   Chapter 18.7, Problem 2.1ACP

Chapter
Section
Textbook Problem

The decomposition of diamond to graphite [C(diamond) → C(graphite)] is thermodynamically favored, but occurs slowly at room temperature. a. Use ΔfG° values from Appendix L to calculate ΔrG° and Keq for the reaction under standard conditions and 298.15 K. b. Use ΔfH° and S° values from Appendix L to estimate ΔrG° and Keq for the reaction at 1000 K. Assume that enthalpy and entropy values are valid at these temperatures. Does heating shift the equilibrium toward the formation of diamond or graphite? c. Why is the formation of diamond favored at high pressures? d. The phase diagram shows that diamond is thermodynamically favored over graphite at 20,000 atmospheres pressure (about 2 GPa) at room temperature. Why is this conversion actually done at much higher temperatures and pressures?

(a)

Interpretation Introduction

Interpretation:

The value of free energy change and equilibrium constants at the given temperatures should be calculated.

Concept introduction:

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

ΔGo=ΔHo-TΔSo

It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°=fG°(products)fG°(reactants)

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

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo=-RTlnK

The rearranged expression is,

K=e-ΔrGoRT

Explanation

The value of ΔrGo and K for the decomposition of diamond at 298.15 K is calculated below.

Given:

Refer to Appendix L for the values of standard free energy values.

The given reaction is,

C(diamond)C(graphite)

The ΔrG° for C(diamond) is 2.9 kJ/mol.

The ΔrG° for C(graphite) is 0 kJ/mol.

ΔrG°=fG°(products)fG°(reactants)=[(1 mol C(graphite)/mol-rxn)ΔfG°[C(graphite)

(b)

Interpretation Introduction

Interpretation:

The value of free energy change and equilibrium constants at the given temperatures should be calculated.

Concept introduction:

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

ΔGo=ΔHo-TΔSo

It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°=fG°(products)fG°(reactants)

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

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo=-RTlnK

The rearranged expression is,

K=e-ΔrGoRT

(c)

Interpretation Introduction

Interpretation:

It should be identified that formation of diamond favour at high pressures or not.

Concept introduction:

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

ΔGo=ΔHo-TΔSo

It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°=fG°(products)fG°(reactants)

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

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo=-RTlnK

The rearranged expression is,

K=e-ΔrGoRT

(d)

Interpretation Introduction

Interpretation:

The reason that why given conversion is favoured at much higher temperatures and pressures should be identified.

Concept introduction:

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

ΔGo=ΔHo-TΔSo

It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°=fG°(products)fG°(reactants)

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

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo=-RTlnK

The rearranged expression is,

K=e-ΔrGoRT

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