of an MX₂ type salt in terms of its solubility product (Ksp), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Salt and Its Dissociation**:
- Let the salt be MX₂, where M is a cation and X is an anion.
- When MX₂ dissolves in water, it dissociates according to the following equation:
\[ \text{MX}_2 (s) \rightleftharpoons \text{M}^{2+} (aq) + 2 \text{X}^{-} (aq) \]

2. **Define Solubility**:
- Let the solubility of MX₂ be \( S \) moles per liter. This means that when MX₂ dissolves, \( S \) moles of MX₂ will produce \( S \) moles of M²⁺ and \( 2S \) moles of X⁻.

3. **Write the Expression for Ksp**:
- The solubility product (Ksp) expression for the dissociation of MX₂ is given by:
\[ K_{sp} = [\text{M}^{2+}][\text{X}^{-}]^2 \]
- Substituting the concentrations in terms of solubility \( S \):
\[ K_{sp} = [S][2S]^2 \]

4. **Simplify the Ksp Expression**:
- Expanding the expression:
\[ K_{sp} = S \cdot (2S)^2 = S \cdot 4S^2 = 4S^3 \]

5. **Rearranging to Find Solubility**:
- To find the solubility \( S \) in terms of Ksp:
\[ S^3 = \frac{K_{sp}}{4} \]
- Taking the cube root of both sides:
\[ S = \sqrt[3]{\frac{K_{sp}}{4}} \]

### Final Result:
Thus, the solubility \( S \) of the MX₂ type salt in terms of its solubility product \( K_{sp} \) is:
\[ S = \sqrt[3]{\frac{K_{sp}}{4}} \]