Chapter 18, Problem 46PS

Interpretation Introduction

Interpretation:

The equilibrium constant for the given reaction should be calculated. The sign of ${\text{Δ}}_{\text{r}}{G}^{\text{°}}$ and magnitude of $K_{\text{p}}$ should be explained.

Concept introduction:

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

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

$\Delta G^{\circ }$ is related to the equilibrium constant $K$ by the equation,

  ${\Delta }_{\text{r}}{G}^{\circ }=-RT\ln K_{\text{p}}$.

The rearranged expression is,

  $K_{\text{p}}=e^{-\frac{{\Delta }_{\text{r}}{G}^{\circ }}{RT}}$