Chemistry 125: Lecture 38January 11, 2010

Reaction Rates: Trajectories, Transition State Theory, and Bond Dissociation Energies

This

For copyright notice see final page of this file

Welcome Back

Update from Prof. Leiserowitz on Hemozoin Alignment

400nm thick disk cut from

chemically fixedmalaria-infected red blood cell

Cut into ~40 slices each

imaged by SEM and reconstructed in 3D by computer

tomography

Update from Prof. Leiserowitz on Hemozoin Alignment

400nm thick disk cut from

chemically fixedmalaria-infected red blood cell

3 or 4 hemozoin crystals identically oriented on {100}

[2 (?) others may have been damaged during slicing]

Semester 1 : Bonds and Molecular Structure

(and some thermodynamics)

Semester 2 : Reactions and Synthesis

(and some spectroscopy)

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

Classical Trajectories &

The Potential Energy Surface

Visualizing Reaction

Time-Lapse“Classical”(Molecular Mechanics)

Trajectory for non-reactive

collision of 13 atoms

6 molecules40 Dimensions

(3n + time)by E. Heller

faster

slower

heavier

lighter

rotatingslowly

rotatingrapidly

&vibrating

TooComplicated(for our purposes)

Potential Energy“Surface” for StretchingDiatomic Molecule A-B

A-B Distance

PotentialEnergy

Rolling Ball Maps A-B Vibration

Potential Energy Surface

for LinearTriatomic A-B-C

Cliff

Pass(Transition State

or Transition Structure)

Plateau

Valley

ridge

+ maxim

umminim

um

*

* So 2-D specifies structure

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

Unreactive Trajectory:(A bounces off vibrating B-C)

Potential Energy Surface

for LinearTriatomic A-B-C

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)

H3 SurfaceHenry Eyring

(1935)

Crazy angle of axes means that classical trajectories can be modeled by rolling marble.

Transition State(“Lake Eyring”)

H + H-Br

John McBride (1973)

“I wanted to catch a little one”

Studying Lots ofRandom Trajectories

Provides Too Much Detail

Summarize Statisticallywith Collective

Enthalpy (H) & Entropy (S)

“steepest descent” path Slice along

this path, then flatten and tip up to create…

(not a trajectory)

“Reaction Coordinate” Diagram(for a one-step atom transfer)

Not a realistic trajectory, but rather a sequence of three species

StartingMaterials Products

Transition “State”

G

each with H and S, i.e. Free Energy (G)

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.

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"

Are Average Bond Energies “Real” or just a trick for

reckoning molecular enthalpy ?

Bond Dissociation Energiesare real.

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

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.

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

H3C H + X X H3C X + H X

FClBrI

37584636

105”””

142163151141

251187160129

1361038871

115847258

Possibility of Halogenation(Equilibrium)

109199

12

Cost Return Profit

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)

• •• •

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

Free-Radical Chain Substitution

X-HR-H

X-XR-X

•X •Rcyclicmachinery

End of Lecture 38Jan. 11, 2010

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