Which of the following correctly ranks the lattice energy of the salts NaCl, MgO, and KBr from highest to lowest?

• A. NaCl > KBr > MgO
• B. NaCl > MgO > KBr
• C. KBr > NaCl > MgO
• D. MgO > NaCl > KBr

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 mainly on the charges of the ions and the distance between them (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 of the ions, and \(r\) is the distance between the ion centers (sum of ionic radii).
3. Compare the charges of the ions in each salt: NaCl has Na\(^+\) and Cl\(^-\) (charges +1 and -1), MgO has Mg\(^{2+}\) and O\(^{2-}\) (charges +2 and -2), and KBr has K\(^+\) and Br\(^-\) (charges +1 and -1). Higher charges lead to stronger lattice energy.
4. Consider the ionic sizes: smaller ions lead to smaller \(r\) and thus higher lattice energy. Mg\(^{2+}\) and O\(^{2-}\) are smaller than K\(^+\) and Br\(^-\), and Na\(^+\) and Cl\(^-\) are intermediate in size.
5. Combine the effects of charge and ionic size to rank the lattice energies: MgO has the highest lattice energy due to higher charges and relatively small ions, followed by NaCl, and then KBr with the lowest lattice energy.