   # Two processes that can be used to generate hydrogen are the electrolysis of water 2 H 2 O( ℓ ) → 2 H 2 (g) + O 2 (g) and the reaction of methane with steam CH 4 (g) + H 2 O(g) → 3 H 2 (g) + CO(g) (a) Calculate Δ r G ° for each reaction. (b) For each reaction, calculate Δ G ° per mole of hydrogen produced. (c) Which process do you think is better to use to obtain hydrogen? Explain. ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 85SCQ
Textbook Problem
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## Two processes that can be used to generate hydrogen are the electrolysis of water2 H2O(ℓ) → 2 H2(g) + O2(g)and the reaction of methane with steamCH4(g) + H2O(g) → 3 H2(g) + CO(g) (a) Calculate ΔrG° for each reaction. (b) For each reaction, calculate ΔG° per mole of hydrogen produced. (c) Which process do you think is better to use to obtain hydrogen? Explain.

(a)

Interpretation Introduction

Interpretation:

The standard free energy change for the given reactions should be calculated.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔGo. 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)

### Explanation of Solution

The standard free energy change for the electrolysis of water and the reaction of methane with steam is calculated below.

Given:

Refer to Appendix L for the standard free energy change values.

The standard free energy change value of H2O(l) is 237.15 kJ/mol.

The standard free energy change value of O2(g) is 0 kJ/mol.

The standard free energy change value of H2(g) is 0 kJ/mol.

The balanced chemical equation is,

2H2O(l)2H2(g)+O2(g)

The expression for the free energy change is:

ΔrG°=fG°(products)fG°(reactants)=[[(1 mol O2(g)/mol-rxn)ΔfG°[O2(g)](2 mol H2(g)/mol-rxn)ΔfG°[H2(g)]]-(2 mol H2O(l)/mol-rxn)ΔfG°[ H2O(l)] ]

Substitute the values,

ΔrG°=[[(1 mol O2(g)/mol-rxn)(0)(2 mol H2(g)/mol-rxn)(0)]-(2 mol H2O(l)/mol-rxn)(-237.15 kJ/mol) ]ΔrG°=474.3 kJ/mol-rxn

The standard free energy change value of CH4(g) is 50.8 kJ/mol.

The standard free energy change value of H2O(g) is 228.59 kJ/mol.

The standard free energy change value of H2(g) is 0 kJ/mol

(b)

Interpretation Introduction

Interpretation:

For given reactions the ΔGo value for per mole of hydrogen produced should be calculated.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔGo. 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)

(c)

Interpretation Introduction

Interpretation:

From the reactions the one that is better in production of hydrogen should be explained.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔGo. 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)

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