Chapter 14, Problem 64A

Interpretation Introduction

Interpretation: The empirical formula of $M_X{A}_Y$ is to be determined.

Concept introduction: Ionic compound is formed by the transference of electrons from one atom to another. The empirical formula of a compound is the formula which expresses the simplest whole number ratio of the atoms.

Explanation of Solution

Assume the 2-D structure of an ionic compound, $M_X{A}_Y$where M is the metal cation which is smaller in size and are present in face-centred cubic unit cell.

A is the anion which is larger in size and are present in simple primitive cubic unit cell.

For fcc unit cell, particles are present at the corners and at the centre of each face.

There are 8 lattice points at the corners and 6 lattice points at the centre of each face.

Contribution of each atom at corners is 1/8 and at face centre is 1/2.

Thus, in a face-centred cubic unit cell:

1. 8 corners atoms × 1/8 atom per unit cell = 8 × 1/8 = 1
2. 6 face-centred atoms × 1/2 atom per unit cell = 6 × 1/2 = 3

Therefore, total number of atoms per unit cell = 3 + 1 = 4 atoms

For simple primitive cubic unit cell, total number of atoms = 8 × 1/8 = 1 atom

Larger atoms tend to stay in simple primitive cubic unit cell and smaller size atoms are present in fcc lattice.

Conclusion

The empirical formula of an ionic compound is $M_{4}A$ .