Question

Assume the two-dimensional structure of an ionic compoundis

What is the empirical formula of this ionic compound?

Short answer

The empirical formula for this ionic compound is MX₂

Step-by-step solution

Given Information

From the given picture, it is clear that the compound has MX₂ empirical formula. Here the compound has a small ion which is assumed to be a cation, and the larger atom is assumed to be an anion.

${\mathrm{M}}^{2+}$ions are at the corners, and 8X^-ions are at the tetrahedral voids.

Concept Introduction

Any compound's two-dimensional (2D) structure manifests the projection of the actual three-dimensional structure on a 2D plane.

Derivation of the empirical formula

In the unit cell, there are four corners repeating where each corner has $\frac{1}{8}$of cation, and one cation is on the face-centered of the cube or $\frac{1}{2}$for the total of one cation.

All of the anions are on the face =$\frac{1}{2}\times 4=2$ anions

The empirical formula for this ionic compound is MX₂.