All question types · Spectroscopy & other
Density of a rock-salt crystal
UKChO Round 2 · IChO · unreviewed
Cubic cell edge, formula units per cell and molar mass known; find the density.
Worked example
The cubic unit cell of NaCl has a = 560.7 pm and contains Z = 4 formula units. Find the density in g cm⁻³ (M = 58.44 g mol⁻¹).
1. Density from a cubic unit cell: solve for ρ
= 2.202 g cm⁻³
Answer: ρ = 2.20 g cm⁻³
Method
Mass of one cell = ZM/N_A; its volume is a³. Convert a to cm (1 pm = 10⁻¹⁰ cm) before cubing. ρ = ZM/(N_A a³).
Common mistakes
- The rock-salt unit cell holds four NaCl units: 8 corners × ⅛ + 6 faces × ½ = 4 of each ion.
Formulas used
Density from a cubic unit cell