Chemistry 125: Lecture 39 January 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 Mechanism Discovered by Experiment e.g. Rate = k [A] [B] 1/4 The Rate-Limiting Step Importance of “Dominant” species in B 4 4 B [dominant species]  quantity added (how much you think you have) Minor species tag along following the Law of Mass Action. B 4 dominant / B reactive

(CH 3 Li) 4 Distorted Cubic Tetramer H3CH3CCH 3 O : Excess ether rips aggregates apart by competing for vacant Li AOs. Me 2 O: :OMe 2 Me O : 4 Me 2 O 4 CH 3 Li 3 Me 2 O 8 Me 2 O :OMe 2 Me 2 O: :OMe 2 2 Me 2 O: 4

[CH 3 Li] 4 K = (CH 3 Li) 4 Distorted Cubic 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 CH 3 Li [(CH 3 Li) 4 ] [CH 3 Li] 4  Reaction becomes 1 st order. 1/4 [CH 3 Li]  [(CH 3 Li) 4 ] Reaction order proves that monomer is reactive but tetramer is dominant in hydrocarbon. 3 Me 2 O 4 Me 2 O + 8 Me 2 O

Grinding Grinding a Crystal Suspension Noorduin, et al. (J. Am. Chem. Soc. 2008) Tiny shards that would normally dissolve are rescued by coalescing (2 nd 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 minor until populations equalize. (S)-Crystals(R)-Crystals (S)(R) Base  -H atoms (on C adjacent to C=O) are easy to exchange with base Faster conversion for minor crystals? via solution

So we’ve seen the guidance rate laws can provide for under- standing reaction mechanism. 0 th Order 1 st Order 2 nd Order Fractional Order Negative Order

Back to Bond Dissociation Energies for Predicting 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 sensitive than C-H to sp 3  sp 2 (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.

R-X Bond Dissociation Energies (kcal/mole) X R Phenyl (and vinyl) have good  overlap; sp 2 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

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

R-X BDE : Alkyl Variation in Detail X R “sp 2 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. BDE relative to CH 3 X (kcal/mole) “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 * *

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. BDE relative to CH 3 X (kcal/mole)

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. BDE relative to CH 3 X (kcal/mole) t Bu-R Molecular Mechanics Strain Energies in Starting Material

t-Bu van der Waals Energy26.9kcal/mole5.2 “Idealized” Bond Lengths and 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) Residual Total Strain: 12.2 kcal/mole (includes 2.2 torsion)

R-X BDE : Alkyl Variation in Detail X R For X = alkyl almost all of the Me to t-Bu change is due to strain energy in the 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. BDE relative to CH 3 X (kcal/mole) t Bu-R Me-R molecular mechanics strain energies The 9.9 kcal/mole difference in initial Strain accounts for all 8.9 kcal/mole diff. in BDE Ditto 1.5  2.6 But not for H-R

R-X BDE : Corrected for R-X Strain X R Me-R Et-R i Pr-R t Bu-R BDE corr relative to CH 3 X (kcal/mole) Alternative to hypothesis of radical stabilization by substitution Intrinsic C-C bond strength (corrected for strain) is practically insensitive to substitution.

R-X BDE : Corrected for R-X Strain X R Me-R Et-R i Pr-R t 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. BDE corr relative to CH 3 X (kcal/mole)

R-X BDE : Corrected for R-X Strain X R Intrinsic C-C bond strength (corrected for strain) is practically insensitive to substitution. Me-R Et-R i Pr-R t Bu-R H-R But 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-R Br-R I -R BDE corr relative to CH 3 X (kcal/mole) 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 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 E a (or  G ‡ ). Compared to What?

The Hammond Postulate (1955) George S. Hammond ( ) “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 permission, E. Menger

The more exothermic a reaction - the more similar the transition state to starting material (in both energy and structure) Starting Material Product endo product 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 influence stability. endo product 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 PhCH 2 H CH 3 Relative to H-CH 3 HCH 3 H CH 3 CCH 3

Reactivity/Selectivity “Principle” More Reactive Less Reactive More Selective Less Selective k Cl / k Cl ~ 1 k Br / k Br >> 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)

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