STATEMENT-1: Solubility of `BaSO_(4)` in 0.1 M `Na_(2)SO_(4)is 10^(-9)` M hence its `K_(sp)` is `10^(-18).`
STATEMENT-2: In aqueous solution, solubility product of `BaSO_(4)=S^(2).` (Where S is solubility of `BaSO_(4)`)

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To solve the problem, we need to evaluate the two statements provided regarding the solubility product (Ksp) of barium sulfate (BaSO₄).

### Step-by-Step Solution:

**Step 1: Analyze Statement 1**
- The statement claims that the solubility of BaSO₄ in 0.1 M Na₂SO₄ is \(10^{-9}\) M and that its Ksp is \(10^{-18}\).
- When BaSO₄ dissolves, it dissociates into Ba²⁺ and SO₄²⁻ ions:
\[ \text{BaSO}_4 (s) \rightleftharpoons \text{Ba}^{2+} (aq) + \text{SO}_4^{2-} (aq) \]

**Step 2: Calculate the Effective Concentration of SO₄²⁻**
- In a 0.1 M Na₂SO₄ solution, Na₂SO₄ dissociates to give 0.1 M SO₄²⁻ ions:
\[ \text{Na}_2\text{SO}_4 \rightarrow 2 \text{Na}^+ + \text{SO}_4^{2-} \]
- Therefore, the total concentration of SO₄²⁻ ions in the solution is:
\[ [\text{SO}_4^{2-}] = 0.1 \, \text{M} + 10^{-9} \, \text{M} \approx 0.1 \, \text{M} \]
(since \(10^{-9}\) M is negligible compared to 0.1 M).

**Step 3: Calculate Ksp**
- The solubility product expression for BaSO₄ is:
\[ K_{sp} = [\text{Ba}^{2+}][\text{SO}_4^{2-}] \]
- Substituting the values:
\[ K_{sp} = (10^{-9})(0.1) = 10^{-10} \]
- The statement claims \(K_{sp} = 10^{-18}\), which is incorrect.

**Conclusion for Statement 1:**
- Statement 1 is **false**.

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**Step 4: Analyze Statement 2**
- The second statement claims that in aqueous solution, the solubility product of BaSO₄ is \(S^2\), where \(S\) is the solubility of BaSO₄.
- From the dissociation:
\[ \text{BaSO}_4 (s) \rightleftharpoons \text{Ba}^{2+} (aq) + \text{SO}_4^{2-} (aq) \]
- If the solubility of BaSO₄ is \(S\), then:
\[ [\text{Ba}^{2+}] = S \quad \text{and} \quad [\text{SO}_4^{2-}] = S \]
- Thus, the Ksp expression becomes:
\[ K_{sp} = S \cdot S = S^2 \]

**Conclusion for Statement 2:**
- Statement 2 is **true**.

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### Final Conclusion:
- Statement 1 is false, and Statement 2 is true. Therefore, the correct option is **D**.