1. Chapter 8: Entropy, Free Energy and the Second Law of Thermodynamics
University Chemistry
Chapter 8: Entropy, Free Energy and the Second Law of Thermodynamics
Copyright © The McGraw-Hill Companies, Inc.  Permission required for reproduction or display.

2. Spontaneous Processes
A spontaneous reaction occurs without external intervention under the given set of conditions.
A reaction is nonspontaneous if it does not occur without external intervention under the specified set of conditions..
Spontaneous (자발적)
Nonspontaneous (비자발적)
In general, processes that occur spontaneously in one direction cannot, under the same conditions, also take place spontaneously in the reverse direction.

3. The expansion of a gas into an evacuated bulb is spontaneous,
Heat flows from a hotter object to a colder one, but the reverse never
happens spontaneously.
The expansion of a gas into an evacuated bulb is spontaneous,
but the reverse process (the concentration of all the molecules into one
bulb) is nonspontaneous.
A piece of sodium metal reacts violently with water to form sodium
hydroxide and hydrogen gas, but hydrogen gas does not react with sodium
hydroxide to form water and sodium metal.
Iron exposed to water and oxygen forms rust, but rust does not
spontaneously change back to iron.
Can we predict the direction? Quantitatively? By enthalpy?

4. Does a decrease in enthalpy mean a reaction proceeds spontaneously?
Spontaneous reactions
CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l) DH0 = kJ
H+ (aq) + OH- (aq) H2O (l) DH0 = kJ
H2O (s) H2O (l) DH0 = 6.01 kJ
NH4NO3 (s) NH4+(aq) + NO3- (aq) DH0 = 25 kJ
H2O

5. How do we tell the direction of a spontaneous process?
Reversibly Exothermic Process
Irreversibly Exothermic Process
Heat Transfer to the Surroundings
Define entropy change:

6. Statistical Definition of Entropy
The microstates that arise from the combination of two dice and the corresponding macrostates.
The most probable macrostate has an overwhelmingly large number of microstates compared to other macrostates.

7. Microstates, Entropy, and the Second Law of Thermodynamics
Some possible ways of distributing four molecules between two equal compartments.
Entropy is a measure of the number of possible microstates available to a system in a given macrostate.
Entropy change

8. Second law of thermodynamics: The entropy of any isolated system increases in any spontaneous process and remains unchanged in an equilibrium (reversible) process.
spontaneous process:
reversible (or equilibrium) process:
DSuniv is negative, the process is nonspontaneous in the direction described. Instead, it is spontaneous in the opposite direction.

12. Processes that lead to an increase in entropy (DS > 0)

14. Thermodynamic Definition of Entropy
between two states A and B
Clausius inequality
Constant T
Constant T

16. Entropy Change Due to Heating

18. Phase Transitions

20. The Efficiency of Heat Engines: The Carnot Cycle
A Simple Heat Engine

21. Department of Chemistry, KAIST
Sadi Carnot invented such a conceptual engine in 1824, which operates in a cycle consisting of the 4 reversible cycles shown in Fig.11.5.
Isothermal expansion
Adiabatic compression
Net
work
Adiabatic expansion
Isothermal compression
P-V diagram for the Carnot Cycle
Department of Chemistry, KAIST

22. Carnot heat engine, four-step cycle:
For a cyclic process: DUsys(cycle) = 0
DSsys(cycle) = 0.

23. efficiency (e)
Restrictions: second law

24. Carnot engine working in the reverse direction.
coefficient of performance
Refrigerators and air conditioners supply work to remove heat qc from a cold heat source and deposit heat qh into a hot heat sink.

25. Changes in temperature
Third law of thermodynamics states that the entropy of a pure substance in its thermodynamically most stable form (i.e., crystalline form) is zero at the absolute zero of temperature, independent of pressure.
Or for a pure substance in its thermodynamically most stable state the absolute entropy is zero.
Changes in temperature
Third law entropies
Third-law entropies per mole of material measured at the standard pressure of 1 bar are referred to as standard molar entropies, denoted by So.

26. The increase in the entropy of a substance at constant pressure from absolute zero to its gaseous state at some temperature.
phase transitions

28. Residual entropy: value of the entropy at 0 K for systems for which the third law is not applicable.
real crystal
defects in orientation
S > 0 at 0 K.
defect free arrangement
third law will hold for this crystal,
S = 0 at 0 K.
experimental

29. Entropy Changes in the System by Reaction(DSrxn)
Standart state: most stable state at p=1 atm at a given T
The standard entropy of reaction (DS0 ) is the difference in standard entropies between the products and reactants:
rxn
aA + bB cC + dD
DS0
rxn
dS0(D)
cS0(C) = [ + ] -
bS0(B)
aS0(A)
What is the standard entropy change for the following reaction at 250C? CO (g) + O2 (g) CO2 (g)
S0(CO) = J K-1 mol-1
S0(CO2) = J K-1 mol-1
S0(O2) = J K-1 mol-1
DS0
rxn
= 2 x S0(CO2) – [2 x S0(CO) + S0 (O2)]
DS0
rxn
= – [ ] = J K-1 mol-1

32. A guideline to judge the sign of DSrxn
When gases are produced (or consumed)
If a reaction produces more gas molecules than it consumes, DS0 > 0.
If the total number of gas molecules diminishes, DS0 < 0.
If there is no net change in the total number of gas molecules, then DS0 may be positive or negative BUT DS0 will be a small number.
What is the sign of the entropy change for the following reaction? 2Zn (s) + O2 (g) ZnO (s)
The total number of gas molecules goes down, DS is negative.

34. Temperature Dependence of Standard Entropy Changes
Assume is temperature independent.

36. Spontaneity and Gibbs Free Energy
Spontaneity in a nonisolated system at constant T
Clausius inequality:
constant P

37. Define Gibbs free energy by
Spontaneity criterion for a process occurring at constant P and T,
DGsystem < 0 for a spontaneous process at constant T & P DGsystem = reversible process (or simply DG = 0)
DGsystem < forbidden process

38. Gibbs Free Energy and Nonexpansion Work
DU = q + w
We will see in Chap. 13 that Wmax electric = -DGchem reaction

39. states are converted to products in their standard states.
Standard Gibbs free energy of reaction (DG°rxn) is the Gibbs free energy change for a reaction that occurs under standard-state conditions when reactants in their standard
states are converted to products in their standard states.
aA + bB cC + dD
DG0
rxn
dDG0 (D) f
cDG0 (C) = [ + ] -
bDG0 (B)
aDG0 (A)
Standard Gibbs free energy of formation (DGf0) of a compound is the Gibbs free-energy change that occurs when 1 mole of the compound is synthesized from its elements in their standard states.
DG0 of any element in its stable form is zero. f

42. Temperature Dependence of DG
DH and DS are both +, DG will be + at low temperatures (where enthalpy dominates) and become - at high temperatures (where entropy dominates).
The temperature at which DG crosses over from + to - (when DH = T DS) depends upon the relative magnitudes of DH and DS.
DH is + and DS is -, DG will always be positive regardless of temperature.
DH is - and DS is +, DG will always be negative regardless of temperature.
DH and DS are both -, DG will be - at low temperatures (where enthalpy dominates) and become + at high temperatures (where entropy dominates). The temperature at which DG crosses over from - to + (when DH = T DS) depends upon the relative magnitudes of DH and DS.

43. Equilibrium Pressure of CO2
Temperature and Spontaneity of Chemical Reactions
CaCO3 (s) CaO (s) + CO2 (g)
DH0 = kJ
Equilibrium Pressure of CO2
DS0 = J K-1
DG0 = DH0 – TDS0
At 25 0C, DG0 = kJ
For DG0 = 0
0 = DH0 – TDS0
DG0 = 0 at 830 0C

49. The Thermodynamics of a Rubber Band
DG = DH - TDS
Upon stretching
DG > 0
DS < 0
Heat is released, DH < 0
High Entropy
Low Entropy

50. Mixing of Pure Substances

51. DHmix = 0, Avogadro’s law entropy of mixing
Gibbs free energy of mixing,

52. For an ideal solution.
ideal solution

54. Coupled reactions: In systems, unfavorable reactions are coupled to energetically favorable processes.
The smaller weight will move upward (a nonspontaneous process)
by coupling it with the falling of a larger weight ( a spontaneous process).

55. The Structure of ATP and ADP in Ionized Forms-

56. - Alanine + Glycine Alanylglycine DG0 = +29 kJ
31 kJ mol-1
-31 kJ mol-1
Alanine + Glycine Alanylglycine
DG0 = +29 kJ -
ATP + H2O + Alanine + Glycine ADP + H3PO4 + Alanylglycine
DG0 = -31 kJ + 29 kJ = -2 kJ