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Chem 125 Lecture 3712/10/08
This material is for the exclusive use of Chem 125 students at Yale and
may not be copied or distributed further.
It is not readily understood without reference to notes or the wiki from the lecture.
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3) The Law of Mass Action
from counting random arrangements of a fixed number of energy bits
2) The Entropy Factor eTS/kT
random
Exponents &Three Flavors of Statistics
1) The Boltzmann Factor e -H/RT
= Wfrom counting W, the number of
molecular structures being grouped
R
k
Same thing:
k is per individual molecule
R is per mole (= k NA)
“there’s a divinity that shapes our ends”
Hamlet V:2
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Cyclohexane Conformers
few"structures"
few"structures"
many "structures"
many quantum statesfewquantum
states
fewquantum
states
Chair(stiff)
Chair(stiff)
Twist-Boat(flexible)
0
5.5
10.8
7.0
kcal
/mol
e
Both classical and quantum views suggest a statistical "entropy" factor (of ~7) favoring twist-boat.
This reduces the room-temperature Boltzmann "enthalpy"
bias of 10-(3/4) 5.5 = 14,000 in favor of chair to about 2,000.
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Experimental EntropyAlthough we discuss entropy theoretically
(in statistical terms), physical chemists can measure it experimentally.
The entropy of a perfectly ordered crystalline material at zero Kelvin is zero ( ln 1 ).
As the material is warmed it gains entropy in increments of (Heat Absorbed)/Temperature.
S = H/T“Floppy” molecules with closely spaced energy levels
absorb more energy, and at lower temperatures, and thus gain more S on warming. Cf. Ethane rotation - Lecture 31
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3) The Law of Mass Action
from counting random arrangements of a fixed number of energy bits
2) The Entropy Factor eTS/kT
Exponents &Three Flavors of Statistics
1) The Boltzmann Factor e -H/RT
= Wfrom counting W, the number of
quantum states being grouped
K =
e-
G/R
T
from counting molecules per volume
weighted
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Law of Mass Action
Late 1700s : Attempts to assemble. hierarchy of “Affinities”
Mid 1800s : Equilibrium “K” as balance of forward and reverse rates...
Early 1800s : Amounts [concentration] can shift reaction direction away. from “affinity” prediction. …
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[concentration]
[A2]
[A] 2
= K
2 A A2
[A2] [A] 2= K
Where does the exponent come from?
Law of Mass Action
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RandomlyDistributed“Particles”
# Particles # Dimers
50 1
100 9
150 19
200 35
250 59
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[D] = K [P] 2
RandomlyDistributed“Particles”
# Particles # Dimers
50 1
100 9
150 19
200 35
250 59
# of Particles
# of
Dim
ers
Increasing concentration increases both the numberof units and the fractionof units that have nearneighbors.
numberfraction
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Equilibrium, Statistics & Exponents
Particle Distribution : Law of Mass Action [A2]
[A] 2
= K
Energy Distribution : H , Boltzmann Factor
K e-H/RT
Counting Quantum States : S
K eS/R
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Free energy determines what can happen (equilibrium)
K = e-G/RT
= 10-(3/4)G kcal/mole@ room Temp
But how quickly will it happen? (kinetics)
Energy & Entropy
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Classical Trajectories &
The Potential Energy Surface
Visualizing Reaction
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Potential Energy“Surface” for StretchingDiatomic Molecule A-B
A-B Distance
PotentialEnergy
Rolling Ball Maps A-B Vibration
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Potential Energy Surface
for LinearTriatomic A-B-C
Cliff
Pass(Transition State)
Plateau
Valley
ridge
+ maxim
umminim
um
*
* So 2-D specifies structure
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Vibration of A-B with distant C spectator
Slice and fold back
Potential Energy Surface
for LinearTriatomic A-B-C
Vibration of B-C with distant A spectator
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Unreactive Trajectory:(A bounces off vibrating B-C)
Potential Energy Surface
for LinearTriatomic A-B-C
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C flies away from
vibrating A-B
Reactive Trajectory
A approaches non-vibrating B-C
Potential Energy Surface
for LinearTriatomic A-B-C “classical” trajectory
(not quantum)
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H3 SurfaceHenry Eyring
(1935)
Crazy angle of axes means that classical trajectories can be modeled by rolling marble.
Transition State(“Lake Eyring”)
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H + H-Br
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Studying Lots ofRandom Trajectories
Provides Too Much Detail
Summarize Statisticallywith Collective
Enthalpy (H) & Entropy (S)
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“steepest descent” path Slice along
path, then flatten and tip up to create…
(not a trajectory)
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“Reaction Coordinate” Diagram(for a one-step atom transfer)
Not a trajectory, but a sequence of three species
StartingMaterials Products
Transition “State”
G
each with H and S, i.e. Free Energy (G)
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Free Energy determineswhat can happen (equilibrium)
K = e-G/RT
= 10-(3/4)G kcal/mole@ room Temp
and how rapidly (kinetics)
k (/sec) = 1013 e-G /RT‡
‡= 1013-(3/4)G kcal/mole@ room Temp
Amount of ts
(universal) Velocity
of ts theory
Since the transition stateis not truly in equilibrium
with starting materials, and the velocity is not universal,the theory is approximate.
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Using Energies to Predict Equilibria and Rates for
One-Step Reactions:Free-Radical Halogenation
H CH3Cl Cl••
H Cl
•
CH3 Cl Cl•
CH3Cl
Cl
"free-radical chain"
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Are Average Bond Energies “Real” or just a trick for
reckoning molecular enthalpy ?
Bond Dissociation Energiesare real.
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BondDissn Energies
99
90113
89
105111
89
115
111
123136.2
127
8485
8585
91
9774
122 85 72 5459 46
516756
5857
57
7272
7473
8463
9294
best values as of 2003
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Ellison I
Larger halogen
Poorer overlap with H(at normal bond distance)
& less e-transfer to halogen•H
• I
•H
• F• •
• •
less e-stabilization
weaker bond Diagram qualitative; not to scale.
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Ellison II
No special stabilizationSOMO orthogonal to *)
C-H bond unusually strong(good overlap from sp2
C)Vinyl
C-H bond normal(sp3
C , as in alkane)Allyl Special stabilization
SOMO overlaps *)
hard
111
PhenylDittoDitto
hard
113
easy
89
DittoDitto
Benzyleasy
90
All H-Alkyl 100 ± 5Same trend as
H-Halogen
Special Cases
•SOMOC•
• • • •
•
• •
•
Are unusual BDE values due to unusual bonds or unusual radicals?
oractually
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H3C H + X X H3C X + H X
FClBrI
37584636
105”””
142163151141
251187160129
1361038871
115847258
Possibility of Halogenation(Equilibrium)
109199
12
Cost Return Profit
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H3C H + X X H3C X + H X
Possibility of Halogenation(Equilibrium)
FClBrI
37584636
105”””
142163151141
251187160129
1361038871
115847258
109199
12
Cost Return Profit
Is break-two-bonds-then-make-two a plausible Mechanism?at RT (~300K)?
at ~3000K? 1013 10-106 = 10-93/sec 1013 10-10.6 = 250/sec
How about rate (which depends on Mechanism)?
No Way! Yes (unless there is a faster one)
• •• •
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H H2
H2 H
HHH
H H H
HenryEyring
(1935)Dissociation followed by association requires high activation energy.
SLOW
Make-as-you-break “displacement” is much easier.
FAST
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Free-Radical Chain Substitution
X-HR-H
X-XR-X
•X •Rcyclicmachinery
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H3C-H + X2 HX + H3CX
FClBrI
37584636
105”””
142163151141
251187160129
1361038871
115847258
Possibility of Halogenation(Equilibrium)
109249
12
Cost Return Profit
H3C-H HXX•
X2 H3CXH3C•
37584636
1361038871
Step 1
312
1734
Step 2
78262622
(Mechanism for Reasonable Rate)
How can we predict activation energy?
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Organic Chemistry
Paul D. Bartlett1907-1997
Physical
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http
://os
ulib
rary
.ore
gons
tate
.edu
/spe
cial
colle
ctio
ns/c
oll/p
aulin
g/bo
nd/a
udio
/199
7v.1
-boo
kdun
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Jack Dunitz: At the time when I was reading that book I was wondering whether chemistry was really as interesting as I had hoped it was going to be. And I think I was almost ready to give it up and do something else. I didn't care very much for this chemistry which was full of facts and recipes and very little thought in it, very little intellectual structure. And Pauling's book gave me a glimpse of what the future of chemistry was going to be and particularly, perhaps, my future.1939
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The Chemical BondIs there an Atomic Force Law?
Feeling & Seeing Molecules and Bonds
Understanding Bonding & Reactivity through H = E
How chemists learned to treasureComposition, Constitution,
Configuration, Conformationand Energy
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Is there an Atomic Force Law?
Feeling & Seeing Molecules and Bonds
Understanding Bonding & Reactivity through H = E
How chemists learned to treasureComposition, Constitution,
Configuration, Conformationand Energy
The Chemical Bond
How does science know?
Compared to what?
Were chemical bonds discovered or invented?
Some Big Questions:
Would we even have chemical bonds without our own chemical forbearers?
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End of Lecture 37Dec. 10, 2008
Good Luck on the Final!