   Chapter 18, Problem 55GQ

Chapter
Section
Textbook Problem

Is the combustion of ethane, C2H6, product-favored at equilibrium at 25 °C?C2H6(g) + 7/2 O2(g) → 2 CO2(g) + 3 H2O(g)Answer the question by calculating the value of ΔS° (universe) at 298 K, using values of ΔfH° and S° in Appendix L. Does the answer agree with your preconceived idea of this reaction?

Interpretation Introduction

Interpretation:

It should be predicted that if the combustion of ethane is product-favored at equlibrium using calculation of ΔS(universe).

Concept introduction:

The universe consists of two parts, system and surroundings. The entropy change for the universe is the sum of entropy change for the system and for surroundings.

ΔS(universe)= ΔS(system)+ΔS(surroundings)

The ΔS(universe) should be greater than zero for a spontaneous process.

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

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

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

ΔS(surroundings)=ΔrHT

Here, ΔrHo is the enthalpy change for the reaction.

Explanation

The ΔS(universe) for the combustion of ethane is calculated below.

The Appendix L referred for the values of standard entropies and enthalpies.

The standard entropy of C2H6(g) is 229.2 J/Kmol.

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

The standard entropy of CO2(g) is 213.74 J/Kmol.

The standard entropy of H2O(g) is 188.84 J/Kmol.

The standard enthalpy of C2H6(g) is 83.85 kJ/mol.

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

The standard enthalpy of CO2(g) is 393.509 kJ/mol.

The standard enthalpy of H2O(g) is 241.83 kJ/mol.

The balanced chemical equation is:

C2H6(g)72O2(g)2CO2(g)+3H2O(g)

Calculation for ΔSo(system):

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

ΔS(system)=ΔrS°=nS°(products)nS°(reactants)=[[(2 mol CO2(g)/mol-rxn)S°[CO2(g)]+(3 mol H2O(g)/mol-rxn)S°[H2O(g)]][(1 mol C2H6(g)/mol-rxn)S°[C2H6(g)]+(3.5 mol O2(g)/mol-rxn)S°[O2(g)]]]

Substituting the values,

ΔS(system)=[[(2 mol CO2(g)/mol-rxn)(213.74 J/Kmol)+(3 mol H2O(g)/mol-rxn)(188.84 J/Kmol)][(1 mol C2H6(g)/mol-rxn)(213.74 J/Kmol)+(3.5 mol O2(g)/mol-rxn)(205.07 J/Kmol)]]=62

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