1. Chapter 19: Spontaneous Change: Entropy and Free Energy
Chemistry 140 Fall 2002
CHEMISTRY
Ninth
Edition
GENERAL
Principles and Modern Applications
Petrucci • Harwood • Herring • Madura
Chapter 19: Spontaneous Change: Entropy and Free Energy
Philip Dutton
University of Windsor, Canada
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General Chemistry: Chapter 19
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2. Contents 19-1 Spontaneity: The Meaning of Spontaneous Change
Chemistry 140 Fall 2002
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
19-8 Coupled Reactions
Focus On Coupled Reactions in Biological Systems
General Chemistry: Chapter 19
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3. 19-1 Spontaneity: The Meaning of Spontaneous Change
General Chemistry: Chapter 19
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4. General Chemistry: Chapter 19
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)
General Chemistry: Chapter 19
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5. General Chemistry: Chapter 19
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.
General Chemistry: Chapter 19
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6. 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
General Chemistry: Chapter 19
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7. The Boltzmann Equation for Entropy
Chemistry 140 Fall 2002
The Boltzmann Equation for Entropy
S = k lnW
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.
Ludwig Boltzmann.
Associated the number of energy levels in a system with the number of ways of arranging the particles in these levels.
General Chemistry: Chapter 19
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8. Boltzmann Distribution
General Chemistry: Chapter 19
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9. General Chemistry: Chapter 19
Entropy Change
ΔS =
qrev T
For changes occurring at constant temperature
General Chemistry: Chapter 19
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10. 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 K
ΔSfus =
ΔHfus
Ttr =
6.02 kJ mol-1 K
= 2.2010-2 kJ mol-1 K-1
General Chemistry: Chapter 19
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11. General Chemistry: Chapter 19
Chemistry 140 Fall 2002
Trouton’s Rule
ΔS =
ΔHvap
Tbp
 87 kJ mol-1 K-1
Failures of this rule are understandable:
Water and hydrogen bonding. Sliquid is lower than expected so ΔS is larger than 87.
General Chemistry: Chapter 19
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12. General Chemistry: Chapter 19
Raoult’s Law
PA =  APA
General Chemistry: Chapter 19
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13. General Chemistry: Chapter 19
Chemistry 140 Fall 2002
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)]
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14. Entropy as a Function of Temperature
General Chemistry: Chapter 19
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15. Vibrational Energy and Entropy
General Chemistry: Chapter 19
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16. General Chemistry: Chapter 19
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.
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17. Free Energy and Free Energy Change
Chemistry 140 Fall 2002
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.
General Chemistry: Chapter 19
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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
General Chemistry: Chapter 19
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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.
J. Willard Gibbs
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20. Table 19.1 Criteria for Spontaneous Change
General Chemistry: Chapter 19
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21. 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)]
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22. 19-6 Free Energy Change and Equilibrium
General Chemistry: Chapter 19
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23. Free Energy Change and Equilibrium
Condensation Equilibrium Vaporization
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24. Relationship of ΔG° to ΔG for Non-standard Conditions
2 N2(g) + 3 H2(g) NH3(g)
ΔG = ΔH - TΔS
ΔG° = ΔH° - TΔS°
For ideal gases ΔH = ΔH°
ΔG = ΔH° - TΔS
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25. Relationship Between S and S°Vf
qrev = -w = RT ln Vi
ΔS =
qrev T
= R ln Vf Vi
ΔS = Sf – Si
= R ln Vf Vi Pi Pf
= -R ln
S = S°
- R ln P P°
= S° 1
= S° - R ln P
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26. N2(g) + 3 H2(g) 2 NH3(g) SN2 = SN2 – Rln PN2 SH2 = SH2 – Rln PH2
SNH3 = SNH3 – Rln PNH3
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 + Rln
PN2PH2
PNH3 2 3
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27. ΔG Under Non-standard Conditions
ΔSrxn = ΔS°rxn + Rln
PN2PH2
PNH3 2 3
ΔG = ΔH° - TΔS
ΔG = ΔH° - TΔS°rxn – TR ln
PN2PH2
PNH3 2 3
ΔG = ΔG° + RT ln
PN2PH2 2
PNH3 3
ΔG = ΔG° + RT ln Q
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28. 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
General Chemistry: Chapter 19
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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.
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30. Significance of the Magnitude of ΔG
General Chemistry: Chapter 19
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31. The Thermodynamic Equilibrium Constant: Activities.
Chemistry 140 Fall 2002
The Thermodynamic Equilibrium Constant: Activities.
For ideal gases at 1.0 bar:
S = S°
- R ln P P°
= S° 1
PV=nRT or P=(n/V)RT, pressure is an effective concentration
Therefore, in solution:
S = S°
- R ln c c°
= S°
- R ln a
The effective concentration in the standard state for an ideal solution is c° = 1 M.
General Chemistry: Chapter 19
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32. General Chemistry: Chapter 19
Activities
For pure solids and liquids:
a = 1
For ideal gases:
a = P (in bars, 1 bar = atm)
For ideal solutes in aqueous solution:
a = c (in mol L-1)
General Chemistry: Chapter 19
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33. The Thermodynamic Equilibrium Constant, Keq
A dimensionless equilibrium constant expressed in terms of activities.
Often Keq = Kc or KP, but not always.
Must be used to determine ΔG.
ΔG = ΔG° + RT ln
agah…
aaab…
General Chemistry: Chapter 19
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34. 19-7 ΔG° and Keq as Functions of Temperature
ΔG° = ΔH° -TΔS°
ΔG° = -RT ln Keq
ln Keq =
-ΔG° RT =
-ΔH°
TΔS° +
ln Keq =
-ΔH° RT
ΔS° R +
General Chemistry: Chapter 19
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35. General Chemistry: Chapter 19
Van’t Hoff Equation
If we evaluate this equation for a change in temperature:
Keq2
-ΔH°
ΔS°
-ΔH°
ΔS°
ln = + - +
Keq1
RT2 R
RT1 R
Keq2
-ΔH° 1 1 = - ln
Keq1 R T2 T1
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36. General Chemistry: Chapter 19
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37. Temperature Dependence of Keq
Assume ΔH° and ΔS° do not vary significantly with temperature.
ln Keq =
-ΔH° RT
ΔS° R +
slope =
-ΔH° R
-ΔH° = R  slope
= J mol-1 K-1  2.2104 K
= -1.8102 kJ mol-1
General Chemistry: Chapter 19
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38. General Chemistry: Chapter 19
19-8 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.
General Chemistry: Chapter 19
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39. General Chemistry: Chapter 19
Smelting Copper Ore
Cu2O(s) → 2 Cu(s) + ½ O2(g) ΔG°673K = +125 kJ Δ
Cu2O(s) → 2 Cu(s) + ½ O2(g)
Non-spontaneous reaction:
+125 kJ
C(s) + ½ O2(g) → CO(g)
Spontaneous reaction:
-175 kJ
Cu2O(s) + C(s) → 2 Cu(s) + CO(g)
-50 kJ
Spontaneous reaction!
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40. Focus On Coupled Reactions in Biological Systems
General Chemistry: Chapter 19
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41. The Biological Standard State
ADP3- + HPO42- + H+ → ATP4- + H2O
ΔG° = -9.2 kJ mol-1
ΔG = ΔG° + RT ln
aATPaH2O
aADPaPiaH3O+
But [H3O+] = 10-7 M not 1.0 M.
ΔG = -9.2 kJ mol kJ mol-1
= kJ mol-1 = ΔG°'
ADP to ATP is not spontaneous and biological systems use glucose.
General Chemistry: Chapter 19
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42. Focus On Coupled Reactions in Biological Systems
Glucose → 2 lactate + 2 H+
-218 kJ
2 ADP HPO H+ → 2 ATP H2O
+64 kJ
2 ADP HPO42- + glucose → 2 ATP H2O + 2 lactate
-153 kJ
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43. End of Chapter Questions
Work a problem from both ends to find the key log. a b c d d? e? e f
Answer
General Chemistry: Chapter 19
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44. End of Chapter Questions
Work a problem from both ends to find the key log. a b c d d? e? e f
Answer
General Chemistry: Chapter 19
Prentice-Hall © 2007