Which of the following ionic solids would have the largest lattice energy?

• A. NaCl
• B. KBr
• C. CaS
• D. MgO

Answer: (D)

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 general trend from the Born-Landé equation, which shows lattice energy is proportional to the product of the charges of the ions and inversely proportional to the sum of their ionic radii: \[ U \propto \frac{Q_1 \times Q_2}{r_1 + r_2} \] where \(Q_1\) and \(Q_2\) are the ionic charges, and \(r_1\) and \(r_2\) are the ionic radii.
3. Compare the charges of the ions in each compound: - NaCl: Na\(^+\) and Cl\(^-\) (charges +1 and -1) - KBr: K\(^+\) and Br\(^-\) (charges +1 and -1) - CaS: Ca\(^{2+}\) and S\(^{2-}\) (charges +2 and -2) - MgO: Mg\(^{2+}\) and O\(^{2-}\) (charges +2 and -2)
4. Consider the ionic sizes: Mg\(^{2+}\) and O\(^{2-}\) ions are smaller than Ca\(^{2+}\) and S\(^{2-}\) ions, and both are smaller than the monovalent ions in NaCl and KBr. Smaller ionic radii mean ions are closer together, increasing lattice energy.
5. Combine these factors: MgO has ions with higher charges (+2 and -2) and smaller ionic radii, leading to a larger lattice energy compared to the other compounds listed.