   # Heating some metal carbonates, among them magnesium carbonate, leads to their decomposition. MgCO 3 (s) → MgO(s) + CO 2 (g) (a) Calculate Δ r G ° and Δ r S ° 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? ### Chemistry & Chemical Reactivity

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

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 25PS
Textbook Problem
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## 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 of Solution

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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