Chapter 21, Problem 23PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Write a balanced chemical equation for the preparation of H2 (and CO) by the reaction of CH4 and water. Using data in Appendix L, calculate ΔrH°, ΔrG°, and ΔrS° for this reaction at 298 K.

Interpretation Introduction

Interpretation:

The value of ΔrH°, ΔrS° and ΔrG for the preparation of hydrogen should be calculated.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrG. It is related to entropy and entropy by the following expression,

ΔrG=ΔrHTΔrS

Here, ΔrH is the change in enthalpy and ΔrS is the change in entropy.

The enthalpy change is expressed as,

ΔrH°=nΔfH°(products)nΔfH°(reactants)

The entropy change is expressed as,

ΔrS°=nS°(products)nS°(reactants)

Explanation

The value of Î”rHÂ°Î”rSÂ° and Î”rGâˆ˜ for the preparation of hydrogen is calculated below.

Given:

Refer to Appendix L for the values of standard entropies and enthalpies.

CH4(g)+H2O(g)â†’CO(g)+3H2(g)Î”fHÂ°(kJ/mol)âˆ’74.87âˆ’241.83âˆ’110.5250Sâˆ˜(J/Kâ‹…mol)186.26188.84197.674130.7

The enthalpy change can be determined as follows,

Î”rHÂ°=âˆ‘nÎ”fHÂ°(products)âˆ’âˆ‘nÎ”fHÂ°(reactants)=[[(1Â molÂ CO(g)/mol-rxn)Î”fHÂ°[CO(g)]+(3Â molÂ H2(g)/mol-rxn)Î”fHÂ°[H2(g)]]âˆ’[(1Â molÂ CH4(g)/mol-rxn)Î”fHÂ°[CH4(g)]+(1Â molÂ H2O(g)/mol-rxn)Î”fHÂ°[H2O(g)]]Â ]Â

Substitute the values,

Î”rHÂ°=[[(1Â molÂ CO(g)/mol-rxn)(âˆ’110.525Â kJ/mol)+(3Â molÂ H2(g)/mol-rxn)(0Â kJ/mol)]âˆ’[(1Â molÂ CH4(g)/mol-rxn)(âˆ’74.87Â kJ/mol)+(1Â molÂ H2O(g)/mol-rxn)(âˆ’241

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