Alkali halides commonly have either the sodium chloride structure or the cesium chloride structure. The molar mass of CsCl is 2.88 times the molar mass of NaCl, and the edge length of the unit cell for NaCl is 1.37 times the edge length of the CsCl unit cell. Determine the ratio of the density of CsCl to the density of NaCl.

Question

Quizplus · Accepted Answer

The density (ρ) of a substance is given by the formula ρ = mass/volume. For a crystalline solid, this can be approximated as the molar mass (M) divided by the volume of the unit cell (V), multiplied by Avogadro's number (N_A), i.e., ρ = M / V * N_A. Given that the molar mass of CsCl is 2.88 times that of NaCl and the edge length of the NaCl unit cell is 1.37 times that of CsCl, we can calculate the volume ratio of their unit cells based on their edge lengths cubed (since volume = edge length^3 for a cubic unit cell). The volume of NaCl's unit cell is 1.37^3 times that of CsCl's. Therefore, the density ratio of CsCl to NaCl, considering the molar mass and volume differences, is (2.88 / 1.37^3), which simplifies to approximately 1.85, indicating that CsCl is denser than NaCl by this factor.

Alkali Halides Commonly Have Either the Sodium Chloride Structure or the Cesium