   Chapter 18, Problem 101SCQ

Chapter
Section
Textbook Problem

Write an equation for the decomposition of 1.0 mol of gaseous methanol to the elements in their standard states. (a) How does the value of ΔrG° change as the temperature increases? (b) Is there a temperature between 400 K and 1000 K at which the decomposition is product-favored at equilibrium?

(a)

Interpretation Introduction

Interpretation:

The change in value of ΔrG° as temperature increases for given decomposition reaction of methanol to elements should be identified.

Concept introduction:

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

ΔrGorHo-TΔrSo

The sign of ΔrGo should be positive for a product-favored reaction. Thus, spontaneous reactions are referred to those that have negative free energy formation.

Explanation

The changes in ΔrGo on the decomposition of methanol is predicted below.

Given:

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

The standard entropy of CH3OH(l) is 127.19 J/Kmol.

The standard entropy of H2(g) is 130.7 J/Kmol.

The standard entropy of C(s) is 5.6 J/Kmol.

The standard entropy of O2(g) is 205.07 J/Kmol.

The standard enthalpy of CH3OH(l) is 238.4 kJ/mol-rxn.

The standard enthalpy of H2(g) is 0 kJ/mol-rxn.

The standard enthalpy of C(s) is 0 kJ/mol-rxn.

The standard enthalpy of O2(g) is 0 kJ/mol-rxn.

The balanced chemical equation is:

CH3OH(l)C(s) + 2H2(g) + 12O2(g)

The expression for the standard entropy change is,

ΔrS°nS°(products)-nS°(reactants)=[[(1 mol C(s)/mol-rxn)S°[C(s)]+(0.5 mol O2(g)/mol-rxn)S°[O2(g)]+(2 mol H2(g)/mol-rxn)S°[H2(g)]]-(1 mol CH3OH(l)/mol-rxn)S°[CH3OH(l)]]

Substitute the values,

ΔrS°=[[(1 mol C(s)/mol-rxn)(5.6 J/K×mol)+(0

(b)

Interpretation Introduction

Interpretation:

The temperature at which decomposition is product favored at equilibrium should be identified.

Concept introduction:

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

ΔrGorHo-TΔrSo

The sign of ΔrGo should be positive for a product-favored reaction. Thus, spontaneous reactions are referred to those that have negative free energy formation.

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