Question

Chromium forms a crystalline solid with a body-centered cubic unit cell. The edge length of its unit cell is 291 pm. Calculate the density of chromium metal in g/cm^3.
a. 7.84 g/cm^3
b. 6.33 g/cm^3
c. 7.01 g/cm^3
d. 8.23 g/cm^3
e. 5.08 g/cm^3

Answer 1

Answer:

c. 7.01 g/cm³

Explanation:

To dinf density of the Chromium we need to find first the mass of the unit cell and then its volume.

A body-centered cubic unit cell has:

2 atoms per cubic unit cell.

Volume = Edge length³

Mass of 2 atoms of Cr - Molar mass: 51.9961g/mol-:

2 atoms Cr * (1mol / 6.022x10²³ atoms) = 3.321x10⁻²⁴ moles Cr * (51.9961g/mol) =

1.72687x10⁻²²g

Volume:

291pm = (291x10⁻¹²m)³= 2.4642x10⁻²⁹m³* (1cm³/1x10⁻⁶m³) =

2.4642x10⁻²³cm³

Density, ratio of mass and volume is:

Density: 1.72687x10⁻²²g / 2.4642x10⁻²³cm³ =

7.01g/cm³

Right option is:

c. 7.01 g/cm³