`A(OH)_(2)` is a partially soluble substance and its `K_(sp) ` value is `4 xx 10^(-12)` . Which of the following statement is / are correct ?

Options

A. The solubility is unaffected by pH of the medium
B. Its solubility increases in a buffered medium having pH = 2
C. Its solubility decreases in a buffered medium having pH=9
D. Its saturated solution has pH = 10.3

Answer

To solve the question regarding the solubility of the partially soluble substance \( A(OH)_2 \) with a given \( K_{sp} \) value of \( 4 \times 10^{-12} \), we will analyze the statements provided.

### Step-by-Step Solution:

1. **Understanding the Dissociation of \( A(OH)_2 \)**:
- The dissociation of \( A(OH)_2 \) in water can be represented as:
\[ A(OH)_2 \rightleftharpoons A^{2+} + 2OH^{-} \]
- From this, we can see that for every mole of \( A(OH)_2 \) that dissolves, it produces 1 mole of \( A^{2+} \) and 2 moles of \( OH^{-} \).

2. **Writing the Expression for \( K_{sp} \)**:
- The solubility product constant \( K_{sp} \) can be expressed as:
\[ K_{sp} = [A^{2+}][OH^{-}]^2 \]
- If we let the solubility of \( A(OH)_2 \) be \( S \), then:
\[ [A^{2+}] = S \quad \text{and} \quad [OH^{-}] = 2S \]
- Substituting these into the \( K_{sp} \) expression gives:
\[ K_{sp} = S(2S)^2 = 4S^3 \]

3. **Calculating the Solubility \( S \)**:
- Setting \( K_{sp} = 4 \times 10^{-12} \):
\[ 4S^3 = 4 \times 10^{-12} \]
- Dividing both sides by 4:
\[ S^3 = 10^{-12} \]
- Taking the cube root:
\[ S = 10^{-4} \, \text{mol/L} \]

4. **Determining the Concentration of \( OH^{-} \)**:
- Since \( [OH^{-}] = 2S \):
\[ [OH^{-}] = 2 \times 10^{-4} = 2 \times 10^{-4} \, \text{mol/L} \]

5. **Finding the pOH and pH**:
- The pOH can be calculated as:
\[ pOH = -\log[OH^{-}] = -\log(2 \times 10^{-4}) = -\log(2) - \log(10^{-4}) = -0.301 + 4 \approx 3.699 \]
- Therefore, the pH is:
\[ pH = 14 - pOH = 14 - 3.699 \approx 10.301 \]

6. **Analyzing the Statements**:
- **Statement 1**: "Solubility is unaffected by pH of the medium." - **Incorrect**. The solubility is affected by pH, as shown by the reactions with \( H^+ \).
- **Statement 2**: "Its solubility increases in a buffer medium having pH equal to 2." - **Correct**. In acidic conditions, \( H^+ \) ions will react with \( OH^{-} \), removing them from the solution and shifting the equilibrium to the right.
- **Statement 3**: "Its solubility decreases in a buffer medium having pH equal to 9." - **Correct**. In basic conditions, the concentration of \( OH^{-} \) increases, shifting the equilibrium to the left and decreasing solubility.
- **Statement 4**: "Its saturated solution has pH equal to 10.3." - **Correct**. We calculated the pH to be approximately 10.301.

### Conclusion:
The correct statements are **2, 3, and 4**.