Question

In which of the following the hydration energy is higher than the lattice energy?
$\mathrm{A}){\mathrm{BaSO}_{4}}$
$\mathrm{B}){\mathrm{MgSO}_{4}}$
$\mathrm{C}){\mathrm{CaSO}_{4}}$
$\mathrm{D}){\mathrm{SrSO}_{4}}$

Answer 1

Hint: Lattice energy increases as the charge on the ion increases and the size decreases. Hydration energy increases as the size of the ion decreases and charges on it increases.

Complete step by step answer:
-Firstly let us focus on the cationic part of the sulphate salts given to us. Since, the sulphate group is common for all, thus the analysis of the cation will give us the proper answer.
-All the cations i.e., $\mathrm{Ba}^{2+}, \mathrm{Mg}^{2+}, \mathrm{Ca}^{2+}$ and $\mathrm{Sr}^{2+}$ are ions of alkaline earth metals. The alkaline earth metals are found in group 2 of the modern periodic table.
-Let us discuss the group 2- elements now.
-Alkaline earth metal ions are smaller in size and have greater charge than the corresponding alkali metal cations.
-Consequently, the lattice energies of ions of alkaline earth metals are higher than those of corresponding alkali metal cations.
-Down the group, the ionic radii increases and thus the hydration enthalpy decreases.
-The size of the hydration enthalpy is decided by the amount of attraction between the ions and the water molecules. The attractions are stronger when the smaller the ion.
-Also, as ionic radii of alkaline earth metals are smaller, they have higher hydration energy than alkali metals and generally, lattice energy of alkaline earth metal salts are higher than their hydration energy due to smaller size.
-Thus, since the hydration enthalpy decreases down a group, thus the first element in group 2 that is Magnesium will be more soluble or will have more hydration enthalpy than lattice enthalpy.
$\mathrm{MgSO}_{4} \stackrel{7 \mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{MgSO}_{4} .7 \mathrm{H}_{2} \mathrm{O}$

Note: This salt, $\mathrm{MgSO}_{4}$ cannot be used in storage reactors since it readily forms the hydrated compounds thus it hinders the flow of gas transfer and low temperature lift. It is rather used for different medical purposes.