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]
1st step: measure change in
concentration over time under known
conditions.
1.2
Concentration
1
Common techniques:
GC
UV/Vis
NMR
IR
HPLC
0.8
[EtI]
0.6
[EtCN]
0.4
0.2
0
0
2
4
6
8
10
Time
Note: data for EtCN are hypothetical
An aside on reaction deceleration
Crude Data
[EtI] = [NaCN]
1
0.9
0.8
Concentration
0.7
0.6
0.5
[EtCN]
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
Time
6
7
8
9
10
1
Ready; Catalysis
Kinetics-2
Data can be plotted to determine reaction s overall order:
Crude Data (0th Order)
[EtI] = [NaCN]
0th: -d[A]/dt = k à [A] = kt
1.2
1
1st: -d[A]/dt = k[A] à [A] = exp(kt)
ln[A] = kt
Concentration
0.8
0.6
[EtI]
[EtCN]
0.4
2nd: -d[A]/dt = k[A]2 à 1/[A] = kt
(also for k[A][B] if [A] = [B]
R2 = 0.6539
0.2
0
0
2
4
6
8
10
-0.2
Time
2nd order plot
[EtI] = [NaCN]
1st order plot
0
0
2
4
6
8
12
10
-0.5
10
-1
8
1/[EtI]
-1.5
6
4
-2
R2 = 0.9507
-2.5
2
0
-3
0
time
2
4
6
8
10
Time
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
1
0.9
0.8
0.7
[NaCN]=10
0.6
[NaCN]=25
[EtI]
Ln[EtI]
2
R =1
0.5
[NaCN]=50
[NaCN]=100
0.4
[NaCN]=200
0.3
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
time
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]
2
Ready; Catalysis
Kinetics-4
Pseudo-first Order
[NaCN]>>[EtI]=1
Pseudo-first Order
[NaCN]>>[EtI]=1
0
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.9
-0.5
0.8
0.7
[NaCN]=10
0.6
0.4
[NaCN]=200
[NaCN]=25
Ln[EtI]
[NaCN]=100
[NaCN]=50
[NaCN]=100
-1.5
[NaCN]=200
0.3
0.2
y = -24.362x - 0.0073
-2
y = -49.363x - 0.0036
0.1
0
0.05
0.1
0.15
0.2
0.25
y = -9.3583x - 0.0187
y = -199.36x - 0.0009
y = -99.363x - 0.0018
-2.5
0
0.3
time
time
Plot slope v [NaCN]
Replot data in 1st order coordinates
Slope of line = kobs
Pseudo First-Order
250
200
kobs
150
1st
Rxn is
order in NaCN!!
But…is 10-200 equiv NaCN really
representative??
100
50
0
0
50
100
150
200
250
[NaCN]
Ready; Catalysis
Kinetics-5
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%)
Initial Rates
[EtI]=1
zoom in
1
0.9
0.8
0.7
[NaCN]=0.5
0.6
[EtI]
[EtI]
[NaCN]=50
[NaCN]=10
-1
[NaCN]=25
0.5
[NaCN]=1.1
0.5
[NaCN]=2
[NaCN]=4
0.4
[NaCN]=8
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
time
3
Ready; Catalysis
Kinetics-6
Initial Rates
[NaCN]~[EtI]=1
zoom in
Initial Rates
1st 10%
1
1
0.9
0.99
0.8
0.98
0.7
0.5
[NaCN]=2
[NaCN]=4
0.4
0.3
0.93
0.2
0.92
0.1
2
3
4
5
6
[NaCN]=2
[NaCN]=4
[NaCN]=8
y = -0.9854x + 0.9978
0.91
y = -7.5017x + 0.9987
0.9
0
0.04
y0.02
= -3.7244x + 0.9986
0
1
[NaCN]=1.1
0.95
0.94
[NaCN]=8
0
[NaCN]=0.5
0.96
[NaCN]=1.1
[EtI]
[EtI]
y = -0.4553x + 0.9989
R2 = 0.9997
0.97
[NaCN]=0.5
0.6
7
time
y = -1.8356x + 0.9983
0.06
0.08
0.1
0.12
time
Notes
Need more data points/time for initial rate
Order by Initial Rates
8
7
6
Data looks pretty linear for first 10%
y = 0.9x - 0.0
R2 = 1.0
Slope of best-fit line is kobs
4
3
Kobs = k[NaCN][EtI] and [EtI] was constant
2
1
Again, the rxn is first order in [NaCN]
But…we ignored 90% of the reaction.
0
0
1
2
3
4
5
6
7
8
9
[NaCN]
Ready; Catalysis
Kinetics-7
Case Study 1: Bergman, JACS, 1981, 7028
O
Migratory insertion
PR3
(OC)2Mo
(OC)3Mo
CH3
CH3
PR3
1
Confusion: Huge solvent effects on rate and (in related systems) stereochemistry
What's the mechanism??
concerted attack/migration mechanism:
O
(OC)2Mo
hypothetical curves
CO
k
(OC)2Mo
PR3
CH3
1.2
CH3
rate = k[1][PR3]
R3P
1
pre-migration mechanism
0.8
rate
k(obd)
5
O
pre-migration
concerted attack
0.6
(OC)2Mo
0.4
CO
k1
CH3
k-1
0
2
4
6
[p]
8
10
12
rate =
CH3
R3P
0.2
0
(OC)2Mo
k1k2[1][PR3]
k2[PR3] + k-1
notes: you should be able to derive
these equations.
Why not consider an associative
mechanism?
k2
O
(OC)2Mo
PR3
CH3
4
Ready; Catalysis
Kinetics-8
Case Study 1: Bergman, JACS, 1981, 7028
Rxn in THF and 3-MeTHF look like
superposition of concerted attack and premigration
Actual data
Rxn in 2,5 Me2THF only shows concerted attack.
How to explain? Solvent assistance.
O
(OC)2Mo
S
rate =
CO
k1
CH3
k-1
(OC)2Mo
CH3
S
P
R3
k2
k1k2[1][PR3][S]
k2[PR3] + k-1
but [S] is constant, so
kinetically invisible
O
(OC)2Mo
PR3
Ready; Catalysis
CH3
Kinetics-9
Case Study 1: Bergman, JACS, 1981, 7028
O
(OC)2Mo
S
rate =
CO
k1
CH3
k-1
(OC)2Mo
CH3
S
P
R3
k2
k1k2[1][PR3][S]
k2[PR3] + k-1
but [S] is constant, so
kinetically invisible
O
(OC)2Mo
PR3
CH3
Mechanism predicts 1st order dependence on THF.
Do expt in 2,5-Me2THF, add THF (note only minor
change in dipole
5
Ready; Catalysis
Kinetics-10
Case Study 2: Corey, JACS, 1996, 319
cat. OsO4-1
K3Fe(CN)6
OH
OH
96% ee
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
Proposed structure of L*OsO4
(olefin) for allyl benzoate
V=
kcatK[Os]T[olefin] ~ kcat[Os]T[olefin]
=
1 + K[olefin]
Km + [olefin]
These are saturation kinetics!!. Same
as many enzymes and Lewis-Acid
cat Rxns
6
Ready; Catalysis
Kinetics
Case Study 2: Corey, JACS, 1996, 319
Binding appears correlated to selectivity in asymmetric dihydroxylation
Poor correlation between rate and selectivity
120
100
ee
80
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Km
Ready; Catalysis
Kinetics-12
Case Study 3: Jacobsen, JACS, 1996, 10924
The reaction
The data:
7
Ready; Catalysis
Kinetics-13
Case Study 3: Jacobsen, JACS, 1996, 10924
Rate = k[(salen)Cr]2[epoxide]-1[Azide]0
Epoxide inhibits rxn!!
2 Cr s involved in RDS
N3
2
N3
HO
Azide either (a) involved
after RDS or (b) present
in ground state
Cr
O
O
O
2
HN3
N3
Ready; Catalysis
Cr O
Cr O
N3
N3 Cr
N3
Cr
Kinetics-14
Case Study 4: Jacobsen, JACS 1999, 6086 and unpublished work
The rxn:
Data:
Rate = kobs[Co]2
log log plot
2
log[initial rate]
1.5
y = 2.0577x + 3.8479
R2 = 0.9947
1
0.5
0
-2.2
-2
-1.8
-1.6
-1.4
-1.2
-1
-0.5
-1
log[Co]
V = k[A]n
log(V) = log(k[A]n) = n*log(k[A])
8
Ready; Catalysis
Kinetics-15
Case Study 4: Jacobsen, JACS 1999, 6086 and unpublished work
Epoxide Order
ArOH order
14
0.00006
12
0.00005
10
initial rate
initial rate
0.00004
8
6
4
0.00003
0.00002
2
0.00001
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
[epoxide]
0
0
0.5
1
1.5
2
2.5
3
[ArOH]
Saturation kinetics with epoxide
Ready; Catalysis
Inhibition by PhOH
Kinetics-16
Case Study 4: Jacobsen, JACS 1999, 6086 and unpublished work
OPh
2
OPh
HO
Co
O
HOPh
Kd
HOPh
2 PhOH
PhO
Co O
PhO
PhO
Co L
Co O
PhO
Co L
L = epox or PhOH
kcat
rate = kcat[Co]t2[Epox]
Kd[ArOH]+[Epox]
9
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
10
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.
The rxn
Cl
+
NiCl(PPh3)2
Ni(PPh3)4
R
R
The data
1st order in [ArCl]
non-linear inhibition by PPh3
120
80
R2 = 0.9946
75
100
kobs*104
kobs * 104
70
80
60
40
65
60
55
50
20
45
0
40
0
0.2
0.4
0.6
0.8
[ArCl]
1
1.2
1.4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
[PPh3]
11
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)3
Ni(PPh3)2 + PPh3
K < 10-6
Ni(PPh3)3 + ArCl
k1
Ni(PPh3)2 +
k2
Rate =
k' =
ArCl
(PPh3)2NiAr(X) + PPh3
(PPh3)2NiAr(X)
k1[PPh3] + k2K
[Ni]T[ArCl] = kobs[Ni]T
[PPh3]
kobs
[ArCl]
=
k1[PPh3] + k2K
[PPh3]
k'[PPh3] = k1[PPh3] + k2K
For p-Cl2Ph:
k1 = 1 x 10-4
Kk2 = 1.1 x 10-5
k2 ~ 10
plot k'[PPh3] vs. [PPh3]
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
R'
R O
1 (0.1-2 mol%), CO (850 psi),
90 oC, dioxane
O
O
R
O
R'
High yields for terminal and internal epoxides; stereospecific:
12
Ready; Catalysis
Kinetics-case study 7
Coates, JACS, 2007, 4948
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.
Ready; Catalysis
Kinetics-case study 7
R'
R O
1 (0.1-2 mol%), CO (850 psi),
90 oC, dioxane
O
R
O
R'
O
O
R
O
R'
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
Coates, JACS, 2007, 4948
13
Ready; Catalysis
Kinetics-case study 7
Resting state in presence of epoxide (no open LA sites)
Resting state,
no epoxide
Coates, JACS, 2007, 4948
Ready; Catalysis
Recall: ΔG = -RT*ln(K)
Kinetics-Van t Hoff
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
n.b. increasing temperature
decreases contribution of ΔH
Hartwig, JACS, 2006, 9306
14
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
15
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/ PhBr: rate = [ArBr]0[L]0
Small ΔS‡; same rate with sub. ArBr s
Lineweaver-Burk Plot
w/ PhI
w/ArCl
16
Ready; Catalysis
Kinetics
Hartwig, Science, 307, 2005, 1082
Determine the mechanism for oxidative addition of ammonia to Ir(I) olefin complex
Data:
Rxn with ND3 showed no D
incorporation into ligand
17