Chapter 19: Spontaneous Change: Entropy and Free Energy

Prentice-Hall © 2007General Chemistry: Chapter 19Slide 1 of 44

CHEMISTRYNinth

Edition GENERAL

Principles and Modern Applications

Petrucci • Harwood • Herring • Madura

Chapter 19: Spontaneous Change: Entropy and Free Energy


Contents

19-1 Spontaneity: The Meaning of Spontaneous Change

19-2 The Concept of Entropy

19-3 Evaluating Entropy and Entropy Changes

19-4 Criteria for Spontaneous Change: The Second Law of

Thermodynamics

19-5 Standard Free Energy Change, ΔG°

19-6 Free Energy Change and Equilibrium

19-7 ΔG° and Keq as Functions of Temperature


19-1 Spontaneity: The Meaning of Spontaneous Change


Spontaneous Process

A process that occurs in a system left to itself. Once started, no external actions is necessary to make

the process continue.

A non-spontaneous process will not occur without external action continuously applied.

4 Fe(s) + 3 O2(g) → 2 Fe2O3(s)

H2O(s) H2O(l)


Spontaneous Process

Potential energy decreases. For chemical systems the internal energy U is

equivalent to potential energy.

Berthelot and Thomsen 1870’s. Spontaneous change occurs in the direction in which

the enthalpy of a system decreases. Mainly true but there are exceptions.


19-2 The Concept of Entropy

Entropy, S. The greater the number

of configurations of the microscopic particles among the energy levels in a particular system, the greater the entropy of the system.

ΔS > 0 spontaneous

ΔU = ΔH = 0


The Boltzmann Equation for Entropy

Entropy, S States.

The microscopic energy levels available in a system.

Microstates, W. The particular way in which particles are distributed

amongst the states. Number of microstates = W.

The Boltzmann constant, k. Effectively the gas constant per molecule = R/NA.

S = k lnW


Entropy Change

ΔS = qrev

TFor changes occurring at constant temperature


19-3 Evaluating Entropy and Entropy Changes

Phase transitions. Exchange of heat can be carried out reversibly.

ΔS = ΔH

Ttr

H2O(s, 1 atm) H2O(l, 1 atm) ΔHfus = 6.02 kJ at 273.15 K

ΔSfus = ΔHfus

Ttr

°=

6.02 kJ mol-1

273.15 K= 2.2010-2 kJ mol-1 K-1


Trouton’s Rule

ΔS = ΔHvap

Tbp

87 kJ mol-1 K-1


Absolute Entropies

Third law of thermodynamics. The entropy of a pure perfect crystal at 0 K is zero.

Standard molar entropy. Tabulated in Appendix D.

ΔS = [ pS°(products) - rS°(reactants)]


Entropy as a Function of Temperature


Vibrational Energy and Entropy


19-4 Criteria for Spontaneous Change:The Second Law of Thermodynamics.

ΔStotal = ΔSuniverse = ΔSsystem + ΔSsurroundings

The Second Law of Thermodynamics:

ΔSuniverse = ΔSsystem + ΔSsurroundings > 0

All spontaneous processes produce an increase in the entropy of the universe.


Free Energy and Free Energy Change

Hypothetical process: only pressure-volume work, at constant T and P.

qsurroundings = -qp = -ΔHsys

Make the enthalpy change reversible. large surroundings, infinitesimal change in temperature.

Under these conditions we can calculate entropy.


Free Energy and Free Energy Change

TΔSuniv. = TΔSsys – ΔHsys = -(ΔHsys – TΔSsys)

-TΔSuniv. = ΔHsys – TΔSsys

G = H - TS

ΔG = ΔH - TΔS

For the universe:

For the system:

ΔGsys = - TΔSuniverse


Criteria for Spontaneous Change

ΔGsys < 0 (negative), the process is spontaneous.

ΔGsys = 0 (zero), the process is at equilibrium.

ΔGsys > 0 (positive), the process is non-spontaneous.

J. Willard Gibbs

1839-1903


Table 19.1 Criteria for Spontaneous Change


19-5 Standard Free Energy Change, ΔG°

The standard free energy of formation, ΔGf°. The change in free energy for a reaction in which a

substance in its standard state is formed from its elements in reference forms in their standard states.

The standard free energy of reaction, ΔG°.

ΔG° = [ p ΔGf°(products) - r ΔGf°(reactants)]


Free Energy Change and Equilibrium

Condensation Equilibrium Vaporization


Relationship of ΔG° to ΔG for Non-standard Conditions

2 N2(g) + 3 H2(g) 2 NH3(g)

ΔG = ΔH - TΔS ΔG° = ΔH° - TΔS°

For ideal gases ΔH = ΔH°

ΔG = ΔH° - TΔS


Relationship Between S and S°

qrev = -w = RT lnVf

Vi

ΔS = qrev

T= R ln

Vf

Vi

ΔS = Sf – Si = R lnVf

Vi

= R lnPi

Pf

= -R lnPf

Pi

S = S° - R ln

P

P°= S° - R ln

P1

= S° - R ln P


N2(g) + 3 H2(g) 2 NH3(g)

SNH3 =

SNH3 – Rln PNH3

SN2 =

SN2 – Rln PN2

SH2 =

SH2 – Rln PH2

ΔSrxn = 2(SNH3 – Rln PNH3

) – (SN2 – Rln PN2

) –3(SH2 – Rln PH2

)

ΔSrxn = 2 SNH3 – SN2

–3SH2+ Rln

PN2PH2

PNH3

2

3

ΔSrxn = ΔS°rxn + RlnPN2

PH2

PNH3

2

3


ΔG Under Non-standard Conditions

ΔG = ΔH° - TΔS ΔSrxn = ΔS°rxn + RlnPN2

PH2

PNH3

2

2

3

ΔG = ΔH° - TΔS°rxn – TR lnPN2

PH2

PNH3

2

2

3

ΔG = ΔG° + RT lnPN2

PH2

2

PNH3

2

3

ΔG = ΔG° + RT ln Q


ΔG and the Equilibrium Constant Keq

ΔG = ΔG° + RT ln Q

ΔG = ΔG° + RT ln Keq= 0

If the reaction is at equilibrium then:

ΔG° = -RT ln Keq


Criteria for Spontaneous Change

Every chemical reaction consists of both a forward and a reverse reaction.

The direction of spontaneous change is the direction in which the free energy decreases.


Significance of the Magnitude of ΔG


19-7 ΔG° and Keq as Functions of Temperature

ΔG° = ΔH° -TΔS° ΔG° = -RT ln Keq

ln Keq = -ΔG°

RT=

-ΔH°

RT

TΔS°

RT+

ln Keq = -ΔH°

RT

ΔS°

R+


Van’t Hoff Equation

If we evaluate this equation for a change in temperature:

ln = -ΔH°

RT2

ΔS°

R+

-ΔH°

RT1

ΔS°

R+-

=-ΔH°

R

1

T2

1

T1

-

Keq1

Keq2

ln Keq1

Keq2

Chapter 19: Spontaneous Change: Entropy and Free Energy

Documents

Transcript of Chapter 19: Spontaneous Change: Entropy and Free Energy