Rationalize the following lattice energy values: $$ \begin{array}{|lc|} \hline & \text { Lattice Energy } \\ \text { Compound } & (\mathrm{kJ} / \mathrm{mol}) \\ \hline \mathrm{CaSe} & -2862 \\ \mathrm{Na}_{2} \mathrm{Se} & -2130 \\ \mathrm{CaTe} & -2721 \\ \mathrm{Na}_{2} \mathrm{Te} & -2095 \\ \hline \end{array} $$

The given compounds have the following elements: - Ca (Calcium): A group 2 element (alkaline earth metal; metal; charge: +2) - Na (Sodium): A group 1 element (alkali metal; metal; charge: +1) - Se (Selenium): A group 16 element (chalcogen; non-metal; charge: -2) - Te (Tellurium): A group 16 element (chalcogen; non-metal; charge: -2)

The lattice energy of an ionic compound measures the amount of energy required to break one mole of the compound into its constituent ions in the gaseous state or the energy released when the ions come together to form the ionic compound. Lattice energy increases with the increasing charge on the ions and decreases with increasing ionic radii.

There are two pairs of similar compounds: CaSe and CaTe, and Na₂Se and Na₂Te. In both pairs, the metal is the same, while the non-metal is different. The difference between Selenium and Tellurium is their atomic size. As both are in the same group, but Tellurium is below Selenium, Te has a larger atomic radius than Se.

We can now compare the lattice energies within each pair: - CaSe (-2862 kJ/mol) and CaTe (-2721 kJ/mol): As both share the same metal ion (Ca²⁺), the difference in lattice energy is mainly due to the different size of the anions (Se²⁻ and Te²⁻). Since the Te²⁻ ion is larger than the Se²⁻ ion, the lattice energy of CaTe is lower than that of CaSe. - Na₂Se (-2130 kJ/mol) and Na₂Te (-2095 kJ/mol): Both share the same metal ion (Na⁺). As the Te²⁻ ion is larger than the Se²⁻ ion (same reasoning as before), the lattice energy of Na₂Te is lower than that of Na₂Se.

Lower lattice energies correspond to larger interionic distances (and thus weaker electrostatic attractions between ions), while higher lattice energies correspond to smaller interionic distances (stronger electrostatic attractions). In this case, the main reason for the observed trends in lattice energies for the given compounds is the difference in ionic radii of the anions (Se²⁻ and Te²⁻) as well as the charge of the cations (Na⁺ and Ca²⁺). To summarize: - Compounds with Ca²⁺ ions have more negative (higher) lattice energies because of the higher positive charge on Ca²⁺ than on Na⁺. - Compounds with larger anions (Te²⁻) have less negative (lower) lattice energies because the greater interionic distance reduces the electrostatic attraction between the ions.