Chemistry 125: Lecture 38January 10, 2011

Reaction Rates: Radical-Chain Halogenation, Bond Dissociation Energies,

Reaction Rate Laws This

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Semester 1 : Bonds & Molecular Structure

(with some thermodynamics)

Semester 2 : Reaction Mechanisms & Synthesis

(with some spectroscopy)

How Mechanisms are Discovered and Understood in Terms of Structure and Energy

Simplest Reactions - Bond Cleavage & Make-as-You-Break

Solvent Effects on Ionic Reactions

Nucleophilic Substitution and Elimination: Proving Mechanisms

Exam 5 – February 2

Free-Radical Substitution: Reactivity and Selectivity

Electrophilic Addition to Alkenes and Alkynes (and the Role of Nucleophiles)

Conjugation, Aromaticity, & Pericyclic Reactions

Exam 6 – February 28

Polymers and their Properties

Spectroscopy for Structure and Dynamics: UV/VIS, IR, MRI & NMR

Aromatic Substitution

Carbonyl Chemistry Oxidation & Reduction

Exam 7 – April 6

Acid Derivatives – Substitution at C=O

-Reactivity and Classical Condensations

Carbohydrates and Fischer’s Glucose Proof

Final Exam – May 6

Complex Synthesis of Unnatural and Natural Products

Spectroscopy & Synthesis

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

Studying Lots ofRandom Trajectories

Provides Too Much Detail

Summarize Statisticallywith Collective

Enthalpy (H) & Entropy (S)

“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

Using Energies to Predict Equilibria and Rates for

One-Step Reactions

No reaction is conceptually simpler than breaking a bond

in the gas phase to give atoms or free radicals.

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

Ellison’s values as of 2003

from Barney Ellison & his friends

Coming in April

Streitwieser, Heathcock, and Kosower (1992)

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

DittoDittoBenzyleasy

90

All H-Alkyl 100 ± 5Same trend as

H-Halogen

Special Cases

•SOMOC•

• • • •

•

• •

•

Are unusual BDE values due to unusual bonds or unusual radicals?

(Compared to what?)

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 HHenryEyring

(1935)Dissociation followed by association requires high activation energy.

SLOW

Make-as-you-break “displacement” is much easier.

FAST

H CH3Cl Cl••

H Cl

•CH3 Cl Cl

•

CH3ClCl

"free-radical chain"

Make-as-you-break “displacement” is much easier.

FAST

Free-Radical Chain Substitution

X-HR-H

X-XR-X

•X •Rcyclic machinery

preserves “radicalness”

H3C-H + X2 HX + H3CX

FClBrI

37584636

105”””

142163151141

251187160129

1361038871

115847258

Possibility of Halogenation(Equilibrium)

109249

12

Cost Return ProfitH3C-H HX

X•

X2 H3CXH3C•

37584636

1361038871

Step 1

3121734

Step 2

78262622

(Mechanism for Reasonable Rate)

How can we predict activation energy?

Even if we could predict the rate of Step 1 or Step 2, how would we reckon the overall rate with two reaction steps?

We must learn to cope with such Complex Reactions

Digression on Reaction Order & Complex Reactions

The kinetic analogue of the Law of Mass Action

(i.e. dependance of rate on concentrations)

can provide insight about reaction mechanism.

Could use a single tap “twice” as large

Rate(amount per second)

Doubled RateChemists can also change

[Concentration]

Rate “Laws”: Kinetic OrderRate = d [Prod] / d t

0th Order: Rate = k

Simple One-Step Reactions

= k concentration(s)?Dependent on MechanismDiscovered by Experiment

0th Order KineticsWould more sheep give a faster rate?

NO!(saturation)

Catalyst e.g. enzyme“Substrate”

Rate But if the catalysis was not initially recognized.

[Catalyst] [Substrate]0 1

Phot

o: A

nton

io V

idig

al b

y pe

rmis

sion

But first-order in substrate at low concentration.[Substrate]1

for high [Substrate]

Rate “Laws”: Kinetic Order

1st Order: Rate = k [A]

Rate = d [Prod] / d t

0th Order: Rate = k

Simple One-Step Reactions

= k concentration(s)?Dependent on MechanismDiscovered by Experiment

(Reasonable)

Product

Time (sec)

Con

cent

ratio

nFirst-Order Kinetics

k = 0.69/sec

Product

Time (sec)

Con

cent

ratio

nFirst-Order Kinetics

Starting Material

1/2

1/4

1/81/16

Exponential Decay

Constant “Half Life”= 0.69 / k

k = 0.69/sec

Reversible First-Order Kinetics

Starting Material Product k-1

k1

at Equilibriumforward rate = reverse rate

k1 [Starting Material] = k-1 [Product]

=k-1

k1[Product][Starting Material]

K

Time (sec)

Con

cent

ratio

nReversible First-Order Kinetics

Starting Material

Product

k1 = 0.69/seck-1 = 0.23/sec

Exponential Decay to Equilibrium Mixture Half Life = 0.69 / (k1 + k-1)

Starting Material Product k-1

k1

( K = 3 )

Rate Laws: Kinetic Order

2nd Order: Rate = k [A]2

“1st Order in A”

Rate = d [Prod] / d t

1st Order: Rate = k [A]

0th Order: Rate = k

Simple One-Step Reactions

= k concentration(s)?Dependent on MechanismDiscovered by Experiment

or Rate = k [A] [B] “Pseudo” 1st OrderIf [B] is (effectively) constant

k

or[B] >> [A]

e.g.[B] a catalyst

Time (sec)

Con

cent

ratio

nSecond- vs First-Order Kinetics

First Order

Second Order

Slows FasterNot Exponential

No Constant Half Life

Rate Laws: Kinetic OrderRate = d [Prod] / d t

Complex Reactions

= k concentration(s)?Dependent on MechanismDiscovered by Experiment

The Rate-Limiting Step

Who Cares? Rapid pre-

equilibrium

reactive intermediate (low concentration)

“ ”with starting material

Starting Material Intermediate k-1

k1Product

k2

Actual

as if 2nd TSwere sole barrier

as if 1st TSwere sole barrier

SMInt Flaky

Excel ProgramAvailable

Prod

TS1TS2

Once Int reaches steady-state

“equilibrium” with SM, it yields

Prod 1/10 as fast as it is formed.

k2 / k-1 ≈ 1/9k1 / k-1 ≈ 1/9Once Int reaches

steady-state “equilibrium” with SM,

SM / Int ≈ 9

Rate Laws: Kinetic OrderRate = d [Prod] / d t

Fractional Order

Complex Reactions

= k concentration(s)?Dependent on MechanismDiscovered by Experiment

The Rate-Limiting Step

End of Lecture 38Jan. 10, 2011

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