`MgSO_(4)` is soluble while `BaSO_(4)` is insoluble in `H_(2)O`. This is because :

Options

A. Lattice energy of `BaSO_(4)` is greater than `MgSO_(4)`
B. `BaSO_(4)` is more covalent than `MgSO_(4)`
C. Hydration energy of `Mg^(2+)` is greater than `Ba^(2+)`
D. Lattice energy of `MgSO_(4)` is greater than `BaSO_(4)`

Explanation

To understand why `MgSO₄` is soluble in water while `BaSO₄` is insoluble, we need to analyze the concepts of hydration energy and lattice energy.

### Step-by-Step Solution:

1. **Understanding Solubility**:
- A compound is soluble in water if the hydration energy (the energy released when water molecules surround and interact with ions) is greater than the lattice energy (the energy required to separate the ions in a solid ionic compound).

2. **Identifying the Ions**:
- `MgSO₄` consists of `Mg²⁺` and `SO₄²⁻` ions.
- `BaSO₄` consists of `Ba²⁺` and `SO₄²⁻` ions.
- The anion `SO₄²⁻` is the same in both compounds, so we will focus on the cations `Mg²⁺` and `Ba²⁺`.

3. **Comparing Hydration Energy**:
- Hydration energy is influenced by the charge and size of the ions. It is directly proportional to the charge and inversely proportional to the size of the ion.
- Both `Mg²⁺` and `Ba²⁺` have the same charge (+2), but their sizes differ. `Mg²⁺` is smaller than `Ba²⁺`.

4. **Effect of Ion Size**:
- Since `Ba²⁺` is larger than `Mg²⁺`, it has a lower hydration energy compared to `Mg²⁺`.
- The smaller size of `Mg²⁺` allows it to interact more effectively with water molecules, resulting in a higher hydration energy.

5. **Comparing Lattice Energy**:
- The lattice energy for both `MgSO₄` and `BaSO₄` is significant, but the key factor is the hydration energy.
- In `MgSO₄`, the high hydration energy exceeds the lattice energy, allowing it to dissolve in water.
- In `BaSO₄`, the lower hydration energy does not exceed the lattice energy, making it insoluble in water.

6. **Conclusion**:
- Therefore, `MgSO₄` is soluble in water because its hydration energy is greater than its lattice energy, while `BaSO₄` is insoluble because its hydration energy is less than its lattice energy.

### Final Answer:
`MgSO₄` is soluble in water while `BaSO₄` is insoluble due to the higher hydration energy of `Mg²⁺` compared to `Ba²⁺`, which allows `MgSO₄` to overcome its lattice energy and dissolve.

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