This question involves comparing hydration enthalpy and lattice enthalpy for alkaline earth metal sulphates. Let's understand these concepts first.

Key Concepts:

Lattice Enthalpy (ΔH_lattice): The energy released when one mole of an ionic compound is formed from its gaseous ions. It measures the strength of ionic bonds in the solid crystal.

Hydration Enthalpy (ΔH_hyd): The energy released when one mole of gaseous ions is dissolved in water to form hydrated ions. It represents the ion-water interaction strength.

For a salt to be highly soluble in water, the hydration enthalpy (energy released during hydration) should be greater than the lattice enthalpy (energy required to break the crystal lattice). This makes the dissolution process exothermic and favorable.

Trend in Alkaline Earth Metals:

As we move down the group from Be to Ba:

• Ionic size increases
• Lattice enthalpy decreases (ions are larger, so less strongly attracted)
• Hydration enthalpy decreases (larger ions are less effectively hydrated)

However, the rate of decrease differs: lattice enthalpy decreases more rapidly than hydration enthalpy down the group.

Analysis of Options:

For BeSO₄ (Beryllium sulphate):

• Be²⁺ is the smallest cation in the group
• High charge density (small size + high charge)
• Very high lattice enthalpy (small ions closely packed)
• Very high hydration enthalpy (small ions strongly attract water molecules)

But crucially, for Be²⁺, the hydration enthalpy is exceptionally high due to its small size and high charge density, potentially exceeding its lattice enthalpy.

For larger cations (Ca²⁺, Sr²⁺, Ba²⁺):

• Lattice enthalpy decreases significantly
• Hydration enthalpy decreases but less dramatically
• However, for sulphates specifically, solubility decreases down the group (BaSO₄ is insoluble)
• This indicates lattice enthalpy > hydration enthalpy for larger cations

Why BeSO₄ is the answer:

Beryllium ion (Be²⁺) has the smallest ionic radius, giving it the highest charge density. This results in:

• Strong ion-dipole interactions with water molecules
• Exceptionally high hydration energy that can overcome the lattice energy
• BeSO₄ is soluble in water, unlike other alkaline earth metal sulphates

For the other options (CaSO₄, SrSO₄, BaSO₄), the lattice enthalpy remains greater than hydration enthalpy, making them less soluble or insoluble.

Related Topics:

Solubility of Ionic Compounds: Depends on the balance between lattice energy (energy required to break the crystal) and hydration energy (energy released when ions are hydrated). When hydration energy > lattice energy, the compound is soluble.

Trends in Group 2 Elements: Understanding how atomic and ionic properties change down the group helps predict chemical behavior, including solubility patterns.

Important Formulae:

While not directly calculable from given data, the concepts relate to:

ΔH_solution = ΔH_lattice + ΔH_hyd

When ΔH_solution < 0 (negative), the dissolution is exothermic and favorable.

Final Answer: BeSO₄