Answer to Question #171706 in General Chemistry for billy

Question

Magnesium metal crystallizes with HCP unit cell. Its radius is 0.1599 nm. Calculate the

density of solid crystalline magnesium in g/cm3?

Answer 1

Magnesium is hcp with c/a =1.624,

the atomic radius of magnesium r =0.1599 nm.

Solution: density = n*MW / (Vc*NA)

For hcp n = 6,

a = 2r = 2 * 0.1599 × 10^-9 m

= 3.198 × 10^-10 m,

c = 1.624 * 3.198 × 10^-10 m

= 5.193 × 10^-10 m,

NA = 6.02*10^23 atoms/mol.

MW magnesium = 24.3 g/mol.

Vc = 2.598a²c

= 2.598 × (3.198×10^-10 m)² × (5.193×10^-10 m) = 1.380 × 10^-22 cm³.

Density = (6 × 24.3)/(1.380×10^-22 × 6.023 ×10²³) = 1.754 g/cm³.