Chapter 12, Problem 12.10P

Interpretation Introduction

Interpretation:

The molar entropy of nitrogen gas at 298 K has to be calculated.

Concept Introduction:

The entropy of distinguishable particle in terms of partition function can be calculated using following formula.

$S=\frac{U-U\left(0\right)}{T}+N_{A}k\ln q$

Where,

    $\begin{array}{l}S=entropy\\ U-U\left(0\right)=changein\mathrm{int}ernalenergy\\ k=plank\text{'}scons\tan t\\ q=partitionfunction\end{array}$

The expression for the translational partition function is given below.

$q^T=\frac{{\left(2\pi mkT\right)}^{\frac{3}{2}}V}{h^3}$

Where,

    $\begin{array}{c}{q}^T=translationalpartitionfunction\\ m=molecularmass\\ T=temperature\\ h=plank\text{'}scons\tan t\\ V=volumeats\tan dardconditions\\ k=boltzmanncons\tan t\end{array}$

The expression for rotational partition function is given below.

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

Where,

    $\begin{array}{c}{q}^R=rotationalpartitionfunction\\ k=boltzmanncons\tan t\\ T=temperature\\ h=plank\text{'}scons\tan t\\ \sigma =symmetrynumber\\ B=rotationalcons\tan t\end{array}$