Chapter 18.6, Problem 18.7CYU

Interpretation Introduction

Interpretation:

The value of ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ for given reaction $\text{C}\left(\text{s}\right){\text{ + CO}}_{\text{2}}\left(\text{g}\right)\rightleftarrows \text{2CO}\left(\text{g}\right)$ should be determined which then used to calculate the equilibrium constant for the reaction.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$. It can be calculated in a similar manner as entropy and enthalpy. The expression for the free energy change is:

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}\text{= }\sum {\text{nΔ}}_{\text{f}}{\text{G}}^{\text{°}}\left(\text{products}\right)\text{- }\sum {\text{nΔ}}_{\text{f}}{\text{G}}^{\text{°}}\left(\text{reactants}\right)$

${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ is related to the equilibrium constant $\text{K}$ by the equation,

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{= - RTlnK}}_{\text{p}}$.

The rearranged expression required to calculate equilibrium constant from ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ is as follows,

  ${\text{K}}_{\text{p}}{\text{= e}}^{\text{-}\frac{{\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}}{\text{RT}}}$