The hydration energy of `Mg^(2+)` ions is lesser than that of:

Options

A. `Al^(3+)`
B. `Ba^(2+)`
C. `Na`
D. none of these

Answer

To determine which ion has greater hydration energy than `Mg^(2+)`, we need to analyze the ionic sizes and their relationship with hydration energy.

### Step-by-Step Solution:

1. **Understanding Hydration Energy**:
- Hydration energy is the amount of energy released when one mole of an ion is surrounded by water molecules.
- It is inversely proportional to the size of the ion: smaller ions have higher hydration energy because they can attract water molecules more effectively.

2. **Identify the Ions**:
- We are comparing the hydration energy of `Mg^(2+)` with `Al^(3+)`, `Ba^(2+)`, and `Na^+`.

3. **Compare Ionic Sizes**:
- **Sodium Ion (`Na^+`)**: This ion is larger than `Mg^(2+)` because it is in the first group of the periodic table.
- **Barium Ion (`Ba^(2+)`)**: This ion is larger than `Mg^(2+)` as it is located below magnesium in the same group.
- **Aluminum Ion (`Al^(3+)`)**: This ion is smaller than `Mg^(2+)` because it has a higher charge (+3) and is located in the third group of the periodic table.

4. **Determine Hydration Energies**:
- Since `Al^(3+)` is smaller than `Mg^(2+)`, it will have a greater hydration energy.
- `Na^+` and `Ba^(2+)` are larger than `Mg^(2+)`, so they will have lower hydration energies.

5. **Conclusion**:
- The hydration energy of `Mg^(2+)` is lesser than that of `Al^(3+)` because `Al^(3+)` is smaller in size and thus has a higher hydration energy.

### Final Answer:
The hydration energy of `Mg^(2+)` ions is lesser than that of `Al^(3+)`.

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