The solubility of `Fe(OH)_(3)` would be maximum in :

Options

A. 0.1 M NaOH
B. 0.1 M HCl
C. 0.1 M KOH
D. 0.1M `H_(2)SO_(4)`

Answer

To determine the conditions under which the solubility of `Fe(OH)3` is maximized, we need to analyze how the solubility product constant (Ksp) and the concentration of hydroxide ions (OH⁻) affect the solubility of the compound.

### Step-by-Step Solution:

1. **Understanding the Dissolution Reaction**:
- The dissolution of `Fe(OH)3` can be represented as:
\[ Fe(OH)_3 (s) \rightleftharpoons Fe^{3+} (aq) + 3OH^{-} (aq) \]
- The solubility product (Ksp) expression for this equilibrium is:
\[ K_{sp} = [Fe^{3+}][OH^{-}]^3 \]

2. **Effect of Hydroxide Ion Concentration**:
- The solubility of `Fe(OH)3` is inversely related to the concentration of hydroxide ions (OH⁻). If the concentration of OH⁻ increases, the solubility of `Fe(OH)3` decreases due to the common ion effect.

3. **Adding Acid**:
- When an acid (like HCl or H2SO4) is added to the solution, it increases the concentration of H⁺ ions. The H⁺ ions will react with OH⁻ ions to form water:
\[ H^{+} + OH^{-} \rightarrow H_2O \]
- This reaction decreases the concentration of OH⁻ ions, which shifts the equilibrium to the right, thus increasing the solubility of `Fe(OH)3`.

4. **Comparing Different Acids**:
- HCl provides 1 mole of H⁺ per mole of HCl.
- H2SO4 provides 2 moles of H⁺ per mole of H2SO4.
- Therefore, H2SO4 will be more effective in decreasing the concentration of OH⁻ ions compared to HCl, leading to a greater increase in the solubility of `Fe(OH)3`.

5. **Conclusion**:
- The maximum solubility of `Fe(OH)3` will occur in a solution with a strong acid, particularly H2SO4, due to its higher contribution of H⁺ ions compared to HCl.

### Final Answer:
The solubility of `Fe(OH)3` would be maximum in a solution of H2SO4.