Question

NaF, KF, MgO and CaO are crystalline solids. They have NaCl structure. Their lattice energies vary in the order

• A. NaF < KF < MgO < CaO
• B. KF < NaF < CaO < MgO
• C. MgO < CaO < NaF < KF
• D. CaO < MgO < NaF < KF

Hint:

Lattice energy is influenced by the charge and size of the ions. Smaller ions with higher charges result in higher lattice energy.

Answer 1

The Correct Option is B

To determine the order of lattice energies for the given compounds (NaF, KF, MgO, and CaO) with NaCl structure, we need to understand the factors affecting lattice energy. Lattice energy is defined as the energy released when one mole of an ionic crystalline compound is formed from its gaseous ions.

The lattice energy is influenced by the charges on the ions and the sizes of the ions involved. The formula for lattice energy (approximate) according to the Born-Lande equation is:

• \(U = \dfrac{K \cdot Q_1 \cdot Q_2}{r_0}\)

Where:

• \(U\) is the lattice energy.
• \(K\) is the Madelung constant (depends on the structure type).
• \(Q_1\) and \(Q_2\) are the charges on the ions.
• \(r_0\) is the sum of the radii of the cation and anion.

Factors Affecting Lattice Energy:

• Charge of Ions: Higher charges lead to higher lattice energy since the product \(Q_1 \cdot Q_2\) is larger.
• Size of Ions: Smaller ions or shorter distance \(r_0\) result in higher lattice energy due to stronger attraction.

Analysis of Given Compounds:

• NaF vs KF: Both have the same charge (+1 for Na⁺ and K⁺, -1 for F^-), but Na⁺ is smaller than K⁺ leading to higher lattice energy for NaF compared to KF.
• CaO vs MgO: Both have the same charge (+2 for Ca²⁺ and Mg²⁺, -2 for O^2-), but Mg²⁺ is smaller than Ca²⁺ leading to higher lattice energy for MgO compared to CaO.

Based on the above analysis, the correct order of lattice energies from lowest to highest is:

• \(KF < NaF < CaO < MgO\)

The correct option is: KF < NaF < CaO < MgO.