This document summarizes Chapter 20 from the textbook "General Chemistry: Principles and Modern Applications" by Petrucci, Harwood, and Herring. The chapter discusses spontaneous change, entropy, free energy, and criteria for spontaneity. It defines key concepts like entropy, the second law of thermodynamics, standard free energy change, and how free energy relates to chemical equilibrium. The chapter also examines how these principles apply to temperature dependence of equilibrium constants and coupled chemical reactions.
2. 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 Keq as Functions of Temperature
20-8 Coupled Reactions
Focus On Coupled Reactions in Biological Systems
Prentice-Hall General Chemistry: ChapterSlide 2 of 37
20
3. 20-1 Spontaneity: The Meaning of
Spontaneous Change
Prentice-Hall General Chemistry: ChapterSlide 3 of 37
20
4. 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 General Chemistry: ChapterSlide 4 of 37
20
5. 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 General Chemistry: ChapterSlide 5 of 37
20
6. 20-2 The Concept of Entropy
• Entropy, S.
– The greater the number
of configurations of the
microscopic particles
among the energy
ΔU = ΔH = 0 levels in a particular
system, the greater the
entropy of the system.
ΔS > 0 spontaneous
Prentice-Hall General Chemistry: ChapterSlide 6 of 37
20
7. The Boltzmann Equation for Entropy
S = k lnW
• 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.
Prentice-Hall General Chemistry: ChapterSlide 7 of 37
20
9. Entropy Change
qrev
ΔS =
T
Prentice-Hall General Chemistry: ChapterSlide 9 of 37
20
10. 20-3 Evaluating Entropy and
Entropy Changes
• Phase transitions.
– Exchange of heat can be carried out reversibly.
ΔH
ΔS =
Ttr
H2O(s, 1 atm) H2O(l, 1 atm) ΔHfus° = 6.02 kJ at 273.15 K
°
ΔHfus 6.02 kJ mol-1
ΔSfus = = = 2.2010-2 kJ mol-1 K-1
Ttr 273.15 K
Prentice-Hall General Chemistry: ChapterSlide 10 of 37
20
11. Trouton’s Rule
ΔHvap
ΔS = 87 kJ mol-1 K-1
Tbp
Prentice-Hall General Chemistry: ChapterSlide 11 of 37
20
12. Raoult’s Law
PA = χ APA
°
Prentice-Hall General Chemistry: ChapterSlide 12 of 37
20
13. 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)]
Prentice-Hall General Chemistry: ChapterSlide 13 of 37
20
14. Entropy as a Function of Temperature
Prentice-Hall General Chemistry: ChapterSlide 14 of 37
20
15. Vibrational Energy and Entropy
Prentice-Hall General Chemistry: ChapterSlide 15 of 37
20
16. 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.
Prentice-Hall General Chemistry: ChapterSlide 16 of 37
20
17. 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 General Chemistry: ChapterSlide 17 of 37
20
18. Free Energy and Free Energy Change
For the universe:
TΔSuniv. = TΔSsys – ΔHsys = -(ΔHsys – TΔSsys)
-TΔSuniv. = ΔHsys – TΔSsys
For the system:
G = H - TS
ΔG = ΔH - TΔS
ΔGsys = - TΔSuniverse
Prentice-Hall General Chemistry: ChapterSlide 18 of 37
20
19. 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.
Prentice-Hall General Chemistry: ChapterSlide 19 of 37
20
20. Table 20.1 Criteria for Spontaneous
Change
Prentice-Hall General Chemistry: ChapterSlide 20 of 37
20
21. 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)]
Prentice-Hall General Chemistry: ChapterSlide 21 of 37
20
22. 20-6 Free Energy Change and Equilibrium
Prentice-Hall General Chemistry: ChapterSlide 22 of 37
20
23. Free Energy Change and Equilibrium
Prentice-Hall General Chemistry: ChapterSlide 23 of 37
20
24. 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
Prentice-Hall General Chemistry: ChapterSlide 24 of 37
20
25. Relationship Between S and S°
Vf
qrev = -w = RT ln
Vi
qrev Vf
ΔS = = R ln
T Vi
Vf Pi Pf
ΔS = Sf – Si = R ln = R ln = -R ln
Vi Pf Pi
P P
S = S° - R ln = S° - R ln = S° - R ln P
P° 1
Prentice-Hall General Chemistry: ChapterSlide 25 of 37
20
28. ΔG and the Equilibrium Constant Keq
ΔG = ΔG° + RT ln Q
If the reaction is at equilibrium then:
ΔG = ΔG° + RT ln Keq= 0
ΔG° = -RT ln Keq
Prentice-Hall General Chemistry: ChapterSlide 28 of 37
20
29. 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 General Chemistry: ChapterSlide 29 of 37
20
30. Significance of the Magnitude of ΔG
Prentice-Hall General Chemistry: ChapterSlide 30 of 37
20
31. The Thermodynamic Equilibrium
Constant: Activities
For ideal gases at 1.0 bar:
P P
S = S° - R ln = S° - R ln
P° 1
PV=nRT or P=(n/V)RT, pressure is an effective concentration
Therefore, in solution:
c
S = S° - R ln = S° - R ln a
c°
The effective concentration in the standard
state for an ideal solution is c° = 1 M.
Prentice-Hall General Chemistry: ChapterSlide 31 of 37
20
32. 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)
Prentice-Hall General Chemistry: ChapterSlide 32 of 37
20
33. The Thermodynamic Equilibrium
Constant, Keq
• A dimensionless equilibrium constant expressed
in terms of activities.
• Often Keq = Kc
• Must be used to determine ΔG.
agah…
ΔG = ΔG° + RT ln
aaab…
Prentice-Hall General Chemistry: ChapterSlide 33 of 37
20
34. 20-7 ΔG° and Keq as Functions
of Temperature
ΔG° = ΔH° -TΔS° ΔG° = -RT ln Keq
-ΔG° -ΔH° TΔS°
ln Keq = = +
RT RT RT
-ΔH° ΔS°
ln Keq = +
RT R
Keq2 -ΔH° ΔS° -ΔH° ΔS° -ΔH° 1 1
ln = + - + = -
Keq1 RT2 R RT1 R R T2 T1
Prentice-Hall General Chemistry: ChapterSlide 34 of 37
20
35. Temperature Dependence of Keq
-ΔH° ΔS°
ln Keq = +
RT R
-ΔH°
slope =
R
-ΔH° = R slope
= -8.3145 J mol-1 K-1 2.2104 K
= -1.8102 kJ mol-1
Prentice-Hall General Chemistry: ChapterSlide 35 of 37
20
36. 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.
Prentice-Hall General Chemistry: ChapterSlide 36 of 37
20
40. 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.
Prentice-Hall General Chemistry: ChapterSlide 40 of 37
20