chemistry 125: lecture 39 january 12, 2011 fractional and inverse rate laws, bond dissociation...
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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
Ph Me Et iPr tBu Allyl
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
Ph Me Et iPr tBu Allyl
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
Ph Me Et iPr tBu Allyl
H
tBu
R-X BDE : Alkyl Variation in Detail
X
R
t-Butyl-R seems to show similar radical
stabilization by substitution, but… t Bu-R
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)
-10
-8
-6
-4
-2
0
2
Ph Me Et iPr tBu Allyl
H
Me
Et
iPr
tBu
R-X BDE : Alkyl Variation in Detail
X
R
Me-R
Et-R
i Pr-R
t Bu-R
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)
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
Ph Me Et iPr tBu Allyl
H
Me
Et
iPr
tBu
R-X BDE : Alkyl Variation in Detail
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
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)
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
Ph Me Et iPr tBu Allyl
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
Ph Me Et iPr tBu Allyl
H
Me
Et
iPr
tBu
R-X BDE : Corrected for R-X Strain
X
R
Me-REt-Ri Pr-Rt Bu-R
H-R
Alternative to hypothesis of radical stabilization by substitution
But C-H bonds are weakened by alkylation of the carbon.
Intrinsic C-C bond strength (corrected for strain) is practically insensitive to substitution.
BD
Eco
rr r
elat
ive
to C
H3X
(kc
al/m
ole)
-7
-5
-3
-1
1
3
5
Ph Me Et iPr tBu Allyl
H
Me
Et
iPr
tBu
Cl
Br
I
R-X BDE : Corrected for R-X Strain
X
R
Intrinsic C-C bond strength (corrected for strain) is practically insensitive to substitution.
Me-REt-Ri Pr-Rt Bu-R
H-RBut C-H bonds are weakened by alkylation of the carbon.
Alternative to hypothesis of radical stabilization by substitution
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).
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