Which of the following ionic compounds would be expected to have the highest lattice energy?

• A. MgO
• B. NaCl
• C. KBr
• D. CaS

Answer: (A)

Verified step by step guidance

1. Recall that lattice energy is the energy released when gaseous ions combine to form an ionic solid. It depends primarily on the charges of the ions and the distance between them (which relates to ionic radii).
2. Use the formula derived from Coulomb's law for lattice energy: \(U \propto \frac{Q_1 \times Q_2}{r}\), where \(Q_1\) and \(Q_2\) are the charges on the cation and anion, and \(r\) is the distance between the ion centers (sum of ionic radii).
3. Compare the charges of the ions in each compound: MgO (Mg\(^{2+}\) and O\(^{2-}\)), NaCl (Na\(^{+}\) and Cl\(^{-}\)), KBr (K\(^{+}\) and Br\(^{-}\)), CaS (Ca\(^{2+}\) and S\(^{2-}\)). Higher charges lead to stronger lattice energy.
4. Consider the ionic sizes: smaller ions lead to smaller \(r\) and thus higher lattice energy. Among the given compounds, Mg\(^{2+}\) and O\(^{2-}\) are smaller than Ca\(^{2+}\) and S\(^{2-}\), and both are smaller than the monovalent ions in NaCl and KBr.
5. Conclude that MgO has the highest lattice energy because it has ions with the highest charges and relatively small ionic radii, maximizing the \(\frac{Q_1 \times Q_2}{r}\) ratio.