In which of the following is the hydration energy higher than the lattice energy?

Options

A. `BaSO_4`
B. `MgSO_4`
C. `RaSO_4`
D. `SrSO_4`

Explanation

To determine which of the given compounds has hydration energy higher than lattice energy, we can follow these steps:

### Step 1: Understand the Terms
- **Hydration Energy**: This is the energy released when ions are surrounded by water molecules. It is influenced by the size of the ions; smaller ions typically have higher hydration energy due to stronger interactions with water.
- **Lattice Energy**: This is the energy required to separate ions in a solid ionic compound into gaseous ions. It is also influenced by the size of the ions; smaller ions lead to higher lattice energy because they can get closer together.

### Step 2: Identify the Compounds
The compounds given are:
1. Barium sulfate (BaSO₄)
2. Magnesium sulfate (MgSO₄)
3. Radium sulfate (RaSO₄)
4. Strontium sulfate (SrSO₄)

### Step 3: Analyze the Group Trends
All the compounds belong to the alkaline earth metals (Group 2). As we move down the group from magnesium to barium, the size of the cations increases:
- Mg²⁺ < Sr²⁺ < Ba²⁺ < Ra²⁺

### Step 4: Compare Hydration and Lattice Energies
- **Hydration Energy**: Decreases down the group, but the decrease is more significant due to the square relationship with the ionic radius.
- **Lattice Energy**: Also decreases down the group, but the decrease is less pronounced compared to hydration energy.

### Step 5: Determine Which Compound Has Higher Hydration Energy
- For **Magnesium sulfate (MgSO₄)**: The Mg²⁺ ion is small, leading to a relatively high hydration energy. Thus, for MgSO₄, the hydration energy is greater than the lattice energy.
- For **Barium sulfate (BaSO₄)**, **Strontium sulfate (SrSO₄)**, and **Radium sulfate (RaSO₄)**: The larger cations lead to lower hydration energies, and their lattice energies become more significant, making hydration energy lower than lattice energy.

### Conclusion
Based on the analysis, the compound in which hydration energy is higher than lattice energy is **Magnesium sulfate (MgSO₄)**.

### Final Answer
**Option B: Magnesium sulfate (MgSO₄)**

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