Chapter 14, Problem 14.77E

Interpretation Introduction

Interpretation:

The number of IR-active vibrations for benzene, ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$. is to be calculated.

Concept Introduction:

A molecule having $N$ atoms use $x$, $y$ and $z$ coordinates to describe the position of the each of the atoms. A molecule requires $3N$ coordinates to describe its position in space. For change in position, the number of change in coordinates is same so $N$- molecule needs a total of $3N$ change in coordinates to describe its motion. The atoms are free to move in $3N$ different independent ways so the molecule has $3N$ degree of freedom.

The number of vibrations or degree of freedom of linear molecule is $3N-5$ and the number of vibrations or degree of freedom of nonlinear molecule is $3N-6$.