Chapter 12, Problem 12B.4E

a)

Interpretation Introduction

Interpretation:

The rotational partition function for ${}^1{\text{H}}^{\text{35}}\text{Cl}$ at $\text{298}\text{K}$ with rotational constant $318\text{GHz}$  has to be evaluated.

Concept Introduction:

The rotational partition function has the following expression:

${\text{q}}^{\text{R}}\text{=}\frac{\text{kT}}{\text{hB}}$

$\begin{array}{l}{\text{q}}^{\text{R}}\text{=}\text{Rotational}\text{partition}\text{function}\\ \text{k=}\text{Boltzmann}\text{constant}\text{=}\text{1}\text{.381}{\text{×10}}^{\text{-23}}{\text{JK}}^{\text{-1}}\\ \text{T}\text{=}\text{Temperature}\end{array}$

$\begin{array}{l}\text{h}\text{=}{\text{Plank}}^{\text{'}}\text{s}\text{constant}\text{=}\text{6}\text{.626}{\text{×10}}^{\text{-34}}\text{J}\text{s}\\ \text{B}\text{=}\text{Rotational}\text{constant}\end{array}$

b)

Interpretation Introduction

Interpretation:

The rotational partition function for ${}^{12}{\text{C}}^{16}{\text{O}}_2$ at $\text{298}\text{K}$ with rotational constant $11.70\text{GHz}$  has to be evaluated.

Concept Introduction:

The rotational partition function has the following expression:

${\text{q}}^{\text{R}}\text{=}\frac{\text{kT}}{\text{hB}}$

$\begin{array}{l}{\text{q}}^{\text{R}}\text{=}\text{Rotational}\text{partition}\text{function}\\ \text{k=}\text{Boltzmann}\text{constant}\text{=}\text{1}\text{.381}{\text{×10}}^{\text{-23}}{\text{JK}}^{\text{-1}}\\ \text{T}\text{=}\text{Temperature}\end{array}$

$\begin{array}{l}\text{h}\text{=}{\text{Plank}}^{\text{'}}\text{s}\text{constant}\text{=}\text{6}\text{.626}{\text{×10}}^{\text{-34}}\text{J}\text{s}\\ \text{B}\text{=}\text{Rotational}\text{constant}\end{array}$