Chapter 12, Problem 12.9P

Interpretation Introduction

Interpretation:

The vibrational contribution to the molar entropy of $B{r}_2$ at 1000 K has to be calculated.

Concept Introduction:

The entropy 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 vibrational partition function is given below.

$q^V=\frac{1}{1-e^{\frac{-h\nu }{kT}}}$

At high temperature the expression for vibrational partition will be as follows,

$q^V=\frac{kT}{h\nu }$

Where,

    $\begin{array}{c}{q}^V=vibrationalpartitionfunction\\ h=plank\text{'}scons\tan t\\ k=boltzmanncons\tan t\\ T=temperature\\ \nu =vibrationalfrequency\end{array}$