Solubility product expression of salt `MX_(4)` which is sparingly soluble with a solubility s can be given as

Options

A. `256s^(5)`
B. `16s^(3)`
C. `5c`
D. `25s^(4)`

Explanation

To derive the solubility product expression for the salt \( MX_4 \), which is sparingly soluble, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Dissociation of the Salt:**
The salt \( MX_4 \) dissociates in water according to the following reaction:
\[ MX_4 (s) \rightleftharpoons M^{+} (aq) + 4X^{-} (aq) \]
Here, \( M^{+} \) is the cation and \( X^{-} \) is the anion.

2. **Define Solubility:**
Let the solubility of \( MX_4 \) be \( s \). At equilibrium, the concentration of the ions will be:
- For \( M^{+} \): \( [M^{+}] = s \)
- For \( X^{-} \): Since there are 4 moles of \( X^{-} \) produced for every mole of \( MX_4 \), \( [X^{-}] = 4s \)

3. **Write the Expression for the Solubility Product (Ksp):**
The solubility product \( K_{sp} \) is given by the product of the concentrations of the ions, each raised to the power of their coefficients in the balanced equation:
\[ K_{sp} = [M^{+}][X^{-}]^4 \]

4. **Substitute the Ion Concentrations:**
Substitute the expressions for the concentrations of \( M^{+} \) and \( X^{-} \) into the \( K_{sp} \) expression:
\[ K_{sp} = (s)(4s)^4 \]

5. **Calculate \( (4s)^4 \):**
Calculate \( (4s)^4 \):
\[ (4s)^4 = 256s^4 \]

6. **Combine the Terms:**
Now substitute this back into the expression for \( K_{sp} \):
\[ K_{sp} = s \cdot 256s^4 = 256s^5 \]

### Final Expression:
Thus, the solubility product expression for the salt \( MX_4 \) is:
\[ K_{sp} = 256s^5 \]