Chapter 18, Problem 102SCQ

### 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

# Consider the reaction of NO and Cl2 to produce NOCI. (a) What is ΔS°(system) for this reaction? (b) Does ΔS°(system) change with temperature? (c) Does ΔS°(surroundings) change with temperature? (d) Does ΔS°(universe) always change with an increase in temperature? (e) Do exothermic reactions always lead to positive values of ΔS°(universe)? (f) Is the NO + Cl2 reaction spontaneous at 298 K? At 700 K?

(a)

Interpretation Introduction

Interpretation:

The  ΔSo(system) for reaction between NO(g) and Cl2(g) should be determined.

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

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

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

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

ΔSo(surroundings)=rHoT

Here, ΔrH° is the enthalpy change for the reaction.

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

ΔGo= ΔHo- TΔSo

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

Explanation

The  ΔSo(system) for the reaction is calculated below.

Given:

Refer to Appendix L for the values of standard entropies.

The standard entropy of NOCl(g) is 261.8 J/Kmol.

The standard entropy of NO(g) is 210.76 J/Kmol.

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

The balanced chemical equation is:

NO(g)+12Cl2(g)NOCl(g)

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

ΔSo(system)=ΔrS°nS°(products)-nS°(reactants)=[(1 mol NOCl(g)/mol-rxn)S°

(b)

Interpretation Introduction

Interpretation:

It should be identified that  ΔSo(system) changes with temperature or not.

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

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

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

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

ΔSo(surroundings)=rHoT

Here, ΔrH° is the enthalpy change for the reaction.

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

ΔGo= ΔHo- TΔSo

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

(c)

Interpretation Introduction

Interpretation:

It should be identified that ΔSo(surroundings) changes with temperature.

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

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

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

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

ΔSo(surroundings)=rHoT

Here, ΔrH° is the enthalpy change for the reaction.

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

ΔGo= ΔHo- TΔSo

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

(d)

Interpretation Introduction

Interpretation:

It should be identified that ΔSo(surroundings) changes with increase in temperature or not.

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

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

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

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

ΔSo(surroundings)=rHoT

Here, ΔrH° is the enthalpy change for the reaction.

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

ΔGo= ΔHo- TΔSo

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

(e)

Interpretation Introduction

Interpretation:

It should be identified that does exothermic reaction will always results in positive ΔSo(universe) value.

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

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

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

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

ΔSo(surroundings)=rHoT

Here, ΔrH° is the enthalpy change for the reaction.

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

ΔGo= ΔHo- TΔSo

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

(f)

Interpretation Introduction

Interpretation:

It should be identified that reaction of NO(g) and Cl2(g) is spontaneous or not.

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

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

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

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

ΔSo(surroundings)=rHoT

Here, ΔrH° is the enthalpy change for the reaction.

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

ΔGo= ΔHo- TΔSo

ΔGo is also related to the equilibrium constant K by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

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