Exercise 9 | Liquids and Solids

Chromium has a body-centered cubic lattice with a density of 7.20 g.cm-3.

What is the length of an edge of a unit cell?

d = MVmol 


d = density (g.m-3)

M = mass molar (g.mol-1)

Vmol = molar volume (m3.mol-1)

 

Vmol = Vunit cell × NAN 


Vunit cell = unit cell volume (in m3)

N = number of atom s in a unit cell

NA = Avogadro’s number = 6.022 x 1023 mol-1

 

⇒ d = MVmol 

⇒ Vmol = Md

⇒ Vunit cell = M × Nd × NA

 

Body-centered cubic lattice: 2 atoms per unit cell ⇒ N = 2

⇒ Vunit cell = 52.00 × 27.20 × 106 × 6.022 × 1023

⇒ Vunit cell = 2.40 x 10-29 m3

 

If L = length of the edge

⇒ Vunit cell = L3

⇒ L = 2.88 x 10-10 m = 288 pm