Date post: | 21-Dec-2015 |
Category: |
Documents |
View: | 238 times |
Download: | 6 times |
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 2 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 3 of 44
19-1 Spontaneity: The Meaning of Spontaneous Change
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 4 of 44
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)
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 5 of 44
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.
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 6 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 7 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 8 of 44
Entropy Change
ΔS = qrev
TFor changes occurring at constant temperature
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 9 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 10 of 44
Trouton’s Rule
ΔS = ΔHvap
Tbp
87 kJ mol-1 K-1
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 11 of 44
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)]
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 12 of 44
Entropy as a Function of Temperature
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 13 of 44
Vibrational Energy and Entropy
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 14 of 44
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.
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 15 of 44
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.
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 16 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 17 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 18 of 44
Table 19.1 Criteria for Spontaneous Change
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 19 of 44
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)]
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 20 of 44
Free Energy Change and Equilibrium
Condensation Equilibrium Vaporization
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 21 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 22 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 23 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 24 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 25 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 26 of 44
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.
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 27 of 44
Significance of the Magnitude of ΔG
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 28 of 44
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+
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 29 of 44
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
Prentice-Hall © 2007General Chemistry: Chapter 19Slide 30 of 44