Chapter 18, Problem 77GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Sulfur undergoes a phase transition between 80 and 100 °C.S8(rhombic) → S8(monoclinic)ΔrH° = 3.213 kl/mol-rxn ΔrS° = 8.7 J/K · mol-rxn (a) Estimate ΔrG° for the transition at 80.0 °C and 110.0 °C. What do these results tell you about the stability of the two forms of sulfur at each of these temperatures? (b) Calculate the temperature at which ΔrG° = 0. What is the significance of this temperature?

(a)

Interpretation Introduction

Interpretation:

The ΔrGo value for given transition at temperature 80oCand110oC should be estimated and stability of the two forms at these given temperatures should be defined.

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 ΔrGo value when sulphur undergoes a phase transition is calculated below.

Given:

The given reaction is,

S8(rhombic)S8(monoclinic)

The ΔrH° for the reaction is  3.213 kJ/mol-rxn.

The ΔrS° for the reaction is 8.7 J/Kmol-rxn.

At 80 °C,

ΔrGorHo-TΔrSo

Substituting the value of ΔrH° and ΔrS°.

ΔrGo= 3.213 kJ/mol-rxn-[(353K)(8.7 J/K×mol-rxn)](1 kJ1000 J)= 0

(b)

Interpretation Introduction

Interpretation:

The temperature at which ΔrGo value is zero should be calculated and the significance of that temperature should be identified.

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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