   Chapter 18.7, Problem 2.2ACP

Chapter
Section
Textbook Problem

It has been demonstrated that buckminsterfullerene (C60), another allotrope of carbon (Section 2.3), may be converted into diamond at room temperature and 20,000 atmospheres pressure (about 2 GPa). The standard enthalpy of formation, ΔfH°, for buckminsterfullerene is 2320 kJ/mol at 298.2 K. a. Calculate ΔrH° for the conversion of C60 to diamond at standard state conditions and 2982 K. b. Assuming that the standard entropy per mole of carbon in both C60 and diamond is comparable (both about 23 J/K mol), is the conversion of C60 to diamond product-favoredat room temperature?

(a)

Interpretation Introduction

Interpretation:

The ΔrH° for the conversion of C60 to diamond should be 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

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.

The standard free enthalpy change is expressed as,

ΔrH°=fH°(products)fH°(reactants)

Explanation

The ΔrH° for the conversion of C60 to diamond is calculated below.

Given:

Refer to Appendix L for the values of standard enthalpies.

The standard enthalpy value for C60 is 2320 kJ/mol.

The standard enthalpy value for C(diamond) is 1.8 kJ/mol.

The given reaction is,

C60(s)60 C(diamond)

The standard enthalpy change is,

ΔrH°=fH°(products)fH°(reactants)=[(60 mol C(diamond)/mol-rxn)ΔfH°

(b)

Interpretation Introduction

Interpretation:

The conversion of C60 to diamond should be identified that it is product favoured at room temperature 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

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.

The standard free enthalpy change is expressed as,

ΔrH°=fH°(products)fH°(reactants)

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