Question

The density of aluminum metal is 2.70 g/mL, the atomic mass 26.98 g/mol, the radius of an aluminum atom is 143 picometer and the packing density is 74% theory. Compute Avogardo's number from these data and briefly outline your reasoning/strategy.

Answer 1

Given that  packing density = 74%

It means , it is FCC lattice.

So, 4 atoms per unit cell

Given that

density d = 2.70 g/mL = 2.70 g/cm³

atomic mass M = 26.98 g/mol

radius of an aluminum atom r = 143 picometer = 143 x 10^-10 cm

For FCC, a = r (8)^1/2 =  143 x 10^-10 x (8)^1/2 cm = 404.465 x  10^-10cm

a = edge length =  404.465 x 10^-10cm

We know that

density = [M x no of units in BCC unit cell] /[ a³ x avogadro number]

avogadro number = [M x no of units in FCC unit cell] /[ a³ xdensity ]

= [26.98 g/mol x 4 ] /[ (404.465 x 10^-10 cm)³ x 2.7 g/cm³ ]

= 6.03 x 10²³

Therefore,

Avogardo's number = 6.03 x 10²³