Question

Question: A compound contains three elements: sodium, oxygen, and chlorine. It crystallizes in a cubic lattice. The oxygen atoms are at the corners of the unit cells, the chlorine atoms are at the centers of the unit cells, and the sodium atoms are at the centers of the faces of the unit cells. What is the formula of the compound?

Short answer

Answer

The formula of the compound is Na₃CIO .

Step-by-step solution

Simple cubic lattice

In a simple cubic lattice, all the edge lengths are equal and all the angles are equal to 90⁰ .

Calculation

The oxygen atoms are at the corners of the unit cells.

The number of oxygen atoms in the unit cell:

$8\times \frac{1}{8}=1$

The chlorine atoms are at the centers of the unit cells so, at the centre there will be only one atom.

The sodium atoms are at the centers of the faces of the unit cells.

The number of sodium atoms in the unit cell:

$6\times \frac{1}{2}=3$

Hence, the formula becomes$N{a}_{3}ClO$ .