Chapter 18, Problem 28PS

### 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

# Calculate ΔS°(universe) for the formation of 1 mol HCl(g) from gaseous hydrogen and chlorine. Is this reaction spontaneous under standard conditions at 25 °C? Explain your answer briefly.

Interpretation Introduction

Interpretation:

To calculate ΔS(universe) for the reaction of hydrogen and chlorine to give 1 mol of   hydrogen chloride gas and predict the 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.

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 reaction of hydrogen and chlorine to give hydrogen chloride gas is calculated below.

Given:

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:

12H2(g) + 12Cl2(g)HCl(g)

Calculation of ΔSo(system):

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

ΔS(system)=ΔrS°=nS°(products)nS°(reactants)=[(1 mol HCl(g)/mol-rxn)S°[HCl(g)][(0.5 mol H2(g)/mol-rxn)S°[H2(g)]+(0.5 mol Cl2(g)/mol-rxn)S°[Cl2(g)]]]

Substitute the values,

ΔrS°=[(1 mol HCl(g)/mol-rxn)(186.2 J/Kmol)[(0.5 mol H2(g)/mol-rxn)(130.7 J/Kmol)+(0.5 mol Cl2(g)/mol-rxn)(223.08 J/Kmol)]]=9

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