   Chapter 21, Problem 97GQ

Chapter
Section
Textbook Problem

Using data in Appendix L, calculate ΔrG° values for the decomposition of MCO3 to MO and CO2 where M = Mg, Ca, Ba. What is the relative tendency of these carbonates to decompose?

Interpretation Introduction

Interpretation: To calculate the value of standard Gibbs free energy of reaction (ΔrG) for given metal carbonates.

The relative tendency of given metal carbonates to decompose is to be stated also.

Concept introduction:

The change of Gibbs free energy to form one mole of a substance from its constituent elements when all the substances in the standard form is known as standard Gibbs free energy of formation (ΔfG°).

The standard Gibbs free energy of reaction (ΔrG) in terms of standard Gibbs free energy of formation (ΔfG°)  is written as,

ΔrG=ΔfGproductsΔfGreactants (1)

Explanation

If the value of standard Gibbs free energy of reaction (ΔrG) is positive then the reaction is reactant favored. If the value of standard Gibbs free energy of reaction (ΔrG) is negative then the reaction is product favored and spontaneous.

The value of standard Gibbs free energy of reaction (ΔrG) for the decomposition of given carbonates is calculated below.

Given:

Refer to the appendix L for the value of standard Gibbs free energy of formation (ΔfG°).

The chemical reaction of decomposition of magnesium carbonate (MgCO3) into MgO and CO2 is written as,

MgCO3(s)MgO(s)+CO2(g)

The value of standard Gibbs free energy of formation (ΔfG°) for MgO is

568.93kJmol1.

The value of standard Gibbs free energy of formation (ΔfG°) for MgCO3 is

1028.2kJmol1.

The value of standard Gibbs free energy of formation (ΔfG°) for CO2 is

394.359kJmol1.

Substitute these values in equation (1) to calculate the value of standard Gibbs free energy of reaction (ΔrG) for MgCO3

ΔrG=(568.93kJmol1)+(394.359kJmol1)(1028.2kJmol1)=64.9kJmol1

Therefore, the value of standard Gibbs free energy of reaction (ΔrG) for MgCO3 is

64.9kJmol1.

The chemical reaction of decomposition of calcium carbonate (CaCO3) into CaO and CO2 is written as,

CaCO3(s)CaO(s)+CO2(g)

The value of standard Gibbs free energy of formation (ΔfG°) for CaO is

603.42kJmol1.

The value of standard Gibbs free energy of formation (ΔfG°) for CaCO3 is

1129.16kJmol1.

The value of standard Gibbs free energy of formation (ΔfG°) for CO2 is

394

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