Chem 125 Lecture 3712/10/08

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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

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.

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

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

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. …

[concentration]

[A2]

[A] 2

= K

2 A A2

[A2] [A] 2= K

Where does the exponent come from?

Law of Mass Action

RandomlyDistributed“Particles”

# Particles # Dimers

50 1

100 9

150 19

200 35

250 59

[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

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

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

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)

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

Studying Lots ofRandom Trajectories

Provides Too Much Detail

Summarize Statisticallywith Collective

Enthalpy (H) & Entropy (S)

“steepest descent” path Slice along

path, then flatten and tip up to create…

(not a trajectory)

“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)

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

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?

Organic Chemistry

Paul D. Bartlett1907-1997

Physical

http

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.ore

gons

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.edu

/spe

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colle

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ns/c

oll/p

aulin

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7v.1

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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

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

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?

End of Lecture 37Dec. 10, 2008

Good Luck on the Final!