Chapter 5, Problem 5.12PS

(a)

Summary Introduction

To prove: The equilibrium constant K’_AD for the overall reaction is the product of the three component equilibrium constants for the given reaction:

$\text{A}\rightleftharpoons \text{B}\rightleftharpoons \text{C}\rightleftharpoons \text{D}$

K’_AB,  K’_BC, and K’_CD are the respective equilibrium constants for reaction $\text{A}\rightleftharpoons \text{B}$, $\text{B}\rightleftharpoons \text{C}$ and $\text{C}\rightleftharpoons \text{D}$.

Introduction: In a system, multiple chemical reactions can take place at the same time. Each of the proceeding reactions has their own thermodynamic parameters such as enthalpy, free energy and others. If these reactions take place in a sequential manner and are a part of a bigger chemical process, then the total free energy for the complete system can be calculated using the free energies of the individual reactions.

(b)

Summary Introduction

To prove: For the overall conversion of A to D, $\Delta G°\text{'}$ is the sum of the three component $\Delta G°\text{'}$ values that are:

$\Delta G°{\text{'}}_{\text{AD}}=\Delta G°{\text{'}}_{\text{AB}}+\Delta G°{\text{'}}_{\text{BC}}+\Delta G°{\text{'}}_{\text{CD}}$

Introduction: In a system, multiple chemical reactions can take place at the same time. Each of the proceeding reactions has their own thermodynamic parameters such as enthalpy, free energy and others. If these reactions take place in a sequential manner and are a part of a bigger chemical process, then the total free energy for the complete system can be calculated using the free energies of the individual reactions.

(c)

Summary Introduction

To prove: The $\Delta G\text{'}$ values are also additive.

Introduction: In a system, multiple chemical reactions can take place at the same time. Each of the proceeding reactions has their own thermodynamic parameters such as enthalpy, free energy and others. If these reactions take place in a sequential manner and are a part of a bigger chemical process, then the total free energy for the complete system can be calculated using the free energies of the individual reactions.