   Chapter 18.4, Problem 18.3CYU

Chapter
Section
Textbook Problem

Based on ΔrH° and ΔrS°, predict the spontaneity of the reaction of hydrogen and chlorine to give hydrogen chloride gas under standard conditions (at 298 K). Calculate ΔS° (universe) to verify your prediction. H 2 ( g ) + C l 2 ( g ) → 2   H C l ( g )

Interpretation Introduction

Interpretation:

The ΔSo(universe) for the reaction of hydrogen and chlorine that results in formation of hydrogen chloride gas should be calculated. It should be identified that the calculated ΔS(universe) value is in accordance with the predicted spontaneity of the reaction.

Concept introduction:

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

ΔSo(universe)= ΔSo(system)+ΔSo(surroundings)

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

The  ΔS(system) calculated by using the following expression,

ΔSo(system)rS°=nS°(products)nS°(reactants)

The ΔSo(surroundings) calculated by using the following expression,

ΔSo(surroundings)rHoT

Here, ΔrHo is the enthalpy change for the reaction and T is the temperature.

Explanation

The calculation of ΔSo(universe) for the reaction of hydrogen and chlorine to give hydrogen chloride gas is calculated below.

Given: H2(g)+Cl2(g)2HCl(g)

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

The standard entropy of H2(g) is 130.7 J/Kmol

The standard entropy of Cl2(g) is 223.08 J/Kmol

The standard entropy of HCl(g) is 186.2 J/Kmol

The standard enthalpy of H2(g) is 0 kJ/mol

The standard enthalpy of Cl2(g) is 0 kJ/mol

The standard enthalpy of HCl(g) is -92.31 kJ/mol

The balanced chemical equation is: H2(g)+Cl2(g)2HCl(g)

Calculation for ΔSo(system):

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

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

ΔSo(system)=[(2 mol HCl(g)/mol-rxn)S°[HCl(g)]-[(1 mol H2(g)/mol-rxn)S°[H2(g)]+(1 mol Cl2(g)/mol-rxn)S°[Cl2(g)]]]

Substituting the entropy values referred from appendix L results to yield the answer as follows,

ΔrS°=[(2 mol HCl(g)/mol-rxn)(186.2 J/K×mol)-[(1 mol H2(g)/mol-rxn)(130.7 J/K×mol)+(1 mol Cl2(g)/mol-rxn)(223.08 J/K×mol)]]=18

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