Chapter 18, Problem 18.19E

Interpretation Introduction

Interpretation:

The values of ${\theta }_{\text{v}}$ and $q_{\text{vib}}$ for ${\text{F}}_{\text{2}}$ at $298\text{K}$ are to be calculated.

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 diatomic atom at is represented as,

$q_{\text{vib}}=\frac{1}{1-e^{-hv/kT}}$

Where,

• $k$ represents the Boltzmann constant with value $1.381\times {10}^{-23}\text{J}/\text{K}$.

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

• $h$ represents Plank’s constant with a value $6.626\times {10}^{-34}\text{J}\cdot \text{s}$.

• $v$ represents vibrational frequency.