   # Hydrogen and methane are two possible replacements for gasoline in automobiles. The reactions for their combustion are as follows: H 2 ( g )+ ½ O 2 ( g ) → H 2 O( ℓ ) CH 4 (g) + 2 O 2 ( g ) → CO 2 ( g ) + 2 H 2 O( ℓ ) (a) Calculate Δ r G ° for each reaction. (b) Calculate Δ G ° for each fuel on a per gram basis. (c) Which is a better fuel? 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 86SCQ
Textbook Problem
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## Hydrogen and methane are two possible replacements for gasoline in automobiles. The reactions for their combustion are as follows:H2(g)+ ½ O2(g) → H2O(ℓ)CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(ℓ) (a) Calculate ΔrG° for each reaction. (b) Calculate ΔG° for each fuel on a per gram basis. (c) Which is a better fuel? 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,

H2(g)+12O2(g)H2O(l)

The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)=[(1 mol H2O(l)/mol-rxn)ΔfG°[ H2O(l)]-[(0.5 mol O2(g)/mol-rxn)ΔfG°[O2(g)](1 mol H2(g)/mol-rxn)ΔfG°[H2(g)]] ]

Substitute the values,

ΔrG°[(1 mol H2O(l)/mol-rxn)(-237.15 kJ/mol)-[(0.5 mol O2(g)/mol-rxn)(0)(1 mol H2(g)/mol-rxn)(0)]]= - 237.15 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(l) is 237.15 kJ/mol.

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

(b)

Interpretation Introduction

Interpretation:

The standard free energy change for per gram of each fuel 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:

The better fuel should be identified.

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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