   Chapter 21, Problem 113GQ

Chapter
Section
Textbook Problem

Metal sulfides roasted in air produce metal oxides. 2 ZnS(s) + 3 O 2 (g)  →  2 ZnO(s) + 2 SO 2 (g) Use thermodynamics to decide if the reaction is product- or reactant-favored at equilibrium at 298 K. Will the reaction be more or less product-favored at a high temperature?

Interpretation Introduction

Interpretation:

To calculate the reaction is reactant or product favored at equliribrium at 298 K and the reaction is more or less product favored at higher temperature.

Concept introduction:

The  ΔS(system) can be calculated by the following expression,

ΔS(system)=ΔrS°=nS°(products)nS°(reactants)

Enthalpy of formation of the reaction can be calculated by following expression,

ΔrH°=nΔfH°(products)nΔfH°(reactants)

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

ΔG=ΔHTΔS

Here, ΔrH is the enthalpy change for the reaction.

If the value of ΔrG is negative the reaction is product favored at equilibrium at 298 K.

Explanation

The enthapy of formation, entropy change for the system and free energy change for the given reaction is calculated below.

Given:

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

The standard entropy of ZnS(s) is 57.7 J/Kmol.

The standard entropy of O2(g) is 205.07 J/Kmol.

The standard entropy of SO2(g) is 248.21 J/Kmol.

The standard entropy of ZnO(s) is 43.64 J/Kmol.

The standard enthalpy of ZnS(s) is 205.98 kJ/mol.

The standard enthalpy of O2(g) is 0 kJ/mol.

The standard enthalpy of ZnO(s) is 348.28 kJ/mol.

The standard enthalpy of SO2(g) is 296.84 kJ/mol.

The balanced chemical equation is:

2ZnS(g) + 3O2(g)2ZnO(s)+2SO2(g)

The  ΔS(system) can be calculated by the following expression,

ΔS(system)=ΔrS°=nS°(products)nS°(reactants)=[[(2 mol ZnO(s)/mol-rxn)S°[ZnO(s)]+(2 mol SO2(g)/mol-rxn)S°[SO2(g)]][(2 mol ZnS(s)/mol-rxn)S°[ZnS(s)]+(3 mol O2(g)/mol-rxn)S°[O2(g)]]]

Substitute the values,

ΔS(system)=[[(2 mol ZnO(s)/mol-rxn)S°[(87.28 J/Kmol)]+(2 mol SO2(g)/mol-rxn)S°[(496.42 J/Kmol)]][(2 mol ZnS(s)/mol-rxn)S°[(115

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