Question

Show that a unit cell of sodium chloride contains four Na⁺Cl⁻ units.

Answer 1

Sodium chloride (NaCl) crystallizes in a face-centered cubic (fcc) structure, also called the rock salt structure. In this structure Cl⁻ ions form the face-centered cubic lattice Na⁺ ions occupy all the octahedral voids created by the Cl⁻ ions.

Sodium ions (Na⁺):

12 edge centres, each shared by 4 unit cells:

`12 xx 1/4 = 3  Na^+`

1 body centre, entirely inside the unit cell:

1 × 1 = 1 Na⁺

∴ Total Na⁺ ions = 3 + 1 = 4

Chloride ions (Cl⁻):

8 corners, each shared by 8 unit cells:

`8 xx 1/8 = 1  Cl^-`

6 face centres, each shared by 2 unit cells:

`6 xx 1/2 = 3  Cl^-`

∴ Total Cl⁻ ions = 1 + 3 = 4

Therefore, the unit cell of sodium chloride contains 4 Na⁺ ions and 4 Cl⁻ ions, making a total of 4 NaCl formula units per unit cell.