Sodium sulphate is soluble in water,whereas barium sulphate is sparingly soluble because

Options

A. the hydration energy of sodium sulphate is less than it lattice energy
B. The hydration energy of sodium sulphate is more than its lattice energy
C. The hydration and lattice energy are same in sodium sulphate
D. The lattice energy has no role to play solublity.

Answer

To explain why sodium sulfate is soluble in water while barium sulfate is sparingly soluble, we need to analyze the concepts of lattice energy and hydration energy.

### Step-by-Step Solution:

1. **Understanding Lattice Energy and Hydration Energy**:
- **Lattice Energy**: This is the energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic compound. Higher lattice energy indicates a stronger attraction between the ions.
- **Hydration Energy**: This is the energy released when ions are surrounded by water molecules. It reflects how well the ions interact with water. Higher hydration energy indicates that the ions are more effectively solvated by water.

2. **Comparing Sodium Sulfate and Barium Sulfate**:
- Sodium sulfate (Na₂SO₄) consists of sodium ions (Na⁺) and sulfate ions (SO₄²⁻).
- Barium sulfate (BaSO₄) consists of barium ions (Ba²⁺) and sulfate ions (SO₄²⁻).
- Sodium ions are smaller and have a higher charge density compared to barium ions, which are larger and have a lower charge density.

3. **Effect of Ion Size on Hydration Energy**:
- Smaller cations, like Na⁺, have a higher hydration energy because they can interact more effectively with water molecules. This leads to a greater energy release when they are hydrated.
- In contrast, larger cations like Ba²⁺ have lower hydration energy because they are less effective at interacting with water molecules.

4. **Effect of Ion Size on Lattice Energy**:
- Larger cations, such as Ba²⁺, contribute to a higher lattice energy because the ions are more strongly attracted to each other due to their higher charge and larger size.
- Sodium ions, being smaller, contribute to a lower lattice energy compared to barium ions.

5. **Solubility Determination**:
- For a salt to be soluble in water, the hydration energy must be greater than the lattice energy.
- In the case of sodium sulfate, the hydration energy is greater than the lattice energy, which makes it soluble in water.
- For barium sulfate, the lattice energy is greater than the hydration energy, leading to its sparing solubility in water.

6. **Conclusion**:
- Therefore, the correct explanation for the solubility of sodium sulfate compared to barium sulfate is that the hydration energy of sodium sulfate is greater than its lattice energy, while for barium sulfate, the lattice energy is greater than its hydration energy.

### Final Answer:
Sodium sulfate is soluble in water because the hydration energy of sodium sulfate is greater than its lattice energy, whereas barium sulfate is sparingly soluble because its lattice energy is greater than its hydration energy.