Chapter 18, Problem 18.23E

Interpretation Introduction

Interpretation:

The vibrational partition function for ${\text{NO}}_2\left(\text{g}\right)$ at $250\text{K}$, $500\text{K}$, and $1000\text{K}$ are to be calculated. Whether the changes in $q_{\text{vib}}$ show the expected differences or not is to be stated.

Concept introduction:

A molecule is made up of atoms that are bonded together by covalent bonds. These bonds undergo a to and fro movement to vibrate. This vibration of the molecule contributes to the overall partition function of the system. The vibrational partition function of the polyatomic molecule is represented as,

$q_{\text{vib}}={\displaystyle \prod _{j=1}^{3N-6}\frac{1}{1-e^{-{\theta }_{\text{v,}j}/T}}}$

Where,

• $T$ represents the temperature $\left(\text{K}\right)$.

• ${\theta }_{\text{v,}j}$ represents the $j^{\text{th}}$ vibrational temperature.

• $N$ represents the number of atoms present in the molecule.