Solubility of the alkaline earth's metal sulphates in water decreases in the sequence

Options

A. `Sr gtCagtMg gtBa`
B. `BagtMggtSrgtCa`
C. `CagtSrgtBagtMg`
D. `MggtCagtSrgtBa`

Answer

To determine the solubility of alkaline earth metal sulfates in water, we need to analyze the factors that influence solubility, specifically lattice energy and hydration energy.

### Step-by-Step Solution:

1. **Identify the Alkaline Earth Metals**:
The alkaline earth metals include Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), and Barium (Ba).

2. **Write the Sulfates**:
The sulfates of these metals are:
- Beryllium sulfate (BeSO₄)
- Magnesium sulfate (MgSO₄)
- Calcium sulfate (CaSO₄)
- Strontium sulfate (SrSO₄)
- Barium sulfate (BaSO₄)

3. **Understand Lattice Energy and Hydration Energy**:
- **Lattice Energy**: This is the energy required to separate the ions in a compound. For sulfates, the anion (SO₄²⁻) is relatively large, and the lattice energy remains fairly constant as we move down the group of alkaline earth metals.
- **Hydration Energy**: This is the energy released when ions are surrounded by water molecules. Smaller cations can be surrounded by more water molecules, leading to higher hydration energy.

4. **Analyze the Size of Cations**:
As we move down the group from Beryllium to Barium, the size of the cations increases:
- Be²⁺ < Mg²⁺ < Ca²⁺ < Sr²⁺ < Ba²⁺

5. **Relate Hydration Energy to Cation Size**:
Since hydration energy is inversely proportional to the size of the cation, smaller cations will have higher hydration energy. Thus, the order of hydration energy is:
- Be²⁺ > Mg²⁺ > Ca²⁺ > Sr²⁺ > Ba²⁺

6. **Determine Solubility Order**:
Since solubility is influenced by hydration energy (higher hydration energy leads to higher solubility), the order of solubility of the sulfates will be the same as the order of hydration energy:
- BeSO₄ > MgSO₄ > CaSO₄ > SrSO₄ > BaSO₄

7. **Final Order of Solubility**:
Therefore, the solubility of alkaline earth metal sulfates in water decreases in the sequence:
- **MgSO₄ > CaSO₄ > SrSO₄ > BaSO₄**

### Conclusion:
The correct order of solubility of alkaline earth metal sulfates in water is:
- **Magnesium sulfate (MgSO₄) > Calcium sulfate (CaSO₄) > Strontium sulfate (SrSO₄) > Barium sulfate (BaSO₄)**.