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Ready; Catalysis Kinetics-1
There are only two important things in chemistry, kinetics and thermodynamics. And, exp(-ΔG/RT) = k1/k-1, so there’s really only one thing. Kinetics provides information about the transition state of a reaction. We’ll use a simple example to learn the basic tools, then look at more applications to catalysis.
Crude Data [EtI] = [NaCN]
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10
Time
Conc
entra
tion
[EtI][EtCN]
1st step: measure change in concentration over time under known conditions. Common techniques:
GC UV/Vis NMR IR HPLC
Note: data for EtCN are hypothetical
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
Con
cent
ratio
n
Time
Crude Data [EtI] = [NaCN]
[EtCN]
An aside on reaction deceleration
2
Ready; Catalysis Kinetics-2
Data can be plotted to determine reaction’s overall order: Crude Data (0th Order)
[EtI] = [NaCN]
R2 = 0.6539
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10
Time
Conc
entra
tion
[EtI][EtCN]
2nd order plot[EtI] = [NaCN]
R2 = 1
0
2
4
6
8
10
12
0 2 4 6 8 10
Time
1/[E
tI]
0th: -d[A]/dt = k à [A] = kt 1st: -d[A]/dt = k[A] à [A] = exp(kt)
ln[A] = kt 2nd: -d[A]/dt = k[A]2 à 1/[A] = kt (also for k[A][B] if [A] = [B]
1st order plot
R2 = 0.9507
-3
-2.5
-2
-1.5
-1
-0.5
00 2 4 6 8 10
time
Ln[E
tI]
Ready; Catalysis Kinetics-3
2 common methods to determine order in individual components. Pseudo 1st-order: one component in huge excess (its concentration ~ constant) Collect data at various excessive concentrations
Pseudo-first Order[NaCN]>>[EtI]=1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3
time
[EtI]
[NaCN]=10[NaCN]=25[NaCN]=50[NaCN]=100[NaCN]=200
Note [EtI] =1 à 0, but [NaCN] = 10 à 9 up to 200 à 199 Rate = k[NaCN][EtI] ~ k[NaCN]0[EtI] = kobs[EtI]
3
Pseudo-first Order[NaCN]>>[EtI]=1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3
time
[EtI]
[NaCN]=10[NaCN]=25[NaCN]=50[NaCN]=100[NaCN]=200
Ready; Catalysis Kinetics-4
Pseudo-first Order[NaCN]>>[EtI]=1
y = -199.36x - 0.0009y = -99.363x - 0.0018
y = -49.363x - 0.0036
y = -24.362x - 0.0073
y = -9.3583x - 0.0187
-2.5
-2
-1.5
-1
-0.5
00 0.05 0.1 0.15 0.2 0.25 0.3
time
Ln[E
tI]
[NaCN]=10[NaCN]=25[NaCN]=50[NaCN]=100[NaCN]=200
Pseudo First-Order
0
50
100
150
200
250
0 50 100 150 200 250
[NaCN]
kobs
Replot data in 1st order coordinates Slope of line = kobs
Plot slope v [NaCN]
Rxn is 1st order in NaCN!! But…is 10-200 equiv NaCN really representative??
Ready; Catalysis Kinetics-5
Initial Rates[EtI]=1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7
time
[EtI]
[NaCN]=0.5[NaCN]=1.1[NaCN]=2[NaCN]=4[NaCN]=8
zoom in
An alternative is the method of ‘initial rates’ Keep one component constant (EtI) and vary the other (NaCN), but keep close to synthetic conditions Look at the first 10% of the reaction. Assume concentrations don’t change much at low conversion. i.e. v = k[EtI][NaCN] ~ k[EtI]0[NaCN]0(c = 0 à 10%)
4
Ready; Catalysis Kinetics-6
Initial Rates[NaCN]~[EtI]=1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7
time
[EtI]
[NaCN]=0.5[NaCN]=1.1[NaCN]=2[NaCN]=4[NaCN]=8
zoom in
Notes Need more data points/time for initial rate Data looks pretty linear for first 10% Slope of best-fit line is kobs Kobs = k[NaCN][EtI] and [EtI] was constant Again, the rxn is first order in [NaCN] But…we ignored 90% of the reaction.
Initial Rates1st 10%
y = -0.4553x + 0.9989R2 = 0.9997
y = -0.9854x + 0.9978
y = -7.5017x + 0.9987
y = -3.7244x + 0.9986
y = -1.8356x + 0.99830.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
0 0.02 0.04 0.06 0.08 0.1 0.12
time
[EtI]
[NaCN]=0.5[NaCN]=1.1[NaCN]=2[NaCN]=4[NaCN]=8
Order by Initial Rates
y = 0.9x - 0.0R2 = 1.0
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6 7 8 9
[NaCN]
k(ob
d)
Ready; Catalysis Kinetics-7
Case Study 1: Bergman, JACS, 1981, 7028
(OC)3Mo
Migratory insertion
CH3
PR3(OC)2Mo
O
CH3PR3Confusion: Huge solvent effects on rate and (in related systems) stereochemistry
What's the mechanism??
concerted attack/migration mechanism:
(OC)2MoCO
CH3R3P
(OC)2Mo
O
CH3PR3rate = k[1][PR3]
k
1
(OC)2MoCO
CH3
(OC)2Mo
O
CH3
k1
R3P
(OC)2Mo
O
CH3PR3
k-1
k2
pre-migration mechanism
rate =k1k2[1][PR3]k2[PR3] + k-1
notes: you should be able to derive these equations. Why not consider an associative mechanism?
hypothetical curves
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12
[p]
rate pre-migration
concerted attack
5
Ready; Catalysis Kinetics-8
Case Study 1: Bergman, JACS, 1981, 7028
Actual data Rxn in THF and 3-MeTHF look like superposition of concerted attack and pre-migration
Rxn in 2,5 Me2THF only shows concerted attack. How to explain? Solvent assistance.
(OC)2MoCO
CH3
(OC)2Mo
O
CH3
k1
R 3P
(OC)2Mo
O
CH3PR3
k-1
k2rate =
k1k2[1][PR3][S]k2[PR3] + k-1
SS
but [S] is constant, so kinetically invisible
Ready; Catalysis Kinetics-9
Case Study 1: Bergman, JACS, 1981, 7028
(OC)2MoCO
CH3
(OC)2Mo
O
CH3
k1
R 3P
(OC)2Mo
O
CH3PR3
k-1
k2rate =
k1k2[1][PR3][S]k2[PR3] + k-1
SS
but [S] is constant, so kinetically invisible
Mechanism predicts 1st order dependence on THF. Do expt in 2,5-Me2THF, add THF (note only minor change in dipole
6
cat. OsO4-1K3Fe(CN)6
OH
OH
96% ee
Ready; Catalysis Kinetics-10
Case Study 2: Corey, JACS, 1996, 319
Previous work (JACS 1993, 12226) had shown 1st order in OsO4-L, zero order in Fe(III)
Ready; Catalysis Kinetics-11
Case Study 2: Corey, JACS, 1996, 319
V =kcatK[Os]T[olefin]1 + K[olefin]
= kcat[Os]T[olefin]Km + [olefin]
~
These are saturation kinetics!!. Same as many enzymes and Lewis-Acid cat Rxns
Proposed structure of L*OsO4(olefin) for allyl benzoate
7
Binding appears correlated to selectivity in asymmetric dihydroxylation Poor correlation between rate and selectivity
Ready; Catalysis Kinetics
Case Study 2: Corey, JACS, 1996, 319
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4 0.5 0.6
Kmee
Ready; Catalysis Kinetics-12
Case Study 3: Jacobsen, JACS, 1996, 10924
The reaction
The data:
8
Ready; Catalysis Kinetics-13
Case Study 3: Jacobsen, JACS, 1996, 10924
Rate = k[(salen)Cr]2[epoxide]-1[Azide]0
2 Cr’s involved in RDS Epoxide inhibits rxn!! Azide either (a) involved after RDS or (b) present in ground state
Cr
N3
O
2
CrN3 O CrN3CrN3 O CrN3
O
O2
HN3
HON3
Ready; Catalysis Kinetics-14
Case Study 4: Jacobsen, JACS 1999, 6086 and unpublished work
The rxn:
Data: log log plot
y = 2.0577x + 3.8479R2 = 0.9947
-1
-0.5
0
0.5
1
1.5
2
-2.2 -2 -1.8 -1.6 -1.4 -1.2 -1
log[Co]
log[
initi
al ra
te]
Rate = kobs[Co]2
V = k[A]n log(V) = log(k[A]n) = n*log(k[A])
9
Ready; Catalysis Kinetics-15
Case Study 4: Jacobsen, JACS 1999, 6086 and unpublished work
Epoxide Order
0
2
4
6
8
10
12
14
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
[epoxide]
initi
al ra
te
Saturation kinetics with epoxide
ArOH order
0
0.00001
0.00002
0.00003
0.00004
0.00005
0.00006
0 0.5 1 1.5 2 2.5 3
[ArOH]
initi
al ra
te
Inhibition by PhOH
L
Co
OPh
HOPh
2
CoPhO O CoPhOCoPhO O CoPhO
O
2 PhOH
HOOPh
HOPh
L
L = epox or PhOH
Kd
rate = kcat[Co]t2[Epox]
kcat
Kd[ArOH]+[Epox]
Ready; Catalysis Kinetics-16
Case Study 4: Jacobsen, JACS 1999, 6086 and unpublished work
10
Ready; Catalysis Kinetics-17
Case Study 5: Stahl, JACS 2002, 766
The rxn
The data: DMSO critical, but is not reduced (O2 required) or oxidized (no dimethyl sulfone is formed) 2 formed:O2 consumed = 2 (O2 is a 4 e- oxidant here)
Under the rxn conditions, disproportionation observed (sometimes referred to as ‘catalase activity’)
Pd black (precipitated Pd metal) observed during course of reaction
Ready; Catalysis Kinetics-18
Case Study 5: Stahl, JACS 2002, 766
Also: Pd black correlates with rate decrease Rate independent of [ROH] Conclude oxidation of Pd is rate limiting Predicts rate = k[O2][Pd] (i.e. linear increase in rate with [Pd])
Propose catalyst decomposition is time-dependent. Decomposition is bimolecular; more pronounced at higher [Pd] Described by kdec competitive with kcat Eq 7 models data in trace B
11
Ready; Catalysis Kinetics-19
Case Study 5: Stahl, JACS 2002, 766
Integrated form models experimental data
Proposed mechanism
fast
Ready; Catalysis Kinetics-20
Case Study 6: Foa et al., J. Chem Soc. Dalton, 1975, 2572.
R
Cl
+ Ni(PPh3)4
R
NiCl(PPh3)2
The rxn
The data 1st order in [ArCl]
R2 = 0.9946
0
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2 1.4
[ArCl]
kobs
* 10
4
non-linear inhibition by PPh3
40
45
50
55
60
65
70
75
80
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
[PPh3]
kobs*104
12
Ready; Catalysis Kinetics-21
Case Study 6: Foa et al., J. Chem Soc. Dalton, 1975, 2572.
Proposed mechanism
Ni(PPh3)4 Ni(PPh3)3+ PPh3 K' > 10
Ni(PPh3)2Ni(PPh3)3 + PPh3 K < 10-6
Ni(PPh3)3 k1+ ArCl PPh3(PPh3)2NiAr(X) +
Ni(PPh3)2 k2+ ArCl (PPh3)2NiAr(X)
Rate = k1[PPh3] + k2K[PPh3]
[Ni]T[ArCl] = kobs[Ni]T
k' = kobs[ArCl]
= k1[PPh3] + k2K[PPh3]
k'[PPh3] = k1[PPh3] + k2K
plot k'[PPh3] vs. [PPh3]
For p-Cl2Ph: k1 = 1 x 10-4 Kk2 = 1.1 x 10-5 k2 ~ 10 So Ni[PPh3]2 105x more reactive than Ni[PPh3]3, but much less prevalent
Ready; Catalysis Kinetics-case study 7
Coates, JACS, 2007, 4948
OR
R' 1 (0.1-2 mol%), CO (850 psi),90 oC, dioxane
R R'
OO O
High yields for terminal and internal epoxides; stereospecific:
13
Coates, JACS, 2007, 4948
Ready; Catalysis Kinetics-case study 7
Unusual kinetics observed:
Anhydride formation displays induction period; no anhydride formed until epoxide consumed. Independent rxns similar in rate; show first order dependence on catalyst.
Coates, JACS, 2007, 4948
Ready; Catalysis Kinetics-case study 7
OR
R' 1 (0.1-2 mol%), CO (850 psi),90 oC, dioxane
R R'
OO OO
R R'
O
β-lactone
Rate (lactone) = k[epox]0[CO]0[catalyst]1[Solvent]1 Rate (anhydride) = k[lactone]1[CO]0[catalyst]1[Solvent]-1
Epoxide (and solvent) inhibit lactone à anhydride
14
Coates, JACS, 2007, 4948
Ready; Catalysis Kinetics-case study 7
Resting state in presence of epoxide (no open LA sites)
Resting state, no epoxide
Ready; Catalysis Kinetics-Van’t Hoff
Recall: ΔG = -RT*ln(K) and ΔG = ΔH – TΔS Merging and rearranging gives the Van’t Hoff Equation: ln(K) = (-ΔH/R)(1/T) + (ΔS/R) à Ln(K) vs. 1/T gives ΔH and ΔS
Hartwig, JACS, 2006, 9306
n.b. increasing temperature decreases contribution of ΔH
15
Ready; Catalysis Kinetics-Erying Equation
The Eyring equation: determination of ΔH‡ and ΔS‡.
Supports associative mechanism (usually associative approx -30eu Dissociative +10-20eu)
Stahl, JACS, 2004, 14832
Ready; Catalysis Kinetics-Erying Equation
Potential mechanisms:
Small entropy of activation inconsistent with mechanism a. (Labeling studies ruled out mechanism b).
Bergman, 1995, 6382
16
Ready; Catalysis Kinetics-Erying Equation
Use in asymmetric catalysis
ln(e.r) = (ΔΔH‡/R)(1/T) – ΔΔS‡/R ΔΔH‡ = ΔH‡minor - ΔH‡major ΔΔS‡ = ΔS‡minor - ΔH‡major
Biggest change in selectivity with temperature when ΔΔH‡ dominates. Note with 2e, ee decrease with decreasing T
Jacobsen, JACS, 1998, 948.
Ready; Catalysis Kinetics
Practice problem: oxidative addition of ArX to Pd(0). Hartwig, JACS, 2005, 6944
Kinetics studied for ArCl, ArBr and ArI Your job: derive rate laws for each path; determine which one(s) is(are) consistent with data.
w/ PhI
w/ PhBr: rate = [ArBr]0[L]0 Small ΔS‡; same rate with sub. ArBr’s
w/ArCl
‘Lineweaver-Burk Plot’
17
Ready; Catalysis Kinetics
Hartwig, Science, 307, 2005, 1082
Data: Rxn with ND3 showed no D incorporation into ligand
Determine the mechanism for oxidative addition of ammonia to Ir(I) olefin complex