   Chapter 18, Problem 72GQ

Chapter
Section
Textbook Problem

A crucial reaction for the production of synthetic fuels is the production of H2 by the reaction of coal with steam. The chemical reaction isC(s) + H2O(g)→ CO(g) + H2(g) (a) Calculate ΔrG° for this reaction at 25 °C, assuming C(s) is graphite. (b) Calculate Kp for the reaction at 25 °C. (c) Is the reaction predicted to be product-favored at equilibrium at 25 °C? If not, at what temperature will it become so?

(a)

Interpretation Introduction

Interpretation:

The ΔrG° for the production of H2 by reaction of coal with steam should be calculated.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrG°. It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

ΔrG° is related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

Explanation

The ΔrG° for the given reaction is calculated below.

Given:

The Appendix L referred for the values of standard free energy values.

The given reaction is,

C(s) + H2O(g)CO(g)+H2(g)

The ΔrG° for C(s) is 0 kJ/mol.

The ΔrG° for H2O(g) is 228.59 kJ/mol.

The ΔrG° for CO(g) is 137.168 kJ/mol.

The ΔrG° for H2(g) is 0 kJ/mol.

ΔrG°fG°(products)fG°(reactants)=[[(1 mol CO(g)/mol-rxn)ΔfG°[CO(g)]+(1 mol H2(

(b)

Interpretation Introduction

Interpretation:

The equilibrium constant, Kp for the production of H2 by reaction of coal with steam should be calculated.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrG°. It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

ΔrG° is related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

(c)

Interpretation Introduction

Interpretation:

It should be predicted that whether the reaction is product favoured at equilibrium at temperature 25oC or at temperature it reach equilibrium.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrG°. It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

ΔrG° is related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

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