General Chemistry Principles and Modern Applications 8ed

1. Philip Dutton
University of Windsor, Canada
N9B 3P4
Prentice-Hall © 2002
General Chemistry
Principles and Modern Applications
Petrucci • Harwood • Herring
8th
Edition
Chapter 20: Spontaneous Change:
Entropy and Free Energy

2. Prentice-Hall General Chemistry: Chapter 20Slide 2 of 37
Contents
20-1 Spontaneity: The Meaning of Spontaneous Change
20-2 The Concept of Entropy
20-3 Evaluating Entropy and Entropy Changes
20-4 Criteria for Spontaneous Change:
The Second Law of Thermodynamics
20-5 Standard Fee Energy Change, ΔG°
20-6 Free Energy Change and Equilibrium
20-7 ΔG° and Keqas Functions of Temperature
20-8 Coupled Reactions
Focus On Coupled Reactions in Biological Systems

3. Prentice-Hall General Chemistry: Chapter 20Slide 3 of 37
20-1 Spontaneity: The Meaning of
Spontaneous Change

4. Prentice-Hall General Chemistry: Chapter 20Slide 4 of 37
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)

5. Prentice-Hall General Chemistry: Chapter 20Slide 5 of 37
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.

6. Prentice-Hall General Chemistry: Chapter 20Slide 6 of 37
20-2 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

7. Prentice-Hall General Chemistry: Chapter 20Slide 7 of 37
The Boltzmann Equation for Entropy
• States, S.
– 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

8. Prentice-Hall General Chemistry: Chapter 20Slide 8 of 37
Boltzmann Distribution

9. Prentice-Hall General Chemistry: Chapter 20Slide 9 of 37
Entropy Change
ΔS =
qrev
T

10. Prentice-Hall General Chemistry: Chapter 20Slide 10 of 37
20-3 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
= 2.2010-2
kJ mol-1
K-1

11. Prentice-Hall General Chemistry: Chapter 20Slide 11 of 37
Trouton’s Rule
ΔS =
ΔHvap
Tbp
 87 kJ mol-1
K-1

12. Prentice-Hall General Chemistry: Chapter 20Slide 12 of 37
Raoult’s Law
°PA = χ APA

13. Prentice-Hall General Chemistry: Chapter 20Slide 13 of 37
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 = [ νpS°(products) - νrS°(reactants)]

14. Prentice-Hall General Chemistry: Chapter 20Slide 14 of 37
Entropy as a Function of Temperature

15. Prentice-Hall General Chemistry: Chapter 20Slide 15 of 37
Vibrational Energy and Entropy

16. Prentice-Hall General Chemistry: Chapter 20Slide 16 of 37
20-4 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.

17. Prentice-Hall General Chemistry: Chapter 20Slide 17 of 37
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.

18. Prentice-Hall General Chemistry: Chapter 20Slide 18 of 37
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

19. Prentice-Hall General Chemistry: Chapter 20Slide 19 of 37
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.

20. Prentice-Hall General Chemistry: Chapter 20Slide 20 of 37
Table 20.1 Criteria for Spontaneous
Change

21. Prentice-Hall General Chemistry: Chapter 20Slide 21 of 37
20-5 Standard Free Energy Change, ΔG°
• The standard free energy of formation, ΔGf°.
– The free energy change 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° = [ νp ΔGf°(products) - νr ΔGf°(reactants)]

22. Prentice-Hall General Chemistry: Chapter 20Slide 22 of 37
20-6 Free Energy Change and Equilibrium

23. Prentice-Hall General Chemistry: Chapter 20Slide 23 of 37
Free Energy Change and Equilibrium

24. Prentice-Hall General Chemistry: Chapter 20Slide 24 of 37
Relationship of ΔG° to ΔG for
Nonstandard Conditions
2 N2(g) + 3 H2(g)  2 NH3(g)
ΔG = ΔH - TΔS ΔG° = ΔH° - TΔS°
For ideal gases ΔH = ΔH°
ΔG = ΔH° - TΔS

25. Prentice-Hall General Chemistry: Chapter 20Slide 25 of 37
Relationship Between S and S°
qrev = -w = RT ln
Vf
Vi
ΔS =
qrev
T
= R ln
Vf
Vi
ΔS = Sf – Si = R ln
Vf
Vi
= R ln
Pi
Pf
= -R ln
Pf
Pi
S = S° - R ln
P
P°
= S°- R ln
P
1
= S° - R ln P

26. Prentice-Hall General Chemistry: Chapter 20Slide 26 of 37
2 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
) – 2(SN2
– Rln PN2
) –3(SH2
– Rln PH2
)
ΔSrxn = 2 SNH3
– 2SN2
–3SH2
+ Rln
PN2
PH2
PNH3
2
2
3
ΔSrxn = ΔS°rxn + Rln
PN2
PH2
PNH3
2
2
3

27. Prentice-Hall General Chemistry: Chapter 20Slide 27 of 37
ΔG Under Non-standard Conditions
ΔG = ΔH° - TΔS ΔSrxn = ΔS°rxn + Rln
PN2
PH2
PNH3
2
2
3
ΔG = ΔH° - TΔS°rxn – TR ln
PN2
PH2
PNH3
2
2
3
ΔG = ΔG° + RT ln
PN2
PH2
2
PNH3
2
3
ΔG = ΔG° + RT ln Q

28. Prentice-Hall General Chemistry: Chapter 20Slide 28 of 37
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

29. Prentice-Hall General Chemistry: Chapter 20Slide 29 of 37
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.

30. Prentice-Hall General Chemistry: Chapter 20Slide 30 of 37
Significance of the Magnitude of ΔG

31. Prentice-Hall General Chemistry: Chapter 20Slide 31 of 37
The Thermodynamic Equilibrium
Constant: Activities
S = S° - R ln
P
P°
= S°- R ln
P
1
For ideal gases at 1.0 bar:
S = S° - R ln
c
c°
= S°- R ln a
Therefore, in solution:
PV=nRT or P=(n/V)RT, pressure is an effective concentration
The effective concentration in the standard
state for an ideal solution is c° = 1 M.

32. Prentice-Hall General Chemistry: Chapter 20Slide 32 of 37
Activities
• For pure solids and liquids:
»a = 1
• For ideal gases:
»a = P (in bars, 1 bar = 0.987 atm)
• For ideal solutes in aqueous solution:
»a = c (in mol L-1
)

33. Prentice-Hall General Chemistry: Chapter 20Slide 33 of 37
The Thermodynamic Equilibrium
Constant, Keq
• A dimensionless equilibrium constant expressed
in terms of activities.
• Often Keq = Kc
• Must be used to determine ΔG.
ΔG = ΔG° + RT ln
agah…
aaab…

34. Prentice-Hall General Chemistry: Chapter 20Slide 34 of 37
20-7 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
+
ln =
-ΔH°
RT2
ΔS°
R
+
-ΔH°
RT1
ΔS°
R
+- =
-ΔH°
R
1
T2
1
T1
-
Keq1
Keq2

35. Prentice-Hall General Chemistry: Chapter 20Slide 35 of 37
Temperature Dependence of Keq
ln Keq =
-ΔH°
RT
ΔS°
R
+
slope =
-ΔH°
R
-ΔH° = R  slope
= -8.3145 J mol-1
K-1
 2.2104
K
= -1.8102
kJ mol-1

36. Prentice-Hall General Chemistry: Chapter 20Slide 36 of 37
20-8 Coupled Reactions
• In order to drive a non-spontaneous reactions we
changed the conditions (i.e. temperature or
electrolysis)
• Another method is to couple two reactions.
– One with a positive ΔG and one with a negative ΔG.
– Overall spontaneous process.

37. Prentice-Hall General Chemistry: Chapter 20Slide 37 of 37
Smelting Copper Ore
Cu2O(s) → 2 Cu(s) + ½ O2(g)ΔG°673K = +125 kJΔ
Cu2O(s) + C(s) → 2 Cu(s) + CO(g)
Spontaneous reaction!
Cu2O(s) → 2 Cu(s) + ½ O2(g)Non-spontaneous reaction: +125 kJ
C(s) + ½ O2(g) → CO(g)Spontaneous reaction: -175 kJ
-50 kJ

38. Prentice-Hall General Chemistry: Chapter 20Slide 38 of 37
Focus On Coupled Reactions in
Biological Systems
ADP3-
+ HPO4
2-
+ H+
→ ATP4-
+ H2O
ΔG° = -9.2 kJ mol-1
ΔG = ΔG° + RT ln
aATPaH2O
aADPaPi
aH3O+
But [H3O+
] = 10-7
M not 1.0 M.
ΔG = -9.2 kJ mol-1
+ 41.6 kJ mol-1
= +32.4 kJ mol-1
= ΔG°'The biological standard state:

39. Prentice-Hall General Chemistry: Chapter 20Slide 39 of 37
Focus On Coupled Reactions in
Biological Systems
Glucose → 2 lactate + 2 H+
-218 kJ
2 ADP3-
+ 2 HPO4
2-
+ 2 H+
→ 2 ATP4-
+ 2 H2O +64 kJ
2 ADP3-
+ 2 HPO4
2-
+ glucose → 2 ATP4-
+ 2 H2O + 2 lactate -153 kJ

40. Prentice-Hall General Chemistry: Chapter 20Slide 40 of 37
Chapter 20 Questions
Develop problem solving skills and base your strategy not
on solutions to specific problems but on understanding.
Choose a variety of problems from the text as examples.
Practice good techniques and get coaching from people who
have been here before.