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Transcript of Chapter 17 1. The Austrian physicist Ludwig Boltzmann introduced a model to relate the total number...
1
Chapter 17
The Austrian physicist Ludwig Boltzmann introduced a model to relate the total number of microstates (the multiplicity, W) to entropy (S).
S = k ln W
AN
Rk
Boltzmann constant (k)
units on S is J/K
k = 1.38 x 1023J/K
Gas constant
Avogadro constant
Microstates and Entropy
Boltzmann was the founding father of statistical mechanics, a completely new way of thinking about theoretical physics. His work was ridiculed by his fellow professors.
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Standard Entropy
• Difficult to count the number of microstates directly.
• Measured by calorimetery.
• Standard entropy (S) absolute entropy of a substance at 1 atm (typically at 25C)
• Units of J K-1 mol-1
• All positive values.
• Absolute values (unlike DH which is relative)
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Why is there a –S?
S = k ln W
Al + 6H2O Al(H2O)6 (aq)3+ 2+
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Chapter 17
6
Spontaneity
Spontaneous: process that does occur under a specific set of conditions.
Nonspontaneous: process that does not occur under a specific set of conditions.
The reverse of a spontaneous process is a nonspontaneous one.
Spontaneity depends on temperature.
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Enthalpy (H) is used to quantify the heat flow into or out of a system in a process that occurs at constant pressure.
Predicting Spontaneity
DHrxn = Hproducts – Hreactants
Hproducts < Hreactants
DH < 0
Hproducts > Hreactants
DH > 0Exothermic Endothermic
Enthalpically favorable Enthalpically unfavorable
If we mix reactants and products together will the reaction occur?
Not enough information. We need to know the change in entropy to predict if a reaction will spontaneously occur.
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Entropy (S) Is a measure of the number of specific ways (microstates) in which a thermodynamic system may be arranged.
Predicting Spontaneity
DSrxn = Sproducts – Sreactants
Sproducts < Sreactants
DS < 0
Sproducts > Sreactants
DS > 0Entropy decreases Entropy increases
Entropically unfavorable Entropically favorable
If we mix reactants and products together will the reaction occur?
Still not enough information. We need to know total entropy change to predict if a reaction will spontaneously occur.
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If we mix reactants and products together will the reaction occur?
Predicting Spontaneity
Nonspontaneous process:
DSuniv = DSsys + DSsurr
Equilibrium : DSuniv = 0
DSuniv < 0
Spontaneous process: DSuniv > 0
DSuniv = DSsys + DSsurr
Can calculate from:
DS0rxn nS0(products)= S mS0(reactants)S-
If we know DSsurr we can calculate DSuniv
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DSuniv = DSsys + DSsurr
Can calculate from:
DS0rxn nS0(products)= S mS0(reactants)S-
If we know DSsurr we can calculate DSuniv
Predicting Spontaneity
DS0 rx
n
surr
ound
ing
syst
em
DS su
rr
Surrounding = everything in the universe except the system.
Very, very difficult to measure!If not impossible.
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Exothermic Reaction Endothermic Process
Heat and Entropy
DSsurr > 0
-DHsys
Surroundings + heat = ↑ S
0 < DHsys
DSsurr < 0
+DHsys
Surroundings - heat = ↓ S
0 > DHsys
DSsurr ∝ -DHsys
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Heat and EntropyHeat released by the system increases the disorder of the surroundings.
DSsurr ∝ -DHsys
The effect of -DHsys on the surroundings depends on temperature: – At high temperature, where there is already considerable
disorder, the effect is muted
– At low temperature the effect is much more significant
– The difference between tossing a rock into a calm pool (low T) and a storm-tossed ocean (high T)
DSsurr = -DHsys
T
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DSuniv = DSsys + DSsurr
Predicting Spontaneity
DSsurr = -DHsys
TDSuniv = DSsys + -DHsys
T
-TDSuniv = -TDSsys + DHsys
Substitution:
Multiply by -T:
-TDSuniv = DHsys - TDSsysRearrange:
Both in terms of the system.
This equation relates DSuniv to DHsys and DSsys.
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Gibbs Free Energy
-TDSuniv = DHsys - TDSsys
Josiah Willard Gibbs (1839-1903)
DG = DHsys - TDSsys
First American Ph.D. in Engineering (Yale, 1863)
Praised by Albert Einstein as "the greatest mind in American history"
Died at 64 from an acute intestinal obstruction.
Gibbs free energy (DG)-
• AKA Free energy.
• Relates S, H and T of a system.
• Can be used to predict spontaneity.
• G is a state function.
in K
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Gibbs Free Energy
DG = DHsys - TDSsys
Gibbs free energy (DG)- Can be used to predict spontaneity.
For a constant temperature and constant pressure process:
DG < 0 The reaction is spontaneous in the forward direction.
DG > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction.
DG = 0 The reaction is at equilibrium.
-DG = -T(+DSuniv)
+DG = -T(-DSuniv)
DSuniv > 0
-TDSuniv = DHsys - TDSsys
DSuniv < 0
DG = -T(DSuniv) = 0 DSuniv = 0
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Gibbs Free Energy
DG = DH - TDS• If you know DG for reactants and products then you can
calculate if a reaction is spontaneous. • If you know DG for two reaction then you can calculate if the
sum is spontaneous. • If you know DS, DH and T then you can calculate spontaneity. • Can predict the temperature when a reaction becomes
spontaneous.• If you have DHvap or DHfus and DS you can predict boiling and
freezing points.• If you have DHvap or DHfus and T you can predict the entropy
change during a phase change.• Can predict equilibrium shifts.
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Standard Free Energy ChangesThe standard free-energy of reaction (DG0 ) is the free-energy change for a reaction when it occurs under standard-state conditions.
rxn
aA + bB cC + dD
DG0rxn nDG0 (products)f= S mDG0 (reactants)fS-
DG0rxn dDG0 (D)fcDG0 (C)f= [ + ] - bDG0 (B)faDG0 (A)f[ + ]
Standard free energy of formation (DG0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states.
f
DG0 of any element in its stable form is zero.f
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aA + bB cC + dD
Standard Free Energy ChangesDG is a state function so free energy can be calculated from the
table of standard values just as enthalpy and entropy changes.
DG0rxn nDG0 (products)f= S
mDG0 (reactants)fS-
Standard free energy of formation (DG0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states.
f
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Standard Free Energy Changes
From appendix 3:KClO3(s) DGf = -289.9 kJ/molKCl(s) DGf = -408.3 kJ/molO2(g) DGf = 0 kJ/mol
2KClO3(s) 2KCl(s) + 3O2(g)
Calculate the standard free-energy change for the following reaction:
DG0rxn nDG0 (products)f= S mDG0 (reactants)fS-
DG0rxn = [2(408.3 kJ/mol) + 3(0)] [2(289.9 kJ/mol)]
DG0rxn = 816.6 (579.8)
DG0rxn = 236.8 kJ/mol
DG0rxn < 0 Yes!
Is the reaction spontaneous?
Example
20
17.4
Calculate the standard free-energy changes for the following reactions at 25°C.
(a) CH4(g) + 2O2(g) CO2(g) + 2H2O(l)
From appendix 3:CH4(g) DGf = -50.8 kJ/molO2(g) DGf = 0 kJ/molCO2(g) DGf = -394.4 kJ/molH2O (l) DGf = -237.2 kJ/mol
ΔG°rxn = [ΔG°f (CO2) + 2ΔG°f (H2O)] - [ΔG°f (CH4) + 2ΔG°f (O2)]
ΔG°rxn =[(-394.4 kJ/mol) + (2)(-237.2 kJ/mol)] - [(-50.8 kJ/mol) + (2) (0 kJ/mol)]
ΔG°rxn = -818.0 kJ/mol
Spontaneous?
Yes.
Example
21
17.4
Calculate the standard free-energy changes for the following reactions at 25°C.
(b) 2MgO(s) 2Mg(s) + O2(g)
From appendix 3:MgO(s) DGf = -569.6 kJ/molO2(g) DGf = 0 kJ/molMg(s) DGf = 0 kJ/mol
ΔG°rxn = [2ΔG°f (Mg) + ΔG°f (O2)] - [2ΔG°f (MgO)]
ΔG°rxn = [(2)(0 kJ/mol) + (0 kJ/mol)] - [(2)(-569.6 kJ/mol)]
ΔG°rxn = 1139 kJ/mol
Spontaneous?
No.But the reverse is…
2Mg(s) + O2(g) 2MgO(s)
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More DG° Calculations
DG0rxn nDG0 (products)
f= S
mDG0 (reactants)fS-
To predict spontaneity of any rxn:
1) Pick any reactants and products.
2) Write a balanced equation.
3) Calculate DG0rxn.
4) Is the reaction spontaneous?
Appendix 3
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Another Example
+ O2
C(s, diamond) + O2(g) CO2(g)
DG°rxn = -396.4 kJ
Therefore, diamonds are contributing to global warming!
very slowly
ΔG°rxn = [ΔG°f (CO2)] - [ΔG°f (C, diamond) + ΔG°f (O2)]
From appendix 3:C, diamond(s) DGf = 2.9 kJ/molO2(g) DGf = 0 kJ/molCO2(g) DGf = -394.4 kJ/mol
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More DG° CalculationsSimilar to DH°, one can use the DG° for various reactions to determine DG° for the reaction of interest (a “Hess’ Law” for DG°) Hess’ Law- states that regardless
of the multiple stages or steps of a reaction, the total enthalpy change for the reaction is the sum of all changes.
What is the DG° for this reaction:
Given:C(s, diamond) + O2(g) CO2(g) DG° = -397 kJ
C(s, graphite) + O2(g) CO2(g) DG° = -394 kJ
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More DG° CalculationsWhat is the DG° for this reaction:
C(s, graphite) + O2(g) CO2(g) DG° = -394 kJ
CO2(g) C(s, graphite) + O2(g) DG° = +394 kJ
Given:C(s, diamond) + O2(g) CO2(g) DG° = -397 kJ
C(s, diamond) + O2(g) CO2(g) DG° = -397 kJ
CO2(g) C(s, graphite) + O2(g) DG° = +394 kJ
C(s, diamond) C(s, graphite) DG° = -3 kJ
DG°rxn < 0…..rxn is spontaneous
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Alternative DG CalculationIs the following reaction spontaneous at 298 K?
(assume standard conditions)
KCl(s)(s)3KClO(s)4KClO 43
DH°f (kJ/mol) S° (J/mol.K)
KClO3(s) -397.7 143.1
KClO4(s) -432.8 151.0
KCl (s) -436.7 82.6
Given:
DG°rxn = DH°rxn - TDS°rxn
First Calculate
Given
Then Find
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Alternative DG CalculationKCl(s)(s)3KClO(s)4KClO 43
DH°f (kJ/mol) S° (J/mol.K)KClO3(s) -397.7 143.1KClO4(s) -432.8 151.0KCl (s) -436.7 82.6
kJ
kJkJkJ
KClOHKClHKClOHH fffrxn
144
)7.397(4)7.436()8.432(3
43 34
KJ
KJ
KJ
KJ
KClOSKClSKClOSS rxn
8.36
)1.143(4)6.82()0.151(3
43 34
28
Alternative DG CalculationKCl(s)(s)3KClO(s)4KClO 43
DH°f (kJ/mol) S° (J/mol.K)KClO3(s) -397.7 143.1KClO4(s) -432.8 151.0KCl (s) -436.7 82.6
DH°rxn = -144 kJ DS°rxn = -36.8 J/K
G rxn H rxn TS rxn
144kJ 298K 38.6J K 1kJ
1000J
133kJ
DG°rxn < 0…..rxn is spontaneous at 298 K
Enthalpically favorable Entropically unfavorable
What about at 5000 K?
DG°rxn = 50 kJDG°rxn > 0…rxn is nonspontaneous at 5000 K
(Assuming the same DH and S)
29
DG Temperature Dependence
KCl(s)(s)3KClO(s)4KClO 43
DG°rxn = 50 kJ at 5000 K
DG°rxn = -133 kJ at 298 K Spontaneous
Nonspontaneous
Reaction spontaneity is a temperature dependent phenomenon!
DGrxn = DHrxn - TDSrxn
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DG Temperature Dependence
DG = DH - TDS
Enthalpy:DHrxn < 0 The reaction is enthalpically favorable.
Entropy: DSrxn > 0 The reaction is entropically favorable.
Need both to predict spontaneity. And sometimes temperature!DG < 0 SpontaneousDG > 0 NonspontaneousDG = 0 Equilibrium
1) If DH < 0 and DS > 0, then DG is negative at all T
3) If DH < 0 and DS < 0, then DG depends on T
2) If DH > 0 and DS > 0, then DG depends on T
4) If DH > 0 and DS < 0, then DG is positive at all T
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DG = DH - TDSDG < 0 SpontaneousDG > 0 NonspontaneousDG = 0 Equilibrium
3) DH < 0 and DS < 0
If DH < TDS, then DG is positive.If DH > TDS, then DG is negative.
DG Temperature Dependence
2) DH > 0 and DS > 0
If DH < TDS, then DG is negative.If DH > TDS, then DG is positive.
Nonspontaneous at high TSpontaneous at low T
(Enthalpically favorable, entropically unfavorable)
(Enthalpically unfavorable, entropically favorable)
Spontaneous at high TNonspontaneous at low T
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DG = DH - TDS
DG Temperature Dependence
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DG Temperature Dependence
Nonspontaneous
Spontaneous
Four possible scenarios:
(1) H < 0, S > 0
(2) H > 0, S > 0
(3) H < 0, S < 0
(4) H > 0, S < 0
exothermic
system becomes more disordered
exothermic
system becomes more ordered
endothermic
system becomes more disordered
DSuniv and Spontaneous ReactionsDG = DH - TDS
Class 1: Class 3:
Class 2:
34
35
Predicting T from Gibbs Equation
KCl(s)(s)3KClO(s)4KClO 43
DG°rxn = 50 kJ at 5000 K
DG°rxn = -133 kJ at 298 K Spontaneous
Nonspontaneous
Reaction spontaneity is a temperature dependent phenomenon!
At what temperature will the reaction become spontaneous?
Find T where DG changes from positive to negative.
I.e. when DG =0.
DG = DH – TDS = 0
T = DH/DS
36
Predicting T from Gibbs EquationAt what T is the following reaction spontaneous?
Br2(l) Br2(g)
Given: DH°= 30.91 kJ/mol
DS°= 93.2 J/mol.K
DG = DH – TDS = 0
T = DH/DS
T = (30.91 kJ/mol) /(93.2 J/mol.K)
T = 331.7 K
H > 0, S > 0The reaction will be spontaneous when
T > 331.7 K
Predicting T from Gibbs EquationAt what T is the following reaction spontaneous?
CaCO3 (s) CaO (s) + CO2 (g)
DG0 = DH0 – TDS0 = 0
T = D0H/DS0
DH0 = 177.8 kJ/mol
DS0 = 160.5 J/K·mol
DG0 = 0 at 835 oC
Equilibrium Pressure of CO2
37
Chapter 11
38
Liquid ↔ Gas
At time = 0 At time > 0 At time = ∞
Liquid
# of molecules in =# of molecules out
At equilibrium!
rate of evaporation = rate of condensation
DG = DH - TDSDG < 0 SpontaneousDG > 0 NonspontaneousDG = 0 Equilibrium
39
40
Gibbs Equation and Phase Change
Molar heat of vaporization (DHvap) is the energy required to vaporize 1 mole of a liquid at its boiling point.
H2O (l) H2O (g)
DG = DH – TDS = 0
If we know DHvap and boiling point we can calculate DS!
DS = TDH
= 40.79 kJ/mol
373 KDS
DHvap = 40.79 kJ/molBP(H2O) = 373 K
Example
41
17.5
The molar heats of fusion and vaporization of benzene are 10.9 kJ/mol and 31.0 kJ/mol, respectively. Calculate the entropy changes for the solid → liquid and liquid → vapor transitions for benzene. At 1 atm pressure, benzene melts at 5.5°C and boils at 80.1°C.
solid
liquid
vapor
Example
42
17.5
The molar heats of fusion and vaporization of benzene are 10.9 kJ/mol and 31.0 kJ/mol, respectively. Calculate the entropy changes for the solid → liquid and liquid → vapor transitions for benzene. At 1 atm pressure, benzene melts at 5.5°C and boils at 80.1°C.
Molar heat of vaporization (DHvap) is the energy required to vaporize 1 mole of liquid to gas.
Molar heat of fusion (DHfus) is the energy required to melt 1 mole of solid.
solid → liquid → vaporDHvapDHfus
Example
43
17.5
The molar heats of fusion and vaporization of benzene are 10.9 kJ/mol and 31.0 kJ/mol, respectively. Calculate the entropy changes for the solid → liquid and liquid → vapor transitions for benzene. At 1 atm pressure, benzene melts at 5.5°C and boils at 80.1°C.
solid → liquid → vaporDHvapDHfus
DG = DH – TDS = 0 DS = TDH
fusfus
f
ΔΔ =
(10.9 kJ/mol)(1000 J/1 kJ) =
(5.5 + 273)K
= 39.1 J / K mol
HS
Tvap
vapb
ΔΔ =
(31.0 kJ/mol)(1000 J/1 kJ) =
(80.1 + 273)K
= 87.8 J / K mol
HS
T
45
Chapter 17