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. **Identify the Dissociation of the Salt**:
The salt MX₂ dissociates in water according to the following equation:
\[ MX_2 (s) \rightleftharpoons M^{2+} (aq) + 2X^{-} (aq) \]
Here, M is the cation and X is the anion.

2. **Define Solubility**:
Let the solubility of the salt MX₂ be denoted as \( s \). This means that when MX₂ dissolves, the concentration of M²⁺ ions will be \( s \) and the concentration of X⁻ ions will be \( 2s \) (since there are two X⁻ ions for every one MX₂ that dissolves).

3. **Write the Expression for Ksp**:
The solubility product (Ksp) is defined as:
\[ K_{sp} = [M^{2+}][X^{-}]^2 \]
Substituting the concentrations in terms of \( s \):
\[ K_{sp} = [s][2s]^2 \]

4. **Simplify the Expression**:
Now, we can simplify the expression:
\[ K_{sp} = s \cdot (2s)^2 = s \cdot 4s^2 = 4s^3 \]

5. **Solve for Solubility (s)**:
Rearranging the equation to solve for \( s \):
\[ s^3 = \frac{K_{sp}}{4} \]
Taking the cube root of both sides gives:
\[ s = \left(\frac{K_{sp}}{4}\right)^{\frac{1}{3}} \]

### Final Answer:
The solubility \( s \) of the MX₂ type salt in terms of its solubility product \( K_{sp} \) is:
\[ s = \left(\frac{K_{sp}}{4}\right)^{\frac{1}{3}} \]

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