Question

Calculate the density of ReO3?

The unit cell of rhenium trioxide (ReO3) consists of a cube with rhenium atoms at the corners and an oxygen atom on each of the 12 edges. The atoms touch along the edge of the unit cell. The radii of Re and O atoms in ReO3 are 137 and 73pm. Calculate the density of ReO3

Could you show work?! Thanks so much!

Answer 1

In the unit cell there are:

8 atom x 1/8 = 1 Re atom and

12 atom x ¼ = 3 O atoms

The edge length is

137 + 2x73 + 137 = 420 pm = 420 x 10^-12 m = 4.20x10^-10m= 4.20x10^-8 cm

(in fact, by X-ray diffraction, this length was found to be 3.734 x10^-8 cm)

The cell (cube) volume is

(4.20x10^-8 cm)³ = 7.41x10^-23 cm³ /unit

The volume of 1 mol ReO3 is

7.41x10^-23 cm³ /unit x 6.022x10²³ unit/mol = 44.6 cm³

The density is

234.2 g ReO₃/mol / 44.6 cm³ = 5.25 g/ cm³

(using the experimental value of the Re-O-Re length for calculation, the density will be

closer to the actual value 6.92 g/cm³).