Problem 15 - Entrance Test

1. **Identify the crystal structure and Z value:** KF crystallizes in the rock salt (NaCl) structure. For this structure, the number of formula units per unit cell (Z) is 4. 2. **Determine the edge length (a) of the unit cell:** In the NaCl structure, the shortest distance between a cation (K⁺) and an anion (F⁻) is half the edge length of the unit cell (a/2). Given, the shortest K-F distance = 269 pm. So, a/2 = 269 pm a = 2 × 269 pm = 538 pm 3. **Convert edge length to centimeters:** a = 538 pm = 538 × 10⁻¹⁰ cm = 5.38 × 10⁻⁸ cm. 4. **Calculate the volume of the unit cell (a³):** a³ = (5.38 × 10⁻⁸ cm)³ = 155.753512 × 10⁻²⁴ cm³. 5. **Calculate the molar mass (M) of KF:** M = 58.10 g/mol. 6. **Use the density formula (ρ = (Z × M) / (a³ × NA)):** ρ = (4 × 58.10 g/mol) / (155.753512 × 10⁻²⁴ cm³ × 6.022 × 10²³ mol⁻¹) ρ = 232.4 / (155.753512 × 0.6022) ρ = 232.4 / 93.791 ρ ≈ 2.477 g/cm³. This value is very close to 2.48 g/cm³ (option B).