(a) Does the lattice energy of an ionic solid increase or decrease (i) as the charges of the ions increase, (ii) as the sizes of the ions increase? (b) Arrange the following substances not listed in Table 8.2 according to their expected lattice energies, listing them from lowest lattice energy to the highest: \(\mathrm{MgS}, \mathrm{KI}\), \(\mathrm{GaN}, \mathrm{L} \mathrm{iBr}\)

Lattice energy is the energy required to break one mole of an ionic solid into its constituent gaseous ions. It is typically associated with the electrostatic interactions between the positively and negatively charged ions in the crystal lattice. The magnitude of lattice energy depends on the charges of the ions and the distances between them, as described by Coulomb's law: \[E \propto \frac{q_1 q_2}{r}\] where E is the lattice energy, \(q_1\) and \(q_2\) are the charges of the ions, and r is the distance between the ions.

The lattice energy is proportional to the product of the charges of the ions. If the charges of the ions increase, the lattice energy will also increase, because the electrostatic attraction between the ions becomes stronger.

Considering the formula for lattice energy, it is inversely proportional to the distance between the ions. As the size of the ions increases, the distance between them also increases, leading to a decrease in lattice energy. The electrostatic attraction between larger ions is weaker than between smaller ions.

(i) As the charges of the ions increase, the lattice energy increases. (ii) As the sizes of the ions increase, the lattice energy decreases.

To arrange \(\mathrm{MgS}, \mathrm{KI}\), \(\mathrm{GaN}, \mathrm{LiBr}\), we need to compare their charges and sizes of ions. 1. \(\mathrm{MgS}\): Mg has a charge of +2, S has a charge of -2, and both have relatively small sizes. 2. \(\mathrm{KI}\): K has a charge of +1, I has a charge of -1, and both have relatively large sizes. 3. \(\mathrm{GaN}\): Ga has a charge of +3, N has a charge of -3, and both have relatively small sizes. 4. \(\mathrm{LiBr}\): Li has a charge of +1, Br has a charge of -1, and both have relatively small sizes. Based on the charges and sizes, we expect the lattice energy order to be: Lowest lattice energy: \(\mathrm{KI}\) < \(\mathrm{LiBr}\) < \(\mathrm{MgS}\) < \(\mathrm{GaN}\): Highest lattice energy.