Transcript 2 - Yale University

Chem 125 Lecture 37
12/10/08
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.
Exponents &
Three Flavors of Statistics
“there’s a divinity
that shapes our ends”
1)Same
The
Boltzmann
Factor
e
thing:
Hamlet V:2
k is per individual molecule
R is per mole (= k  NA)
R
-H/RT
from counting random arrangements
of a fixed number of energy bits
k =W
2) The Entropy Factor eTS/kT
from counting W, the number of
molecular structures being grouped
3) The Law of Mass Action
Cyclohexane Conformers
10.8
7.0
kcal/mole
5.5
few
quantum
states
0
few
"structures"
Chair
(stiff)
many "structures"
many quantum states
Twist-Boat
(flexible)
few
quantum
states
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.
few
"structures"
Chair
(stiff)
Experimental Entropy
Although 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
K = e-G/RT
Exponents &
Three Flavors of Statistics
1) The Boltzmann Factor e -H/RT
from counting random arrangements
of a fixed number of energy bits
2) The Entropy Factor eTS/kT = W
weighted
from counting W, the number of
quantum states being grouped
3) The Law of Mass Action
from counting molecules per volume
Law of Mass Action
Late 1700s : Attempts to assemble.
hierarchy of “Affinities”
Early 1800s : Amounts [concentration] can
shift reaction direction away.
from “affinity” prediction. …
Mid 1800s : Equilibrium “K” as balance of
forward and reverse rates...
Law of Mass Action
[concentration]
2A
[A2]
2
[A]
A2
= K
[A2] = K [A] 2
Where does
the exponent
come from?
Randomly
Distributed
“Particles”
# Particles # Dimers
50
1
100
9
150
19
200
35
250
59
# of Dimers
Randomly
Distributed
“Particles”
Increasing concentration
increases both the number
number
of units and the fraction
fraction
of units that have near
neighbors.
[D] = K
# of Particles
# Particles # Dimers
[P] 2
50
1
100
9
150
19
200
35
250
59
Equilibrium, Statistics & Exponents
Particle Distribution : Law of Mass Action
[A2]
= K
2
[A]
Energy Distribution : H , Boltzmann Factor
-H/RT
Ke
Counting Quantum States :
S
S/R
Ke
Free energy determines what
can happen (equilibrium)
-G/RT
e
K=
-(3/4)G
= 10
Energy &
Entropy
kcal/mole
@ room Temp
But how quickly
will it happen? (kinetics)
Visualizing Reaction
Classical Trajectories
&
The Potential Energy Surface
Potential
Energy
Rolling Ball
Maps A-B
Vibration
A-B Distance
Potential Energy
“Surface” for Stretching
Diatomic Molecule A-B
Plateau
Pass
+
(Transition State)
Potential Energy
Surface
for Linear *
Triatomic A-B-C
* So 2-D specifies structure
Valley
Cliff
Vibration of A-B
with distant
C spectator
Potential Energy
Surface
for Linear
Triatomic A-B-C
Vibration of B-C
with distant
A spectator
Slice and
fold back
Unreactive
Trajectory:
(A bounces off
vibrating B-C)
Potential Energy
Surface
for Linear
Triatomic A-B-C
C flies away
from
vibrating A-B
Reactive
Trajectory
Potential Energy
Surface
for Linear
Triatomic A-B-C
“classical” trajectory
(not quantum)
A approaches
non-vibrating B-C
H3 Surface
Henry Eyring
(1935)
Transition State
(“Lake Eyring”)
Crazy angle of axes means that classical trajectories can be modeled by rolling marble.
H + H-Br
Studying Lots of
Random Trajectories
Provides Too Much Detail
Summarize Statistically
with Collective
Enthalpy (H) & Entropy (S)
“steepest descent”
path
(not a trajectory)
Slice along
path,
then flatten
and tip up
to create…
Transition “State”
G
Starting
Materials
Products
“Reaction Coordinate” Diagram
(for a one-step atom transfer)
Not a trajectory, but a sequence of three species
each with H and S, i.e. Free Energy (G)
Free Energy determines
what can happen (equilibrium)
-G/RT
Since the transition state
e
(universal)
K=
-(3/4)G
= 10 the velocity is not universal,
Velocity and
of ts theory
is not truly in equilibrium
kcal/mole
with starting materials,
and
@ room Temp
the theory is approximate.
how rapidly (kinetics)
‡
13
-G
/RT
10 e
k (/sec) =
13-(3/4)G
= 10
‡
Amount
of ts
kcal/mole
@ room Temp
Using Energies to Predict
Equilibria and Rates for
One-Step Reactions:
Free-Radical Halogenation
"free-radical chain"
•
Cl
•
Cl H CH3
•
CH3 Cl Cl
H Cl
•
Cl
CH3Cl
Are Average Bond Energies
“Real” or just a trick for
reckoning molecular
enthalpy ?
Bond Dissociation Energies
are real.
BondDissn Energies
115
84
85
72
72
58
57
99
111
113
90
89
89
105
111
127
85
85
97
74
74
73
84
63
59
72
57
56
67
51
46
54
122
85
123
136.2
91
92
94
best values as of 2003
Ellison I
Larger halogen

Poorer overlap with H
(at normal bond distance)
& less e-transfer to halogen
H •
H •
•
•
••
F
I
••
less e-stabilization

weaker bond
Diagram qualitative; not to scale.
All H-Alkyl 100 ± 5
Same trend as
H-Halogen
Special Cases
Ellison II
C-H bond unusually strong
(good overlap from sp2C)
Ditto
hard Vinyl
111
No special stabilization
SOMO orthogonal to *)
hard Phenyl
Ditto
113
Are unusual BDE values due to unusual bonds or unusual radicals?
C-H bond normal
(sp3C , as in alkane)
Ditto
easy
Allyl
89
easy Benzyl
90
Special stabilization
SOMO overlaps *)
SOMOC
• Ditto
••
•
••

or
actually
••

Possibility of Halogenation
(Equilibrium)
H3C H + X X  H3C X + H X
Cost
F 105 37 142 115
Cl ”
58 163 84
Br ”
46 151 72
I ”
36 141 58
136
103
88
71
Return
Profit
251
187
160
129
109
19
9
12
Possibility of Halogenation
How about rate(Equilibrium)
(which depends on Mechanism)?
H3C• •H + X• •X  H3C X + H X
Cost
F 105 37 142 115
Cl ”
58 163 84
Br ”
46 151 72
I ”
36 141 58
136
103
88
71
Return
Profit
251
187
160
129
109
19
9
12
Is break-two-bonds-then-make-two a plausible Mechanism?
at RT (~300K)? 1013  10-106 = 10-93/sec No Way!
at ~3000K?
1013  10-10.6 = 250/sec Yes (unless there is a faster one)
Henry
Eyring
H2
H
Dissociation followed H
by association requires
high activation energy.
SLOW
(1935)
Make-as-you-break
“displacement” is much easier.
FAST
HHH
H
H2
H
H
Free-Radical Chain Substitution
R-H
X•
R-X
X-H
cyclic
machinery
R•
X-X
Possibility of Halogenation
(Mechanism
for Reasonable Rate)
(Equilibrium)
H3C•
X•
H3C-H +
XHX
X2 
+ H33CX
2  HX
Cost
Step
1
31 136
F 105 136
37 142
37
2 103
Cl ” 103
58 163
58
88
17 46
88
Br ”
46 151
71
34 36
71
I ”
36 141
115
84
72
58
Return
Step 2
Profit
78
251
26
187
26
160
22
129
109
24
9
12
How can we predict activation energy?
Physical
Organic
Chemistry
Paul D. Bartlett
1907-1997
http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/audio/1997v.1-bookdunitz.html
1939
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.
The Chemical Bond
Is there an Atomic Force Law?
Feeling & Seeing Molecules and Bonds
Understanding Bonding & Reactivity
through H = E
How chemists learned to treasure
Composition, Constitution,
Configuration, Conformation
and Energy
Some
Big Questions:
The Chemical
Bond
Is there an Atomic Force Law?
How does science know?
Feeling & Seeing Molecules and Bonds
Compared to what?
Understanding Bonding & Reactivity
Were
chemical
through
H = bonds
E
discovered
or invented?
How
chemists learned
to treasure
Composition, Constitution,
Would Configuration,
we even have
chemical
bonds
Conformation
without our own
forbearers?
andchemical
Energy
End of Lecture 37
Dec. 10, 2008
Good Luck on the Final!