   Chapter 21, Problem 23PS

Chapter
Section
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 ΔrH°ΔrS° and ΔrG 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)CO(g)+3H2(g)ΔfH°(kJ/mol)74.87241.83110.5250S(J/Kmol)186.26188.84197.674130.7

The enthalpy change can be determined as follows,

ΔrH°=nΔfH°(products)nΔfH°(reactants)=[[(1 mol CO(g)/mol-rxn)ΔfH°[CO(g)]+(3 mol H2(g)/mol-rxn)ΔfH°[H2(g)]][(1 mol CH4(g)/mol-rxn)ΔfH°[CH4(g)]+(1 mol H2O(g)/mol-rxn)ΔfH°[H2O(g)]] ]

Substitute the values,

ΔrH°=[[(1 mol CO(g)/mol-rxn)(110.525 kJ/mol)+(3 mol H2(g)/mol-rxn)(0 kJ/mol)][(1 mol CH4(g)/mol-rxn)(74.87 kJ/mol)+(1 mol H2O(g)/mol-rxn)(241

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