Question

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.

Answer 1

`\large \boxed{1.85:1}`

Step-by-step explanation:

The density of a substance is directly proportional to the molar mass and the number of atoms per unit cell, and inversely proportional to the volume of the unit cell.

The BCC unit cell of CsCl contains one K⁺ and one Cl⁻ ion, while the SC unit cell contains four Na⁺ and four Cl⁻ ions.

`\frac{\text{CsCl density}}{\text{NaCl density}} = \frac{\text{Atoms of Cs}}{\text{Atoms of Ca}} * \frac{\text{MM of CsCl}}{\text{MM of NaCl}} * \frac{\text{Vol. of NaCl unit cell}}{\text{Vol. of CsCl unit cell}}\\\\= (1)/(4) * \frac{\text{2.88}}{\text{1}} * (1.37^(3))/(1^(3)) = (1.85)/(1)\\\\\text{The ratio of the density of CsCl to that of NaCl is $\large \boxed{\mathbf{1.85:1}}$}`