The solubility of sulphates in water decreases from `MgSO_(4) to BaSO_(4)` It is due to the fact that

Options

A. lonic nature increases
B. Size of `M^(2+)` ion increases
C. Lattice energy decreases
D. Hydraction enthalpy of `M^(2+)` ions decreases

Answer

To answer the question regarding the solubility of sulfates in water decreasing from MgSO₄ to BaSO₄, we can analyze the factors affecting solubility, specifically lattice energy and hydration energy.

### Step-by-Step Solution:

1. **Understanding Sulfate Solubility**:
- The solubility of sulfates in water is observed to decrease as we move from magnesium sulfate (MgSO₄) to barium sulfate (BaSO₄).

2. **Factors Affecting Solubility**:
- Solubility is influenced by two main factors: **lattice energy** and **hydration energy**.
- **Lattice Energy**: This is the energy required to separate one mole of an ionic solid into its gaseous ions. Higher lattice energy means less solubility.
- **Hydration Energy**: This is the energy released when water molecules surround and solvate ions. Higher hydration energy means greater solubility.

3. **Trends in Cation Size**:
- As we move down the group from Mg²⁺ to Ba²⁺, the size of the cation increases (Mg²⁺ < Ca²⁺ < Sr²⁺ < Ba²⁺).
- The sulfate ion (SO₄²⁻) remains constant in size.

4. **Effect on Lattice Energy**:
- The increase in cation size leads to a decrease in lattice energy because the distance between the cation and anion increases.
- Thus, the lattice energy decreases as we go from MgSO₄ to BaSO₄.

5. **Effect on Hydration Energy**:
- Larger cations (like Ba²⁺) are surrounded by fewer water molecules compared to smaller cations (like Mg²⁺), leading to a decrease in hydration energy.
- Therefore, hydration energy decreases more significantly than lattice energy as we move down the group.

6. **Comparison of Lattice and Hydration Energies**:
- Although both lattice energy and hydration energy decrease, the decrease in hydration energy is more pronounced than the decrease in lattice energy.
- Since solubility depends on the balance between these two energies, the overall effect is a decrease in solubility from MgSO₄ to BaSO₄.

7. **Conclusion**:
- The solubility of sulfates in water decreases from MgSO₄ to BaSO₄ primarily due to the greater decrease in hydration energy compared to the decrease in lattice energy as the size of the cation increases.