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Chemistry 125: Lecture 38January 10, 2011
Reaction Rates: Radical-Chain Halogenation, Bond Dissociation Energies,
Reaction Rate Laws This
For copyright notice see final page of this file
Welcome Back to Sunny New Haven
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Phillip Lichtor
Senior Peer TutorsEva UribeJack Qian
Julia Rogers
OPTIONAL!
https://webspace.yale.edu/chem125/
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
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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