Final answer:
The compounds in order of increasing magnitude of lattice energy are: Na2O < KBr < NaCl < MgO.
Step-by-step explanation:
The magnitude of lattice energy depends on the product of the charges of the ions and the internuclear distance. In this case, we need to consider the charges of the ions and the relative sizes of the ions. The ions with higher charges or smaller sizes will have higher lattice energies. Let's compare the compounds:
- Na2O: Na+ and O2- ions. Both ions have charges of +1 and -2, so the product of the charges is the same as MgO. However, the size of Na+ is larger than Mg2+, so the internuclear distance is greater. Therefore, Na2O will have a lower lattice energy than MgO.
- KBr: K+ and Br- ions. Both ions have charges of +1 and -1, so the product of the charges is the same as NaCl. The size of K+ is larger than Na+, so the internuclear distance is greater. Therefore, KBr will have a lower lattice energy than NaCl.
- NaCl: Na+ and Cl- ions. Both ions have charges of +1 and -1, so the product of the charges is the same as KBr. The size of Na+ is smaller than K+, so the internuclear distance is smaller. Therefore, NaCl will have a higher lattice energy than KBr.
- MgO: Mg2+ and O2- ions. Both ions have charges of +2 and -2, so the product of the charges is the same as Na2O. The size of Mg2+ is smaller than Na+, so the internuclear distance is smaller. Therefore, MgO will have a higher lattice energy than Na2O.
Therefore, the compounds in order of increasing magnitude of lattice energy are: Na2O < KBr < NaCl < MgO.