Lalic, G.
Chem 530A
Chemistry 530A
Advanced Organic Chemistry
Lecture notes 10
Kinetics: A Practical Approach
Simple Kinetics Scenarios
Fitting Experimental Data
Using Kinetics to Determine the Mechanism
Dougherty, D. A., "Modern Physical Organic Chemistry", Chapter 7
p. 374-397.
Reaction Kinetics as a Tool in Studies Of Reaction Mechanism
Reaction Kinetics and Reaction Mechanism
The mechanism of the reaction tells us how the starting materials are
transformed into products. Ideally, we would like to know the energies of all the
SM, P, Intermediates, and all transition states (i.e. the full energy diagram).
Often we settle for less and we try to distinguish between several reasonable
general hypotheses.
The ultimate goal of kinetics experiments is to derive a rate law which gives
a quantitative relationship between the concentrations of the starting
materials and the rate of the reaction. That means that we know quite a bit
about the mechanism of the reaction.
We experimentaly observe the changes in concentrations of reactants,
intermediates, and/or products over time and try to fit the data to theoretical
rate laws that correspond to our mechanistic hypotheses. We also try to
determine kinetic order of reactants and the overall kinetic order of the reaction
which can be very helpful in discrediting wrong hypotheses.
Simple Kinetics Scenarios
First order kinetics:
A
P
d[P]/dt = -d[A]/dt = k[A]
-d[A]/dt = k[A] rate law
ln[A] = ln[A]0 - kt integrated rate law
[A] = [A]0e-kt integrated rate law
Second order kinetics: 2A
reaction is second order in A
P
-d[A]/dt = k[A]2 rate law
1/[A] = kt + 1/[A]0 integrated rate law
A+B
P
-d[A]/dt = k[A][B] rate law
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-d[A]/dt = k[A][B] becomes d[P]/dt = -d[A]/dt = k1[B]
k1 = k[A]
Reaction becomes pseudo-first order. Behaves like it is 1st order, but it is not.
We use large excess of A relative to B, so [A] does not change during the
course of the reaction. This removes [A] for the overall order of the reaction.
As a reasult, we can isolate [B] and determine the order in B more easily.
Even when dealing with complicated reactions, we can isolate the influence
that the change in the concentration of one of the reagents has on the rate of
the reaction by making the starting concentration of all the other substrates
large relative to the substrate we are isolating, We usually need a 10 fold
excess of other substrates.
n-th order kinetics:
nA
P
-d[A]/dt = k[A]n rate law
1/(n-1)(1/[A]n-1-1/[A]0n-1) = kt integrated rate law
Ideal picture looks like this (except for 0 order reactions):
relative concentration
Lalic G.
[P]
1.0
A+B
P
0.5
[SM]
0
0 t1/2
5xt1/2
10xt1/2
t
Monitoring concentration changes over time:
Every kinetics experiment requires monitoring the change in the concentration
of the starting materials, products, and/or intermediates with time.
[1/([B]0 - [A]0)]ln([A]0[B]/[B]0[A]) = kt integrated rate law
[B]0 = [A]0 goes to 1/[A] = kt + 1/[A]0
Pseudo-f irst order kinetics: A+B
P
What if, in a reaction of second order, [A] does not change during the
course of the reaction?
In Situ method: Concentration of relevant species is determined in situ,
usually by NMR (reaction performed in an NMR tube) or IR (IR probe inside
the reaction flask).
Sampling method: Taking samples from the reaction mixture at different time
points and determining concentrations of relevant species by an appropriate
analytical technique (NMR, GC,HPLC, MS etc.).
Initial and "Total" Kinetics Experiments
Initial rate measurements
relative concentration
In the first 5 to 10% conversion, we can assume that the rate is constant
because concentrations of reactants do not change significantly. As a result,
we obtain a linear plot (relative concentration vs. time). The slope of this plot
gives as the rate of the reaction.
We monitor the concentrations of relevant species throughout the course
of the rection. In pricinple, a single measurement does allow us to
determine the overall order or the order in a reagent.
0.1
-d[SM]/dt = d[P]/dt = rate
0.05
Slope = rate of the reaction
[P]
1.0
0.5
0
[SM]
0
0 t1/2
t
A single measurement of initial rate does not allow us to determine the overall
kinetic order of the reaction or the kinetic order in any of the reagents.
If we repeat the experiment and systematically change [SM] under pseudofirst order conditions we can obtaine the order in SM.
rate
The shape gives us the order.
Flat line is 0, sloped line is a
first order, parabole is second
order and so on.
first order
zero order
Chem 530A
"Total kinetics"
relative concentration
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Notice that every data point is
a separate experiment in which
we monitored change in [SM]
and/or [P] over time.
[A]0
Initial rate kinetics:
Allows us to make certain simplifications because changes in
concentrations are small.
Good for monitoring slow reactions.
We assume that the first 5% of the reaction are representative of
the whole reaction!
5xt1
10xt1/2
t
/2
To obtain information about the reaction's rate law, we fit the experimental
data to the theoretical rate law in the integrated form. There are several
methods to fit the experimental data.
reaction
integrated rate law
A
P
rate
law
k[A]
2A
P
k[A]2
1/[A] = kt + 1/[A]0
k[A][
B]
[1/([B]0 - [A]0)]ln([A]0[B]/[B]0[A]) = kt
[B]0 = [A]0 goes to 1/[A] = kt + 1/[A]0
k[A]n
1/(n-1)(1/[A]n-1-1/[A]0n-1) = kt
A+B
nA
P
P
ln([A]/[A]0) = -kt
Direct fit:
The experimental data are fitted directly to the integrated rate law in
the form of [A] = f(t). Often, fit will be good for multiple rate laws and it
is hard to establish which one fits the best, but worth trying.
Mechanisms of Complex Organic Reactions
Lalic G.
Kinetics
Consider the following transformation. What can we learn about the
mechanism of this reaction from kinetics experiments?
Br
+
CN
CN
+
Predictions
Br
Hypotheses:
SN2
Br
+
CN
k1
k1
+
k-1
CN
+
rate law
rate = k1[RBr][CN]
SN1
rate law
rate = k2[R+][CN]
[R+] hard to determine
This approximation allows us to get a rate law independant of [R+]
d[R+]/dt = 0
CN
k2
Br
The net rate of the formation of I is assumed to be negligible.
Br
CN
+
k1[RBr] = k2[R+][CN] + k-1[R+][Br]
[R+] = k1[RBr]/(k2[CN] + k-1[Br])
Br
SN1
Reaction diagrams of complex reactions
SN2
SN2
steady state approximation (SSA)
Br
SN1
Chem 530A
rate law
SSA works often, because common intermediates are often unstable and an
appreciable concentration of intermediates rarely accumulated.
Single step. Elementary reaction.
If SSA is valid for a system then -d[SM]/dt = d[P]/dt.
TS
case 1:
E
under normal reaction conditions [CN] ~ [Br] during
most of the reaction.
k2 > k-1
k2[CN] >> k-1[Br]
RBr
SN1 Two-step processes with two transition states. Assuming that we know
relative stabilities of all species involved, there are two scenarios:
E
E
k-1 > k2
I
RBr
RCN
This situation is discribed in the first reaction diagram. In this scenario, the
first step determines the rate of the overall reaction and we call this step
the rate determining step.
In general, the rate determining step is the step associated with the
highest energy transition state. Not the one with the highest activation
energy! This also means that this step is the first irreversible step.
However read the paper!!!!!!!
No k2, [CN]
or [Br] in
the rate law
I
RBr
rate = k1[RBr]
Intuitive picture: every time the cation is formed, it is trapped by CN,
and it never has a chance to get back to bromide.
RCN
k2 > k-1
rate = k2k1[RBr][CN]/(k2[CN] + k-1[Br])
RCN
Using kinetics experiments we cannot obtain information
about the parts of the reaction mechanism that take place after
the rate determining step.
Lalic G.
Chem 530A
case 2: k2 ~ k-1
rate = k2k1[RBr][CN]/(k2[CN] + k-1[Br])
By changing the [CN]0 and [Br]0, we can change the rate law. At the high
enough [CN]0/[Br]0 ratio, the rate law will become k1[RBr].
saturated in CN
R
Rmax = k1[RBr] kmax = k1
Rinitial = k2k1[RBr][CN]/(k2[CN] + k-1[Br])
Initial rate
measurements
In the first 5 to 10% conversion, we can assume that the rate will be constant
because the concentrations of RBr and CN will not change significantly. At the
same time, [CN] is going to be much higher than [Br], and k2[CN] >> k-1[Br] is
likely to hold.
0.1
-d[SM]/dt = d[P]/dt = rate
kinitial = k2k1[CN]/(k2[CN] + k-1[Br])
If [CN] and [Br] are constant, for
example, when [CN]0 and [Br]0 large:
kinitial = k1(1/(1+k-1[Br]/k2[CN]))
Rmax
[CN]0
k-1[Br]/k2[CN] will always be positive so
kinitial < k1
This is an example of saturation kinetics = reaching the [reactant] at
which rate becomes independant of the [ractant]. That usually means that we
changed the rate determining step.
Does this mean that the reaction diagram changes as we change the
concentration of the reactants? NO! The diagram deals only with rate
constants and not with k2[CN] and k-1[Br]. In discussing the reaction
diagrams and rate determining steps, we assume that the concentrations of
species involved are similar.
case 3: What does the rate law simplify to if k-1[Br] >> k2[CN]?
Experiments
Slope = rate of the reaction
0.05
0
t
0
Remember, a single measurement of initial rate does not allow us to determine
the overall kinetic order of the reaction or the kinetic order in any of the reagents.
Then we vary [CN]0 while keeping [RBr]0 the same.
SN1
rate = k1[RBr]0
rate/[RBr]0 = k1 = kobs
kobs not a function of [CN]0
SN2
rate =k1[RBr]0[CN]0
rate/[RBr]0 = k1[CN]0 = kobs
kobs is a function of [CN]0
kobs (1/s)
SN2
Slope is the order of
the reaction in CN.
Several reasonable choices that would allow us to distinguish between
SN1 and SN2.
Overall kinetic order of the reaction
SN1
Kinetic order in CN
Kinetic order in Br
The choice of our experiments depends on our intuition and practical
considirations.
A reasonable start would be to use 1 equivalent of RBr and 1 equivalent of CN.
[CN]0
Order between zero and one would indicate the SN1 mechanism operating
under non-saturation conditions, or that both mechanisms are operational.
Competition Experiments
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"Total kinetics"
Could we use these reactions under these conditions to determine the relative
rates of reactions of these two nucleophiles with a carbocation?
We can do the experiment with [CN] ~ [RBr]. We can fit the data obtained
under these conditions using Van't Hoff's method and, with a little bit of
luck, in a single experiment, we can obtain the overall order of the
reaction. If Van't Hoff's plot indicates that the reaction is first order, it is
likely SN1 in a saturation regime. If the plot indicates the second order,
than the reaction is likely SN2. Something in between would indicate that
we are in non-saturation regime or that both mechanism are operational.
An experiment with high [CN] relative to [RBr] so that the reaction is pseudofirst order. Besides, this maximizes the probability that the reaction operates in
the saturation regime.
SN2
Br
k1
k -1
CN
k 2CN
CN
Br +
N3
N3
The observed ratio of the two products (product distribution) is a direct
reflection of k 2CN/k 2N3
rate/[RBr]0 = k 1 = k obs
k obs not a function of [CN]0
rate =k 1[RBr]0[CN]0
What if we did the same experiment but added both nucleophiles at the
same time? (same conc. of nucleophiles simplifies the math, but it is not
necessary)
k 2N3
By using Van't Hoff's method, we can obtain order in RBr from a single
measurement. By doing experiments with different [CN]0, we can obtain
kobs vs. [CN]0 plot that will give us order in CN.
rate = k 1[RBr]0
The rate determining step obscures the kinetics of all subsequent steps.
SN1
If we want more inf ormation we can do the f ollowing:
SN1
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rate determining step
rate/[RBr]0 = k 1[CN]0 = k obs
k obs is a function of [CN]0
product determining step
Competition experiments
Br
+
CN
Br
+
N3
kobsCN
kobsN3
CN
+
Br
N3
+
Br
RCN
If we did kinetics experiments with the same [RBr] in the saturation
regime with N3- and CN- as nucleophiles, would the rates differ?
SN1
Br
k1
k -1
+
Br
Nu
k2
-d[RBr]/dt = rate = k 2k 1[RBr][Nu]/(k 2[Nu] + k -1[Br])
k 2[Nu] >> k -1[Br]
rate = k1[RBr]
Nu
RN3
RBr
+
Br
The rate of the reaction is determined by rates of all the steps prior to and
including the rate determining step, i.e., by all the steps that contribute to the
rate law.
The product distribution is determined by the relative rates of product
determining step(s).
Competition experiments allow us to gain insight into the product determining
steps regardless of their position relative to the rate determining step.