Chapter 12, Problem 12.12P

Interpretation Introduction

Interpretation:

The standard molar Gibbs energy of carbon dioxide gas at 298 K relative to its value at 0K has to be calculated.

Concept Introduction:

Standard molar Gibbs energy can be calculated using following formula.

  $G_m^{\Theta }-G_m^{\Theta }\left(0\right)=-RT\ln \frac{q_m^{\Theta }}{N_A}$

Where,

    $\begin{array}{c}{G}_m^{\Theta }-G_m^{\Theta }\left(0\right)=s\tan dardmolarGibbsenergy\\ q_m^{\Theta }=partitionfunctionats\tan dardconditions\\ R=universalgascons\tan t\\ T=temperature\\ N_A=avogadronumber\end{array}$

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,

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

The expression for vibrational partition function is given below.

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

Where,

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