Chapter 13, Problem 13B.10BE

Interpretation Introduction

Interpretation:

The vibrational partition function of $\text{HCN}$ at $\text{900}\text{K}$ given the wavenumbers, $\text{3311}{\text{cm}}^{-1}$, $\text{712}{\text{cm}}^{-1}$, $\text{2097}{\text{cm}}^{-1}$ has to be calculated.

Concept introduction:

Statistical thermodynamics is used to describe all the possible configurations in a system at given physical quantities such as pressure, temperature, and a number of particles in the system. The important quantity in the thermodynamic is partition function that is represented as,

  $q={\displaystyle \sum _i{g}_i{e}^{-\beta {\in }_i}}$

The vibrational partition function for molecules is represented as shown below.

$q^{\text{V}}=\frac{1}{\text{1}-e^{-\beta hc\tilde{\nu }}}$