Question

An FCC lattice has lattice parameter of a=400 pm. calculate molar volume of the lattice including all the empty spaces?

Answer 1

Given:

Lattice parameter, a = 400 pm = 400 × 10⁻¹⁰ cm

The Lattice is Face Centred Cubic.

To Find:

Molar volume of the lattice.

Calculation:

Volume of 1 unit cell = a³

⇒ V = (400 × 10⁻¹⁰)³

⇒ V = 64 × 10⁻²⁴ cm³

- Volume of 1 mole of unit cells = $N_{A}$ × V

⇒ V' = 6.022 × 10²³ × 64 × 10⁻²⁴

⇒ V' = 38.541 cm³

- Molar Volume = 38.54/4 = 9.64 cm³ (or mL)

- Hence, molar volume of the given lattice is 9.64 cm³ (or 9.64 mL).