Chapter 18, Problem 18.21E

Interpretation Introduction

Interpretation:

The values of $q_{\text{vib}}$ for ${\text{H}}_{\text{2}}\text{S}$ at $310\text{K}$ is to be determined.

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,

$q_{\text{vib}}={\displaystyle \prod _{i=1}^{3N-6}\frac{1}{1-e^{-h{v}_i/kT}}}$

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

• $v$ represents the $i^{\text{th}}$ vibrational frequency.

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