Chapter 12, Problem 1PS

Outline a two-dimensional unit cell for the pattern shown here. If the black squares are labeled A and the white squares are B, what is the simplest formula for a “compound” based on this pattern?

Interpretation Introduction

Interpretation:

The simplest formula of the compound has to be identified.

Answer to Problem 1PS

The simplest formula of the compound is ${\text{AB}}_{\text{8}}$.

Explanation of Solution

According to the picture, we consider the unit pattern as combination of two molecules,

There are seventy two white squares and nine black squares in the two dimensional unit cell patterns.

$\begin{array}{l}\text{Formula}\text{of}\text{the}\text{pattern}\text{=}\text{9}\text{black squares}\text{+72}\text{white squares}\text{+}\\ \text{therefore,}\\ \text{Formula}\text{of}\text{the}\text{pattern}{\text{=A}}_{\text{9}}\text{(blacksquares)}\text{+}{\text{B}}_{\text{72}}\text{(white squares}\text{)}\\ \text{Simplfy}\text{the}\text{pattern}\\ \text{Simplest}\text{formula}\text{of}\text{the}\text{pattern}{\text{=AB}}_{\text{8}}\end{array}$

Conclusion

The simplest formula of the compound was identified.