Assertion (A): `Na_(2)SO_(4)` is soluble in water while `BaSO_(4)` is insoluble.
Reason (R ): Latice enthalpy of `BaSO_(4)` exceeds its hydration enthalpy.

Options

A. If both A and R are true and R is the correct explanation of A.
B. If both A and R are true but R is not the correct explanation of A.
C. If A is true but R is false
D. If A is false but R is true.

Explanation

To solve the assertion and reason question regarding the solubility of sodium sulfate (`Na₂SO₄`) and barium sulfate (`BaSO₄`), we will analyze both the assertion and the reason step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that `Na₂SO₄` is soluble in water while `BaSO₄` is insoluble.
- This is a known fact in chemistry. Sodium sulfate is soluble in water due to its ionic nature and the ability of its ions to interact favorably with water molecules. In contrast, barium sulfate is known to be insoluble in water.

2. **Understanding the Reason**:
- The reason states that the lattice enthalpy of `BaSO₄` exceeds its hydration enthalpy.
- Lattice enthalpy is the energy required to break the ionic bonds in a solid ionic compound to form gaseous ions. Hydration enthalpy is the energy released when these gaseous ions are surrounded by water molecules.
- For a compound to dissolve, the energy released during hydration must be greater than the energy required to break the lattice (lattice enthalpy). If the lattice enthalpy is greater than the hydration enthalpy, the compound will not dissolve.

3. **Comparing Lattice and Hydration Enthalpies**:
- `BaSO₄` has a high lattice enthalpy due to the strong ionic bonds formed between barium ions and sulfate ions.
- The hydration enthalpy of `BaSO₄` is relatively low compared to its lattice enthalpy, which means that not enough energy is released during hydration to overcome the energy required to break the ionic lattice.
- In contrast, `Na₂SO₄` has a lower lattice enthalpy and a higher hydration enthalpy, allowing it to dissolve in water.

4. **Conclusion**:
- Both the assertion and the reason are true. The reason accurately explains why the assertion is correct. Thus, the correct answer is that both statements are true, and the reason is the correct explanation of the assertion.

### Final Answer:
- Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.