Chemistry 125: Lecture 39 January 12, 2011 Fractional and Inverse Rate Laws, Bond Dissociation...

Chemistry 125: Lecture 39January 12, 2011

Fractional and Inverse Rate Laws, Bond Dissociation Energies, Radical-Chain Halogenation,

Reactivity-Selectivity “Principle” This

For copyright notice see final page of this file

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.

Rate Laws: Kinetic Order

Rate = d [Prod] / d t

Fractional Order

Complex Reactions

= k concentration(s)?

Dependent on MechanismDiscovered by Experiment

e.g. Rate = k [A] [B]1/4

The Rate-Limiting Step

Importance of“Dominant” species

in B4 4 B

[dominant species] quantity added (how much you think you have)

Minor species tag along following the Law of Mass Action.

B4 dominant / B reactive

(CH3Li)4

DistortedCubic

Tetramer

H3C CH3O:

Excess ether rips aggregates apart by competing for vacant Li AOs.

Me 2O: :OMe

2Me MeO

:

• 4 Me2O 4 CH3Li • 3 Me2O8 Me2O

:OMe2

Me 2

O:

Me2O: :O

Me 2

2

Me2O:

Me 2

O:

Me

2 O:

4

[CH3Li]4 K =

(CH3Li)4

DistortedCubic

Tetramer

Excess ether rips aggregates apart by bonding with

vacant Li AOs to make monomer

dominant.

Reaction of monomer in hydrocarbon

solvent is 1/4iorder in

reagent added.

4 CH3Li[(CH3Li)4] [CH3Li]4

Reaction becomes 1st order.

1/4 [CH3Li] [(CH3Li)4]

Reaction order proves that monomer is reactive but tetramer is dominant

in hydrocarbon.

• 3 Me2O

• 4 Me2O

+ 8 Me2O

Grinding

Grinding aCrystal Suspension

Noorduin, et al.(J. Am. Chem. Soc. 2008)

Tiny shards that would normally

dissolve are rescued by coalescing

(2nd Order)

(majority solid dissolves slower than minority).

Curious shapes:negative order?

Spontaneously Deracemized!(possible mechanism for the origin

of a single-handed biosphere?)

Racemization:identical rate constants for the two enantiomers guarantee faster rate for

major minoruntil populations equalize.(S)-Crystals (R)-Crystals

N

O NH2

HN

O NH2

H

(S) (R)

Base

-H atoms (on C adjacent to C=O)

are easy to exchange with base

Faster conversionfor minor crystals?

via solution

So we’ve seen the guidance rate laws can provide for under-standing reaction mechanism.

0th Order1st Order2nd Order

Fractional Order Negative Order

Back toBond Dissociation Energies

forPredicting Rate Constants

Free-Radical Substitutions are Simple[because of minimal solvent influence]

and very Important for Atmospheric Chemistry, Combustion, and Oxidation,

and they provide great examples of Selectivity,a pervasive Theme in Synthesis & Biochemistry

Ellison II

Check with more examples

Hybridization (C-H) &

Resonance (SOMO//* mix) (C•)

WHY?

i.e. Do we have to just suck it up and memorize this, or can we rationalize such lore?

Overlap (C-X) &

E-Match (C-X)

C-C more sensitivethan C-H to

sp3 sp2 (C•) &

“hyperconjugation”(SOMO//* mix) (C•)

?N.B. We’re assuming the BDE difference is due to difference in radical stabilities, not difference in RH

Often relative values are possible to understand, even when absolute values are not.

0

20

40

60

80

100

120

Ph Me Et iPr tBu Allyl

H

Me

Et

iPr

tBu

Cl

Br

i

R-X Bond Dissociation Energies (kcal/mole)

X

R

Phenyl (and vinyl) have good overlap; sp2 C-X bonds.

Allyl (and benzyl) are “resonance stabilized” radicals.

(Stabilization of starting material strengthens bond. See above)

(Stabilization of product radical weakens bonds. See above)

R-H > R-C R-Cl > R-Br > R-I

0

20

40

60

80

100

120


H

Me

Et

iPr

tBu

Cl

Br

i

R-X Bond Dissociation Energies (kcal/mole)

X

R

R-H > R-C R-Cl > R-Br > R-I

Modest variation with R from methyl to t-butyl

-10

-8

-6

-4

-2

0

2


H

R-X BDE : Alkyl Variation in Detail

X

R

“sp2 sigma bond to C (vs. H) preferentially stabilizes the more-substituted radicals.”

(C-C overlap more sensitive to hybridization than C-H overlap)

Cf. Jones & Fleming, p. 479

H-R

If this trend is due to radical stabilization by substitution, other X-R bond strengths should show the same trend.

BD

E r

elat

ive

to C

H3X

(kc

al/m

ole)

“Probably a bit of stabilization from

SOMO overlap with C-H and C-H”

(not nearly as much as with C=C and C=C in allyl or benzyl)

Cf. Jones & Fleming, pp. 478-9

*

*

-10

-8

-6

-4

-2

0

2


H

tBu


X

R

t-Butyl-R seems to show similar radical

stabilization by substitution, but… t Bu-R

H-R


BD

E r

elat

ive

to C

H3X

(kc

al/m

ole)

-10

-8

-6

-4

-2

0

2


H

Me

Et

iPr

tBu


X

R

Me-R

Et-R

i Pr-R

t Bu-R

H-R


BD

E r

elat

ive

to C

H3X

(kc

al/m

ole)

12.2

8.3

5.0

2.3

t Bu-R

MolecularMechanics

Strain Energies inStarting Material

t-Bu t-Bu

van der Waals Energy 26.9 kcal/mole5.2

“Idealized”Bond

Lengthsand

Angles

“Relaxed”Structure

Crunch!“steric hindrance”

van der Waals Energy drop by 16.8 to 5.2 kcal/mole

comes at the expense of bond stretching and bending.

van der Waals Energy Drop: 16.8 kcal/mole(26.9 to 5.2 kcal/mole)

1.52Å

1.57Å

109.5°

112.3°

comes at the expense of bond stretching and bending.(which increase from 0 to 4.8 kcal/mole)

van der Waals Energy Drop: 16.8 kcal/mole(26.9 to 5.2 kcal/mole)

ResidualTotal Strain:12.2 kcal/mole

(includes 2.2 torsion)

-10

-8

-6

-4

-2

0

2


H

Me

Et

iPr

tBu


X

R

For X = alkylalmost all of the Me to t-Bu change is

due to strain energy inthe starting material.

Me-R

Et-R

i Pr-R

t Bu-R

H-R


BD

E r

elat

ive

to C

H3X

(kc

al/m

ole)

12.2

8.3

5.0

2.3

t Bu-R

0.8

1.51.9

2.3Me-R

molecularmechanics

strain energies

1.9

1.5

0.8

0

The

9.9

kca

l/m

ole

diff

eren

ce in

init

ial S

trai

nac

coun

ts f

or a

ll 8

.9 k

cal/

mol

e di

ff. i

n B

DE

Dit

to1.

5

2.6

But not for H-R

-10

-8

-6

-4

-2

0

2


Me

Et

iPr

tBu

R-X BDE : Corrected for R-X Strain

X

R

Me-REt-Ri Pr-Rt Bu-R

BD

Eco

rr r

elat

ive

to C

H3X

(kc

al/m

ole)

Alternative to hypothesis of radical stabilization by substitution

Intrinsic C-C bond strength (corrected for strain) is practically insensitive to substitution.

-10

-8

-6

-4

-2

0

2


H

Me

Et

iPr

tBu


X

R


H-R


But C-H bonds are weakened by alkylation of the carbon.


BD

Eco

rr r

elat

ive

to C

H3X

(kc

al/m

ole)

-7

-5

-3

-1

1

3

5


H

Me

Et

iPr

tBu

Cl

Br

I


X

R



H-RBut C-H bonds are weakened by alkylation of the carbon.


While C-Cl and C-Br are strengthened by alkylation of the carbon.

Cl-RBr-R

I-R

BD

Eco

rr r

elat

ive

to C

H3X

(kc

al/m

ole)

No one I know of understands this, but the textbooks seem to be wrong.

Can we use energies of stable structures that we “understand” to infer the energies of transition states, so as to predict reactivity?

How can we predict activation energy?

Might exothermic reactions be faster than endothermic ones?

relative

relative

analogous

∧

∧

∧

How can we predict activation energy?

This is no easy task a priori, especially when interaction with

solvent is important.But often one can say something

sensible about relative values of Ea (or G‡).

Compared to What?

The Hammond Postulate (1955)

George S. Hammond (1921-2005)

“If two states, as for example, a transition state and an unstable interme-diate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures.”

This stimulated organic chemists to think about transition states and try to generalize plausibly

about reaction coordinates.

by p

erm

issi

on, E

. Men

ger

The more exothermic a reaction - the more similar the transition state to starting material

(in both energy and structure)

StartingMaterial

Product

endoproduct

At least among one-step reactions

that are closely analogous, such as

X• + H-R.

.X-H + •R…..

The more exothermic a reaction - the more similar the transition state to starting material

(in both energy and structure)

There is “likely” a continuum

between starting material and product with respect to the factors that

influencestability.

endoproduct

An effect mostly influencing the

energy of the product of an endothermic

reaction should have a similar (slightly

smaller) influence on its (late) transition

state.

Rates of slower reactions should be more sensitive to overall G!

An effect mostly influencing the

energy of the product of an exothermic

reaction should have a small influence on its (early) transition

state.

e.g. resonance stabilization

PhCH2

H

PhCH2

•CH3Relative to H-CH3 H•••CH3

H

CH3CCH3

Reactivity/Selectivity “Principle”

More Reactive

Less Reactive

More Selective

Less SelectivekCl / kCl ~ 1

kBr / kBr >> 1

Consider a similar pair of reactions(e.g. H-abstraction from R’H by Cl• and by Br•)

Consider two analogous reactions (e.g. H-abstraction from RH by Cl• and by Br•)

End of Lecture 39Jan. 12, 2011

Copyright © J. M. McBride 2011. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).

Use of this content constitutes your acceptance of the noted license and the terms and conditions of use.

Materials from Wikimedia Commons are denoted by the symbol .

Third party materials may be subject to additional intellectual property notices, information, or restrictions.

The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0

http://creativecommons.org/licenses/by-nc-sa/3.0/us

Chemistry 125: Lecture 39 January 12, 2011 Fractional and Inverse Rate Laws, Bond Dissociation...

Documents

Transcript of Chemistry 125: Lecture 39 January 12, 2011 Fractional and Inverse Rate Laws, Bond Dissociation...