Concept: Lattice Energy

Lattice energy is the energy required to completely separate one mole of a solid ionic compound into gaseous constituent ions. It is a measure of the strength of the ionic bonds in a crystal lattice. According to Born-Landé equation, lattice energy is directly proportional to the product of the charges of the ions and inversely proportional to the sum of their ionic radii.

The formula for lattice energy (U) can be approximated as:

$U\propto \frac{q_1{q}_2}{r_1+r_2}$

where $q_1$ and $q_2$ are the charges of the cation and anion, respectively, and $r_1$ and $r_2$ are their respective ionic radii.

Why (A) MgO is correct:

All the given oxides (MgO, CaO, SrO, BaO) have the same anion, ${\mathrm{O}}^{2-}$, and the cations are all divalent ($\mathrm{M}{\mathrm{g}}^{2+},\mathrm{C}{\mathrm{a}}^{2+},\mathrm{S}{\mathrm{r}}^{2+},\mathrm{B}{\mathrm{a}}^{2+}$). Therefore, the product of charges ($q_1{q}_2$) is constant for all these compounds. In this case, lattice energy will primarily depend on the sum of ionic radii ($r_1+r_2$).

As we move down Group 2 (Mg, Ca, Sr, Ba), the size of the cation increases. Therefore, $\mathrm{M}{\mathrm{g}}^{2+}$ has the smallest ionic radius among the given cations. Since lattice energy is inversely proportional to the sum of ionic radii, the compound with the smallest cation will have the highest lattice energy.

Thus, MgO, having the smallest cation ($\mathrm{M}{\mathrm{g}}^{2+}$), will have the maximum lattice energy.

Option Analysis:

• A) MgO: $\mathrm{M}{\mathrm{g}}^{2+}$ is the smallest cation among the options, leading to the smallest internuclear distance and thus the highest lattice energy.
• B) CaO: $\mathrm{C}{\mathrm{a}}^{2+}$ is larger than $\mathrm{M}{\mathrm{g}}^{2+}$, resulting in lower lattice energy compared to MgO.
• C) SrO: $\mathrm{S}{\mathrm{r}}^{2+}$ is larger than $\mathrm{C}{\mathrm{a}}^{2+}$, resulting in lower lattice energy compared to CaO.
• D) BaO: $\mathrm{B}{\mathrm{a}}^{2+}$ is the largest cation among the options, resulting in the lowest lattice energy.

Correct Answer: (A)