Chemistry
Third Edition
Julia Burdge
Lecture PowerPoints
Chapter 18
Entropy, Free Energy,
and Equilibrium
Copyright © 2012, The McGraw-Hill Compaies, Inc. Permission required for reproduction or display.
CHAPTER
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18
Entropy, Free Energy, and
Equilibrium
Spontaneous Processes
Entropy
Entropy Changes in a System
Entropy Changes in the Universe
Predicting Spontaneity
Free Energy and Chemical Equilibrium
Thermodynamics in Living Systems
2
18.1
Spontaneous Processes
Topics
Spontaneous Processes
3
18.1
Spontaneous Processes
Spontaneous Processes
A process that does occur under a specific set of conditions is
called a spontaneous process.
One that does not occur under a specific set of conditions is
called nonspontaneous.
4
18.1
Spontaneous Processes
Spontaneous Processes
5
18.1
Spontaneous Processes
Spontaneous Processes
These exothermic reactions are spontaneous at room
temperature:
This exothermic reaction is not spontaneous at temperatures
above 0°C:
6
18.1
Spontaneous Processes
Spontaneous Processes
So, while exothermicity favors spontaneity, it cannot be the
sole factor that determines spontaneity.
7
18.2
Entropy
Topics
A Qualitative Description of Entropy
A Quantitative Definition of Entropy
8
18.2
Entropy
A Qualitative Description of Entropy
Qualitatively, the entropy (S) of a system is a measure of how
spread out or how dispersed the system’s energy is.
The simplest interpretation of this is how spread out a
system’s energy is in space.
In other words, for a given system, the greater the volume it
occupies, the greater its entropy.
Just as spontaneity is favored by a process being exothermic,
spontaneity is also favored by an increase in the system’s
entropy.
9
18.2
Entropy
A Quantitative Definition of Entropy
where k is the Boltzmann constant (1.38×10–23 J/K) and W is
the number of energetically equivalent different ways the
molecules in a system can be arranged.
10
18.2
Entropy
A Quantitative Definition of Entropy
11
18.2
Entropy
A Quantitative Definition of Entropy
22 = 4 possible
arrangements
42 = 16
possible
arrangements
12
18.2
Entropy
A Quantitative Definition of Entropy
There are three different states possible for this system.
1. One molecule on each side (eight possible arrangements)
2. Both molecules on the left (four possible arrangements)
3. Both molecules on the right (four possible arrangements)
The most probable state is the one with the largest number of
possible arrangements. In this case, the most probable state
is the one with one molecule on each side of the container.
13
18.3
Entropy Changes in a System
Topics
Calculating Ssys
Standard Entropy, S°
Qualitatively Predicting the Sign of Ssys
14
18.4
Entropy Changes in the Universe
Calculating Ssys
15
18.4
Entropy Changes in the Universe
Calculating Ssys
16
SAMPLE PROBLEM
18.1
Determine the change in entropy for 1.0 mole of an ideal gas
originally confined to one-half of a 5.0-L container when the
gas is allowed to expand to fill the entire container at
constant temperature.
Setup
R = 8.314 J/K · mol, n = 1.0 mole, Vfinal = 5.0 L, and
Vinitial = 2.5 L.
17
SAMPLE PROBLEM
18.1
Solution
18
18.3
Entropy Changes in a System
Standard Entropy, S°
It is possible to determine the absolute value of the entropy
of a substance, S; something we cannot do with either energy
or enthalpy.
Standard entropy is the absolute entropy of a substance at 1
atm.
19
18.3
Entropy Changes in a System
Standard Entropy, S°
20
18.3
Entropy Changes in a System
Standard Entropy, S°
For a given substance, the standard entropy is greater in the
liquid phase than in the solid phase. [Compare the standard
entropies of Na(s) and Na(l).]
For a given substance, the standard entropy is greater in the
gas phase than in the liquid phase.
For two monatomic species, the one with the larger molar
mass has the greater standard entropy.
21
18.3
Entropy Changes in a System
Standard Entropy, S°
For two substances in the same phase, and with similar molar
masses, the substance with the more complex molecular
structure has the greater standard entropy.
22
18.3
Entropy Changes in a System
23
18.3
Entropy Changes in a System
Standard Entropy, S°
In cases where an element exists in two or more allotropic
forms, the form in which the atoms are more mobile has the
greater entropy.
24
18.3
Entropy Changes in a System
Standard Entropy, S°
25
SAMPLE PROBLEM
18.2
From the standard entropy values in Appendix 2, calculate the
standard entropy changes for the following reactions at 25°C:
Setup
S°[CaCO3(s)] = 92.9 J/K · mol
S°[CO2(g)] = 213.6 J/K · mol
S°[H2(g)] = 131.0 J/K · mol
S°[Cl2(g)] = 223.0 J/K · mol
S°[CaO(s)] = 39.8 J/K · mol
S°[N2(g)] = 191.5 J/K · mol
S°[NH3(g)] = 193.0 J/K · mol
S°[HCl(g)] = 187.0 J/K · mol
26
SAMPLE PROBLEM
18.2
Solution
27
SAMPLE PROBLEM
18.2
Solution
28
SAMPLE PROBLEM
18.2
Solution
29
18.3
Entropy Changes in a System
Qualitatively Predicting the Sign of Ssys
Sometimes it’s useful just to know the sign of S°rxn.
Several processes that lead to an increase in entropy are
• Melting
• Vaporization or sublimation
• Temperature increase
• Reaction resulting in a greater number of gas molecules
30
18.3
Entropy Changes in a System
Qualitatively Predicting the Sign of Ssys
31
18.3
Entropy Changes in a System
Qualitatively Predicting the Sign of Ssys
32
SAMPLE PROBLEM
18.3
For each process, determine the sign of S for the system:
(a) decomposition of CaCO3(s) to give CaO(s) and CO2(g)
(b) heating bromine vapor from 45°C to 80°C
(c) condensation of water vapor on a cold surface
(d) reaction of NH3(g) and HCl(g) to give NH4Cl(s)
(e) dissolution of sugar in water.
33
SAMPLE PROBLEM
(a)
(b)
(c)
(d)
(e)
18.3
decomposition of CaCO3(s) to give CaO(s) and CO2(g)
heating bromine vapor from 45°C to 80°C
condensation of water vapor on a cold surface
reaction of NH3(g) and HCl(g) to give NH4Cl(s)
dissolution of sugar in water.
Setup
Increases in entropy generally accompany solid-to-liquid,
liquid-to-gas, and solid-to-gas transitions; the dissolving of
one substance in another; a temperature increase; and
reactions that increase the net number of moles of gas.
34
SAMPLE PROBLEM
(a)
(b)
(c)
(d)
(e)
18.3
decomposition of CaCO3(s) to give CaO(s) and CO2(g)
heating bromine vapor from 45°C to 80°C
condensation of water vapor on a cold surface
reaction of NH3(g) and HCl(g) to give NH4Cl(s)
dissolution of sugar in water.
Solution
(a) positive, (b) positive, (c) negative, (d) negative, and (e)
positive.
35
18.4
Entropy Changes in the Universe
Topics
Calculating Ssurr
The Second Law of Thermodynamics
The Third Law of Thermodynamics
36
18.4
Entropy Changes in the Universe
Calculating Ssurr
37
18.4
Entropy Changes in the Universe
The Second Law of Thermodynamics
The second law of thermodynamics says that for a process to
be spontaneous as written (in the for- ward direction), Suniv
must be positive.
An equilibrium process is one that does not occur
spontaneously in either the net forward or net reverse
direction but can be made to occur by the addition or
removal of energy to a system at equilibrium.
38
SAMPLE PROBLEM
18.4
Determine if each of the following is a spontaneous process, a
nonspontaneous process, or an equilibrium process at the
specified temperature:
39
SAMPLE PROBLEM
18.4
Solution
40
SAMPLE PROBLEM
18.4
Solution
41
SAMPLE PROBLEM
18.4
Solution
42
SAMPLE PROBLEM
18.4
Solution
Suniv is zero; therefore, the reaction is an equilibrium process
at 98°C. In fact, this is the melting point of sodium.
43
18.4
Entropy Changes in the Universe
The Third Law of Thermodynamics
According to the third law of thermodynamics, the entropy
of a perfect crystalline substance is zero at absolute zero.
44
18.4
Entropy Changes in the Universe
The Third Law of Thermodynamics
45
18.5
Predicting Spontaneity
Topics
Gibbs Free-Energy Change, G
Standard Free-Energy Changes, G°
Using G and G° to Solve Problems
46
18.5
Predicting Spontaneity
Gibbs Free-Energy Change, G
47
18.5
Predicting Spontaneity
Gibbs Free-Energy Change, G
48
18.5
Predicting Spontaneity
Gibbs Free-Energy Change, G
G < 0
The reaction is spontaneous in the forward
direction (and nonspontaneous in the reverse
direction).
G > 0
The reaction is nonspontaneous in the forward
direction (and spontaneous in the reverse
direction).
G = 0
The system is at equilibrium.
49
18.5
Predicting Spontaneity
Gibbs Free-Energy Change, G
50
SAMPLE PROBLEM
18.5
According to Table 18.4, a reaction will be spontaneous only
at high temperatures if both H and S are positive.
For a reaction in which H = 199.5 kJ/mol and
S = 476 J/K · mol, determine the temperature (in °C) above
which the reaction is spontaneous.
Setup
51
SAMPLE PROBLEM
18.5
Solution
52
18.5
Predicting Spontaneity
Standard Free-Energy Changes, G°
The standard free energy of reaction (G°rxn) is the freeenergy change for a reaction when it occurs under standardstate conditions—that is, when reactants in their standard
states are converted to products in their standard states.
53
18.5
Predicting Spontaneity
Standard Free-Energy Changes, G°
54
18.5
Predicting Spontaneity
Standard Free-Energy Changes, G°
Gf ° is the standard free energy of formation of a
compound—that is, the free-energy change that occurs when
1 mole of the com- pound is synthesized from its constituent
elements, each in its standard state.
55
18.5
Predicting Spontaneity
Standard Free-Energy Changes, G°
56
SAMPLE PROBLEM
18.6
Calculate the standard free-energy changes for the following
reactions at 25°C:
Setup
57
SAMPLE PROBLEM
18.6
Solution
58
SAMPLE PROBLEM
18.6
Solution
59
18.5
Predicting Spontaneity
Using G and  G° to Solve Problems
60
18.5
Predicting Spontaneity
Using G and  G° to Solve Problems
Because G° is a large positive number, the reaction does not
favor product formation at 25°C (298 K).
61
18.5
Predicting Spontaneity
Using G and  G° to Solve Problems
At T > 835°C, G° becomes negative, indicating that the
reaction would then favor the formation of CaO and CO2.
62
18.5
Predicting Spontaneity
Using G and  G° to Solve Problems
At the temperature at which a phase change occurs (i.e., the
melting point or boiling point of a substance), the system is at
equilibrium (G = 0).
63
SAMPLE PROBLEM
18.7
The molar heats of fusion and vaporization of benzene are
10.9 and 31.0 kJ/mol, respectively.
Calculate the entropy changes for the solid-to-liquid and
liquid-to-vapor transitions for benzene.
At 1 atm pressure, benzene melts at 5.5°C and boils at 80.1°C.
Setup
The melting point of benzene is 5.5 + 273.15 = 278.7 K and
the boiling point is 80.1 + 273.15 = 353.3 K.
64
SAMPLE PROBLEM
18.7
Solution
65
18.6
Free Energy and Chemical Equilibrium
Topics
Relationship Between G and G°
Relationship Between G° and K
66
18.6
Free Energy and Chemical Equilibrium
Relationship Between G and G°
67
SAMPLE PROBLEM
18.8
The equilibrium constant, KP, for the reaction
is 0.113 at 298 K, which corresponds to a standard freeenergy change of 5.4 kJ/mol.
In a certain experiment, the initial pressures are P[N2O4] =
0.453 atm and P[NO2] = 0.122 atm.
Calculate G for the reaction at these pressures, and predict
the direction in which the reaction will proceed
spontaneously to establish equilibrium.
68
SAMPLE PROBLEM
18.8
Setup
Solution
Because G is negative, the reaction proceeds spontaneously
from left to right to reach equilibrium.
69
18.6
Free Energy and Chemical Equilibrium
Relationship Between G° and K
70
18.6
Free Energy and Chemical Equilibrium
Relationship Between G° and K
71
18.6
Free Energy and Chemical Equilibrium
Relationship Between G° and K
72
SAMPLE PROBLEM
18.9
Using data from Appendix 2, calculate the equilibrium
constant, KP , for the following reaction at 25°C:
Setup
73
SAMPLE PROBLEM
18.9
Solution
74
SAMPLE PROBLEM
18.10
The equilibrium constant, Ksp, for the dissolution of silver
chloride in water at 25°C,
is 1.6 × 10–10. Calculate G° for the process.
Setup
75
SAMPLE PROBLEM
18.10
Solution
76
18.7
Thermodynamics in Living Systems
Topics
Thermodynamics in Living Systems
77
18.7
Thermodynamics in Living Systems
Thermodynamics in Living Systems
Coupled reactions:
78
18.7
Thermodynamics in Living Systems
Thermodynamics in Living Systems
Coupled reactions play a crucial role in our survival.
79
18.7
Thermodynamics in Living Systems
Thermodynamics in Living Systems
80
18.7
Thermodynamics in Living Systems
Thermodynamics in Living Systems
81
18.7
Thermodynamics in Living Systems
Thermodynamics in Living Systems
82