Solubility of an ionic compound in water is mainly dependent on:
a.Lattice enthalpy , b. Hydration enthalphy
Both these factors oppose each other and the resultant of these determines the solubility of an ionic compound in water. If lattce enthalpy has greater value, the compound is less soluble.
In case hydration enthalpy has greater value, the compound is
highly soluble in water.
Which of the following is more soluble in water?

Options

A. `MgSO_(4)`
B. `CaSO_(4)`
C. `SrSO_(4)`
D. `BaSO_(4)`

Explanation

To determine which sulfate of alkaline earth metals is more soluble in water, we need to analyze the factors affecting solubility: lattice enthalpy and hydration enthalpy.

### Step-by-Step Solution:

1. **Understanding Lattice Enthalpy and Hydration Enthalpy**:
- Lattice enthalpy is the energy required to separate one mole of an ionic compound into its gaseous ions. A higher lattice enthalpy indicates a stronger ionic bond, making the compound less soluble.
- Hydration enthalpy is the energy released when gaseous ions are surrounded by water molecules. A higher hydration enthalpy indicates that the ions are more effectively solvated, leading to greater solubility.

2. **Relationship Between Lattice and Hydration Enthalpy**:
- These two enthalpies oppose each other in determining solubility. If the lattice enthalpy is greater, the compound is less soluble. Conversely, if the hydration enthalpy is greater, the compound is more soluble.

3. **Analyzing Alkaline Earth Metal Sulfates**:
- The sulfates of alkaline earth metals include:
- Magnesium sulfate (MgSO₄)
- Calcium sulfate (CaSO₄)
- Strontium sulfate (SrSO₄)
- Barium sulfate (BaSO₄)

4. **Trend in Solubility**:
- As we move down the group from magnesium to barium, the size of the metal ions increases.
- The hydration enthalpy decreases down the group because larger ions are less effectively solvated by water molecules.

5. **Effect on Solubility**:
- For alkaline earth metal sulfates, the lattice enthalpy remains relatively constant due to the large size of the sulfate ion (SO₄²⁻).
- However, the hydration enthalpy decreases significantly as we move from Mg²⁺ to Ba²⁺, leading to decreased solubility.

6. **Conclusion**:
- Since magnesium sulfate (MgSO₄) has the highest hydration enthalpy among the sulfates of alkaline earth metals, it is the most soluble in water.

### Final Answer:
**Magnesium sulfate (MgSO₄) is more soluble in water.**

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