At 298 K, the `K_(xp)` value of `Fe(OH)_(3)`, in aqucous solution is `3.8 xx 10^(-38)` . The solubility of `Fe^(3+)` ions will increase when

Options

A. `P^(H)` is increased
B. `P^(H)` is 7
C. `P^(H)` is decreased
D. Saturated solution is exposed to sun light

Answer

To solve the problem regarding the solubility of \( \text{Fe}^{3+} \) ions in the presence of \( \text{Fe(OH)}_3 \) at 298 K, we can follow these steps:

### Step 1: Write the dissociation equation for \( \text{Fe(OH)}_3 \)
The dissociation of \( \text{Fe(OH)}_3 \) in aqueous solution can be represented as:
\[ \text{Fe(OH)}_3 (s) \rightleftharpoons \text{Fe}^{3+} (aq) + 3 \text{OH}^- (aq) \]

### Step 2: Write the expression for the solubility product constant \( K_{sp} \)
The solubility product constant \( K_{sp} \) for this equilibrium can be expressed as:
\[ K_{sp} = [\text{Fe}^{3+}][\text{OH}^-]^3 \]
Given that \( K_{sp} = 3.8 \times 10^{-38} \).

### Step 3: Define the solubility in terms of \( S \)
Let the solubility of \( \text{Fe(OH)}_3 \) be \( S \). Then, at equilibrium:
- The concentration of \( \text{Fe}^{3+} \) ions will be \( S \).
- The concentration of \( \text{OH}^- \) ions will be \( 3S \).

Substituting these into the \( K_{sp} \) expression gives:
\[ K_{sp} = S \cdot (3S)^3 = S \cdot 27S^3 = 27S^4 \]

### Step 4: Relate \( K_{sp} \) to solubility \( S \)
Setting the expression for \( K_{sp} \) equal to the given value:
\[ 27S^4 = 3.8 \times 10^{-38} \]

### Step 5: Analyze the effect of changing conditions on solubility
The solubility of \( \text{Fe}^{3+} \) ions will increase if the concentration of \( \text{OH}^- \) ions in the solution decreases. This can happen through various means, such as:
- Adding a strong acid, which will react with \( \text{OH}^- \) ions and decrease their concentration, thus shifting the equilibrium to the right according to Le Chatelier's principle.

### Conclusion
Therefore, the solubility of \( \text{Fe}^{3+} \) ions will increase when the concentration of \( \text{OH}^- \) ions decreases, which is typically achieved by adding an acid to the solution.

### Final Answer
The correct answer is: **The solubility of \( \text{Fe}^{3+} \) ions will increase when the concentration of \( \text{OH}^- \) ions decreases.**

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