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Livro Prentice-Hall 2002
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Philip DuttonUniversity of Windsor, Canada
N9B 3P4
Prentice-Hall © 2002
General ChemistryPrinciples and Modern Applications
Petrucci • Harwood • Herring
8th Edition
Chapter 20: Spontaneous Change: Entropy and Free Energy
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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 Keq as Functions of Temperature
20-8 Coupled Reactions
Focus On Coupled Reactions in Biological Systems
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 3 of 37
20-1 Spontaneity: The Meaning of Spontaneous Change
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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)
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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.
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 8 of 37
Boltzmann Distribution
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 9 of 37
Entropy Change
ΔS = qrev
T
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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= 2.2010-2 kJ mol-1 K-1
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 11 of 37
Trouton’s Rule
ΔS = ΔHvap
Tbp
87 kJ mol-1 K-1
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 12 of 37
Raoult’s Law
°PA = APA
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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 = [ pS°(products) - rS°(reactants)]
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 14 of 37
Entropy as a Function of Temperature
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 15 of 37
Vibrational Energy and Entropy
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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.
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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.
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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.
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 20 of 37
Table 20.1 Criteria for Spontaneous Change
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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° = [ p ΔGf°(products) - r ΔGf°(reactants)]
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 22 of 37
20-6 Free Energy Change and Equilibrium
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 23 of 37
Free Energy Change and Equilibrium
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 25 of 37
Relationship Between S and S°
qrev = -w = RT lnVf
Vi
ΔS = qrev
T= R ln
Vf
Vi
ΔS = Sf – Si = R lnVf
Vi
= R lnPi
Pf
= -R lnPf
Pi
S = S° - R ln
P
P°= S° - R ln
P1
= S° - R ln P
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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
PN2PH2
PNH3
2
2
3
ΔSrxn = ΔS°rxn + RlnPN2
PH2
PNH3
2
2
3
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 27 of 37
ΔG Under Non-standard Conditions
ΔG = ΔH° - TΔS ΔSrxn = ΔS°rxn + RlnPN2
PH2
PNH3
2
2
3
ΔG = ΔH° - TΔS°rxn – TR lnPN2
PH2
PNH3
2
2
3
ΔG = ΔG° + RT lnPN2
PH2
2
PNH3
2
3
ΔG = ΔG° + RT ln Q
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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.
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 30 of 37
Significance of the Magnitude of ΔG
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 31 of 37
The Thermodynamic Equilibrium Constant: Activities
S = S° - R ln
P
P°= S° - R ln
P1
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.
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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)
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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…
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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 2.2104 K
= -1.8102 kJ mol-1
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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.
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 37 of 37
Smelting Copper Ore
Cu2O(s) → 2 Cu(s) + ½ O2(g)ΔG°673K = +125 kJ Δ
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
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 38 of 37
Focus On Coupled Reactions in Biological Systems
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-1 + 41.6 kJ mol-1
= +32.4 kJ mol-1 = ΔG°'The biological standard state:
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 39 of 37
Focus On Coupled Reactions in Biological Systems
Glucose → 2 lactate + 2 H+ -218 kJ
2 ADP3- + 2 HPO42- + 2 H+ → 2 ATP4- + 2 H2O +64 kJ
2 ADP3- + 2 HPO42- + glucose → 2 ATP4- + 2 H2O + 2 lactate -153 kJ
Prentice-Hall © 2002 General Chemistry: Chapter 20 Slide 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.