# 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 Δ r G ° 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?

### Chemistry & Chemical Reactivity

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

Chapter
Section

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 83SCQ
Textbook Problem
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## 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 of Solution

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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