# Density of chromium in g/cm^3?

Chromium crystallizes in a body-centered cubic structure. The molar mass of Cr is 51.996 g/mol. If the length of one side of the unit cell is 295.6 pm, what is the density of chromium in g/cm^3?

Relevance

Convert pm to cm:

(295.6 pm) (1 cm / 10^10 pm) = 2.956 x 10^-8 cm

Get the volume of the unit cell:

(2.956 x 10^-8 cm)^3 = 2.5829 x 10^-23 cm^3

bcc has two atoms per unit cell. calculate the mass of two atoms of chromium:

51.996 g/mol divided by 6.022 x 10^23 atoms/mol = 8.63434 x 10^-23 g/atom

(8.63434 x 10^-23 g/atoms) (2 atoms) = 1.726868 x 10^-22 g

The density:

1.726868 x 10^-22 g / 2.5829 x 10^-23 cm^3 = 6.68 g/cm^3

Wiki gives the value as 7.19. I could have made an error in the above calcs or the answer was deliberately manipulated so as to give an answer different from the published value.

Here are some other bcc problems:

http://chemteam.info/Liquids&Solids/WS-bcc-AP.html

• GeorgeSiO2
Lv 7
3 years agoReport

The experimental value for a is 288.46 pm.