Animated Solution for Chemistry - s and p-Block Elements: Among the sulphates of alkaline earth metals, the solubilities of ${\text{BeSO}}_4$ and ${\text{MgSO}}_4$ in water, respectively, are

Imagine dropping a crystal of an alkaline earth metal sulphate into a beaker of water. Instantly, a microscopic tug-of-war begins. On one side, we have the Lattice Energy ($\Delta H_{\text{lattice}}$)—the structural glue that desperately wants to keep the positive and negative ions locked together in their solid crystal formation. On the other side, we have the Hydration Energy ($\Delta H_{\text{hyd}}$)—the pulling force of the surrounding water molecules trying to rip the ions apart and dissolve them.

For the salt to dissolve, the Hydration Energy must overpower the Lattice Energy. If the water pulls harder than the crystal holds on, the salt dissolves. If the crystal holds on tighter, the salt remains insoluble.

Let's look at how Lattice Energy behaves as we move down the group from Beryllium (${\text{Be}}^{2+}$) to Barium (${\text{Ba}}^{2+}$). Lattice energy is inversely proportional to the sum of the ionic radii ($r_{+}+r_{-}$).

Here is the crucial detail: the sulphate ion (${\text{SO}}_4^{2-}$) is absolutely massive. Because the anion is so large, the relatively small increase in the size of the metal cation as we go down the group barely makes a dent in the overall internuclear distance. Consequently, the Lattice Energy decreases, but it does so very, very slowly. It is a stubborn force that remains relatively constant across the group.

Now, let's examine Hydration Energy. Unlike Lattice Energy, Hydration Energy depends almost entirely on the size of the cation alone ($\Delta H_{\text{hyd}}\propto \frac{1}{r_{+}}$).

Smaller cations, like ${\text{Be}}^{2+}$ and ${\text{Mg}}^{2+}$, have an incredibly high charge density. They act like powerful magnets, attracting water molecules with overwhelming force. However, as we move down the group, the cation size increases, and this charge density drops off a cliff. As a result, the Hydration Energy plummets rapidly from Beryllium down to Barium.

This brings us to the core of the problem. For Beryllium Sulphate (${\text{BeSO}}_4$) and Magnesium Sulphate (${\text{MgSO}}_4$), the cations are so small that their Hydration Energy is astronomically high—far exceeding their Lattice Energy. The water molecules easily rip the crystal apart, making both of these salts highly soluble in water.

However, as we continue down the group to Calcium, Strontium, and Barium, the rapidly falling Hydration Energy crosses below the stubborn Lattice Energy. The water is no longer strong enough to break the crystal, which is why Barium Sulphate (${\text{BaSO}}_4$) is practically insoluble.

Therefore, the solubilities of both ${\text{BeSO}}_4$ and ${\text{MgSO}}_4$ are high, making option (c) the perfect answer!