Hint: Solubility relies on the difference between lattice energy and hydration energy. The quantity of energy needed to change one mole of salt into constituent gaseous ions is known as lattice energy. The quantity of energy evolved when hydration of a mole of ions happens is called hydration energy.
Complete Step by Step Solution:
All the given metal sulphate s options are alkaline earth metals. They belong to the second group. This group consists of elements Beryllium, Magnesium, Calcium, Strontium, Barium, and Radium.
We know that lattice energy is required to break the salt into its gaseous constituent ions.
Hydration energy is the energy released when the ions obtained by the dissolution of a salt in water interact with water dipoles to form hydrated ions.
A salt with higher lattice energy will have a greater intermolecular force which will, in turn, make the breaking down of the solid into cations and anions in water more difficult.
Hence, for dissolution hydration energy must be more than lattice energy.
The lattice energy of sulphate s is almost the same. This is because the sulphate anion has a large size compared to the size of a cation. So, the relative order of solubility of these salts cannot be predicted based on the difference between lattice energy and hydration energy. So, the solubility of beryllium sulphate , barium sulphate , calcium sulphate , and beryllium sulphate depends only on the hydration energy.
Hydration energy increases with an increase in charge and a decrease in size.
A small-sized cation can be held properly by a more number of water molecules thus forming a hydrated cation.
We know that down the group size increases.
Among the given options, magnesium has the smallest size so will form a cation of the smallest size as compared to others.
So, the magnitude of the hydration energy of beryllium will be more.
So, beryllium sulphate will have the highest solubility in water.
So, option D is correct.
Note: The higher the lattice energy, the more tightly the ions are held together in the ionic crystal. So, smaller is the tendency of the ionic solid to split into ions by dissolution and to interact with water dipoles to form hydrated ions i.e., smaller is the solubility of the ionic solids. The greater the tendency of the ionic solid to break into ions in water in order to get hydrated by water molecules, the greater will be the magnitude of hydration energy which will in turn increase the solubility of the solid.