Chapter 14.6, Problem 8E

(A)

Interpretation Introduction

Interpretation:

The standard Gibbs energy of the reaction and equilibrium constant.

Concept Introduction:

Write the given reaction:

  ${\text{C}}_3{\text{H}}_8\rightleftharpoons {\text{C}}_2{\text{H}}_4+{\text{CH}}_4$

Write the expression for Gibbs energy for the given reaction.

  $\begin{array}{l}\Delta G^{f0}={\displaystyle \sum _{\text{product }}{G}^{f0}}-{\displaystyle \sum _{\text{reactant }}{G}^{f0}}\\ \Delta G^{f0}=G^{f0}\left({\text{C}}_2{\text{H}}_4\right)+G^{f0}\left({\text{CH}}_4\right)-G^{f0}\left({\text{C}}_3{\text{H}}_8\right)\end{array}$        (I)

(B)

Interpretation Introduction

Interpretation:

The composition of the exiting stream.

Concept Introduction:

Write an expression for the equilibrium constant.

  $K=\frac{\left[P_{{\text{C}}_2{\text{H}}_4}\right]\left[P_{{\text{CH}}_4}\right]}{\left[P_{{\text{C}}_3{\text{H}}_3}\right]}$        (III)

(C)

Interpretation Introduction

Interpretation:

The composition of the exiting stream, assuming it is at equilibrium.

Concept Introduction:

Write an expression for constant temperature $\left(K_T\right)$.

  $K_T=\frac{\frac{x^2}{1000+x}}{1000-x}$        (V)