   Chapter 18, Problem 98SCQ

Chapter
Section
Textbook Problem

The formation of diamond from graphite is a process of considerable importance. (a) Using data in Appendix L, calculate ΔrS°, ΔrH°, and ΔrG° for this process at 25 °C. (b) The calculations will suggest that this process is not possible at any temperature. However, the synthesis of diamonds by this reaction is a commercial process. How can this contradiction be rationalized? (Note: In the industrial synthesis, high pressure and high temperatures are used.)

(a)

Interpretation Introduction

Interpretation:

The value of ΔrH°, ΔrS° and ΔrGo for the formation of diamond at given temperature at given temperature.

Concept introduction:

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

ΔrGorHo-TΔrSo

Here, ΔrH° is the change in enthalpy and ΔrS° is the change in entropy.

Explanation

The value of ΔrH°, ΔrS° and ΔrGo for formation of diamond is calculated below.

Given:

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

The standard entropy value for C(graphite) is 5.6 J/Kmol.

The standard entropy value for C(diamond) is 2.377 J/Kmol

The standard enthalpy value for C(graphite) is 0 kJ/mol.

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

The given reaction is,

C(graphite)C(diamond)

ΔrH°=fH°(products)fH°(reactants)[(1 mol C(diamond)/mol-rxn)ΔfH°[C(diamond)]-(1 mol C(graphite)/mol-rxn)ΔfH°[C(graphite)]]

Substitute the values,

ΔrH°[(1 mol C(diamond)/mol-rxn)(1.8 kJ/mol)-(1 mol C(graphite)/mol-rxn)(0 kJ/mol)]= 1

(b)

Interpretation Introduction

Interpretation:

The contradiction in production of diamond from graphite with the calculations should be rationalized.

Concept introduction:

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

ΔrGorHo-TΔrSo

Here, ΔrH° is the change in enthalpy and ΔrS° is the change in entropy.

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