   Chapter 18, Problem 41PS

Chapter
Section
Textbook Problem

Heating some metal carbonates, among them magnesium carbonate, leads to their decomposition.MgCO3(s) → MgO(s) + CO2(g) (a) Calculate ΔrG° and ΔrS° for the reaction. (b) Is the reaction product-favored at equilibrium at 298 K? (c) Is the reaction predicted to be product-favored at equilibrium at higher temperatures?

(a)

Interpretation Introduction

Interpretation:

The value of ΔG and ΔS should be calculated.

Concept introduction:

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

ΔG=ΔHTΔS

Here, ΔH is the change in enthalpy and ΔS is the change in entropy.

Explanation

The ΔG and ΔS for the reaction of decomposition of magnesium carbonate is calculated below.

Given:

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

MgCO3(s)MgO(s)+CO2(g)ΔfH°(kJ/mol)1111.69601.24393.509S(J/Kmol)65.8426.85213.74

ΔrH°=nΔfH°(products)nΔfH°(reactants)=[[(1 mol MgO(s)/mol-rxn)ΔfH°[MgO(s)]+(1 mol CO2(g)/mol-rxn)ΔfH°[CO2(g)]](1 mol MgCO3(s)/mol-rxn)ΔfH°[MgCO3(s)]]

Substitute the values,

ΔrH°=[[(1 mol MgO(s)/mol-rxn)(601.24 kJ/mol)+(1 mol CO2(g)/mol-rxn)(393.509 kJ/mol)](1 mol MgCO3(s)/mol-rxn)(1111

(b)

Interpretation Introduction

Interpretation:

The value of ΔG and ΔS should be calculated and predicted that the reaction is product-favoured or not.

Concept introduction:

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

ΔG=ΔHTΔS

Here, ΔH is the change in enthalpy and ΔS is the change in entropy.

(c)

Interpretation Introduction

Interpretation:

The value of ΔG and ΔS should be calculated and predicted that the reaction is product-favoured or not.

Concept introduction:

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

ΔG=ΔHTΔS

Here, ΔH is the change in enthalpy and ΔS is the change in entropy.

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