Question

Enter your answer in the box provided. Aluminum metal crystallizes in a face-centered cubic unit cell. If the length of the cell edge is 404 pm, what is the density of aluminum in g/cm3?

Answer 1

Given

Length = 404 pm

1 pm = 10^-10 cm

404 pm = 404 pm * 10^-10 cm/ 1 pm

= 4.04 * 10^-8 cm

Lets calculate volume of unit cell

= length³

= (4.04 * 10^-8 cm)³

= 6.594 * 10^-23 cm³

Now

Average mass of one atom of Al

27 g/mol/(6.022*10²³atoms/mole)

= 4.48 * 10^-23 g

In FCC 1 unit cell has 4 atoms

So

For 4 Al atoms

Mass = 4 * 4.48 * 10^-23 g

= 1.792 * 10^-22 g

Now density

Mass/volume

= 1.792 * 10^-22 g/6.594 * 10^-23 cm³

= 2.72 g/cm³