Chapter 20.4, Problem 20.9AFP

Interpretation Introduction

Interpretation:

The temperature value for the following reaction has to be calculated using the Appendix B values.

    $2C\left(graphite\right)+O_2\left(g\right)\stackrel{}{\to }2CO\left(g\right)$

Concept introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter $\text{G}$.  All spontaneous process is associated with the decrease of free energy in the system.  The standard free energy change ${\text{(ΔG}}^{\text{°}}{}_{\text{rxn}})$ is the difference in free energy of the reactants and products in their standard state.

${\text{ΔG}}^{\text{°}}{}_{\text{rxn}}\text{=}\sum {\text{nΔG}}_{\text{f}}{}^{\text{°}}\text{(Products)-}\sum {\text{nΔG}}_{\text{f}}{}^{\text{°}}\text{(Reactants)}$

Free energy change$\text{ΔG}$: change in the free energy takes place while reactant converts to product where both are in standard state. It depends on the equilibrium constant $\text{K}$

  $\begin{array}{l}\text{ΔG =}{\text{ΔG}}^{\text{0}}\text{+}\text{RT}\ln \left(\text{K}\right)\\ {\text{ΔG}}^{\text{0}}\text{=}{\text{ΔH}}^{\text{0}}-{\text{TΔS}}^{\text{0}}\end{array}$

  Where,

  $\text{T}$ is the temperature

  $\text{ΔG}$ is the free energy

  ${\text{ΔG}}^{\text{0}}$, ${\text{ΔH}}^{\text{0}}$ and ${\text{ΔS}}^{\text{0}}$ is standard free energy, enthalpy and entropy values.

The formula of $\text{ΔH}$ in terms of $\text{ΔG}$ and $\text{TΔS}$ is,

        ${\text{ΔH}}^{\circ }={\text{ΔG}}^{\circ }+\text{T}\Delta \text{S}$

The formula of $\text{ΔG}$ in terms of equilibrium constant,

        $\Delta G=\Delta G^o-RTln(K)$