Question

Find the number of ion pairs per unit cell in NaCl.

Answer 1

In the NaCl crystal structure, which is based on a face-centred cubic (FCC) unit cell, chloride ions (Cl⁻) are located at the corners and face centers of the cube, while sodium ions (Na⁺) occupy the edge centers and the body center. Each corner ion contributes `1/8` to the unit cell, and each face-centered ion contributes `1/2`.

Thus, the effective number of Cl⁻ ions per unit cell is

= `8 ("at corners") xx 1/8 + 6 ("at face centres") xx 1/2`

= 4

The number of Na⁺ ions per unit cell is

= `12 ("at edge-centres") × 1/4 + 1 ("at body-centre") × 1`

= 4

Therefore, each unit cell of NaCl contains 4 Na⁺ ions and 4 Cl⁻ ions, forming 4 ion pairs per unit cell.