Download Kinetics in the Study of Organic Reaction Mechanisms

California Association of Chemistry Teachers
Robert H. DeWolfe
University of California
at Santo Barbara
Goleta, California
Kinetics in the Study of
Organic Reaction Mechanisms
Since the emergence of chemistry as
a modern experimental science, chemists have become
increasingly interested in the detailed manner in which
chemical transformations occur. That is, chemistry
is concerned with the mechanisms of reactions as
well as with a knowledge of their starting materials
and products.
There are a number of reasons for this preoccupation
with reaction mechanisms. A knowledge of mechanisms aids the synthetic chemist in predicting byproducts and improving reaction conditions, helps
the analytical chemist in choosing optimum conditions
for analytical procedures, and provides a powerful
tool for the biochemist studying the chemical basis
of physiological processes. Reaction mechanisms also
provide a systematic basis, exploited particularly
by organic chemisbs, for classifying chemical reactions
and predicting chemical properties.
The increasingly important role of mechanisms in
organic chemistry is attested to by the number of
excellent textbooks and monographs dealing with
organic reaction mechanisms (1-5, 6-9). Since the
following discussion is concerned only with the rationale of mechanisms studies, specific examples are
omitted. References 1-9 provide an excellent guide
to the original literature dealing with the mechanisms
of specific reactions.
A chemical reaction mechanism may be thought
of as a motion picture of all of the atoms (and their
electrons) involved in the reaction, beginning before
the reacting species approach each other, picturing
their paths during the reaction, and endmg after
the products have been formed ( 1 ) . Such detailed
knowledge of the course of a react,ion can never be
attained in actual practice, and a reaction mechanism
is usually understood to mean all of the simple reactions involving molecules, radicals, and ions, that
take place simultaneously or consecutively in producing the observed over-all reaction (2).
The experimental elucidation of reaction mechanisms
poses some very thorny problems. A knowledge of
the stoichiometry of a reaction, or of the position of
an equilibrium, yields no information on how the
reaction occurs or how the equilibrium is attained.
Chemical thermodynamics, dealimg as it does with
initial and final states, tells nothing about the paths
connecting these states. Since the individual molecular
collisions and interactions comprising a mechanism
cannot be observed directly, their occurrence and
nature must be deduced from indirect evidence of
various kinds.
The most powerful tool for the experimental study
of reaction mechanisms is chemical Kinetics. Kinetics
deals with the rates at which chemical reactions occur,
and with all of the factors which influence these rates,
No reaction mechanism can be considered to be more
than a temporary working hypothesis until it is supported by kinetic data (5).
Like any other tool, chemical kinetics has certain
fundamental limitations. For those who plan to
use kinetic methods in the study of mechanisms, an
understanding of these limitations is highly desirable.
Many chemists who had only a brief introduction to
reaction Kinetics during their formal education fall
into the trap of misinterpreting (or, more commonly,
overinterpreting) kinetic data. What, then, are some
of the things that can, and cannot, be learned about
a reaction by studying its kinetics?'
Perhaps the most useful information furnished by
a kinetic study of a reaction is its rate equation. This
is an equation, derived from rate measurements, which
describes the concentration dependence of a reaction.
For a generalized reaction:
aA
bB + eC ...- products
rate = -dc~/dt = ka~'aPae".. .
(1)
+
+
where aA, a B , etc., refer to the thermodynamic activities
Since the main concern here is the strategy and limitations
of kinetic studies, detailed examples of techniques and principles
are omitted. There are a number of excellent books dealing
with the study of reaction mechanisms which may he consulted
for detailed discussions of kinetic methods (1-9). The discussion of interpretation of rate data by Bunnett (ref. 9, p. 177)
should be of particular interest to all serious students of reaction
mechanisms.
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of species A , B, etc., and C A , C R , etc. refer to their
concentrations. Often, the activities are approximately equal to the concentrations, and
1, m , and n . . .are the powers to which the activities
or concentrations must be raiscd in ordcr to describe
the experimental observations. Since many reactions
involve two or more steps, and since the slowest step
(or steps), which determines the rate of the reaction,
may not involve all of the starting materials, it is not
generally possible to deduce the rate equation from
the stoichiometric equation of the over-all reaction.
Changes in experimental conditions may alter the rate
equation, but the altered form is usually more general,
and includes the original equation as a special caseunless the changes were sufficiently drastic to cause
the reaction to proceed by a different mechanism.
The over-all order of the reaction described by
equation (1) is (1
m f n
. . .). If a reactant
(the solvent, for example) is present in large excess,
rate measurements will not establish the order of the
reaction with respect to it, and the observed order may
be smaller than the true order.
More useful in mechanisms studies than the observed
kiinetic order of a reaction is its molecularify. Molecularity is usually defined, by organic chemists, as
the number of molecules (using the term to include
ions and radicals) which undergo valency changes
in the slowest step of the r e a c t i ~ n . ~
The principal limitation of reaction kinetics in
mechanisms studies is that the experimental rate
equation cannot be depended upon to establish the
molecularity of the rate-limiting step of the reaction.
It will do so only if thcre is a single rate-limiting step
which is not preceded by rapid equilibrium steps, and
if none of the reactants in the rate-limiting reaction
are present in large excess. These conditions are not
always satisfied.
The rate equations for the unimolecular and bimolecular mechanisms of nucleophilic substitution
illustrate this point (8). The bimolecular mechanism
involves a concerted replacement of the leaving group
by the attacking nucleophile-that is, molecules of
the two reactants must collide in order for reaction
to occur:
+
+
Y:
+ R-X
-
Y-R
rat? = k[RXl [Yl
If, however, the nucleophilic reagent Y is present in
surh large excess that its concentration remains prac
tically constant during the reaction (as mould be
true if Y is a soh ent molecule), the reaction follows
first-order kinetirs:
rate = k'[RXI
The unimolecular mechanism of substitution involves preliminary ionization of R X :
I ' h \ s ~ r n l rhemirts i ~ ~ . d ~l i)c l i n vnlc,lcmlnrity :,.I t h e u u ~ n l w r
c f molecules lions, i . d i w I ~ eutr.rine; iwt) the f m u s i t i w 611t1C
of an elementary reaction, i.e., any one step in the overall
reaction.
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Journal of Chemical Education
The experimentally observed rate equation will depend
on the relative values of kz, ki, [X-I, and [Y-1. If
ki >> k2,
rate = k,[RX]
and first order kinetics are ohserved. Jf 1 1 ~<< k2,
rate = klkl(RX)(Y-)/kdX-)
In this case, if X- is present in the reaction nledi~un
in large enough amount so that (X-) remains practically constant during the reaction,
and the reaction follows second order kinetics! In
short, there is no necessary correspondence between
molecularity and observed kiinetic order.
The experimental rate equation of a reaction also
m a y establish the composition of the transition state
for the rate-limiting step of the reaction. I t fails
to do this, however, in the case of reactions not having
a single rate-determining step. When two or more
slow steps of similar rates are involved in a reaction,
complicated rate equations are usually oht,ained which
tell neither the molecularity nor the composition of
the transition state of any individual step in the mechanism. Even for reactions having a single ratedetermining step, the rate equation 15-ill not tell how
the transition state of this step was assembled, what
its structure is, or what happens after the rate-determiniing step. For example, general acid-catalyzed
reactions of a substrate S obey equa.lly well the rate
laws:
rate = k(S)(H+)F(A-),
rate = k'(S)F(HA)i
+ :X
The rate of the reaction depends on the concentrat'ions
of both R X and Y, and second-order kinetics are
usually ohserved:
'
Application of the steady-state approximation ( 2 and 6)
leads to the follo~vinggeneral rate equation for this
mechanism:
due to the fact that:
(H +)(A-) = K(HA) and
(SHt) = Kr(S)(H+)
All of these rate equations indicate t,hat the transition
state of the rate-determining step of the reaction
contains S and the components of the acid HA. (It
may also contain one or more soh-ent molecules.)
The rate equations do not tell whether the observed
reaction involves an attack by A- on SH+, a slow
proton transfer between S and HA, or some other
process which can bring together S, H+, and A- into
a transition state. Equivalent, but apparently different, rate laws for a reaction are found ~vhenever
preequilibria exist between two or more reactants,
or between reactants and catalysts (10).
In summary, the rate equat,ion may indicate the
composition of the transition state of the rate-limiting
step of a reaction. I t will not do so if one of the reactants is present in large excess, or if the reaction
does not have a single rate-limiting step. The rate
equation may also indicate the molccularity of the
reaction, but will not in cases where rapid preequilibria
are involved. Furthermore, the rate equation yields
no information on the structure of the transition state
of the rate-limiting reaction, or on the number and nature of any fast steps which precede or follow the
rate-limiting step.
1f the rate equation of a reaction cannot be relied
upon to establish either the order or the molecularity
of the reaction, and tells nothing about fast steps or
transition state structures, why bother to make the
kmetic study in the first place? The answer to this
question lies in the fact that the kinetic data exclude
all mechanisms from which the observed rate equation
cannot he derived. I n other words, the chief t~lility
of reaction kinetics i n mechanisms studies lies not in
establishing the correct mechanism, but in ruling out
all of the possible mechanisms which are ineonswtent
with the kineticdata.
I n the examples used above, it mas assumed, as
is common practice, that concentrations and activities
of reactant species are the same. This is not usually
the case, except in extremely dilute solutions or in
the gas phase at low pressures. A rigorous treatment
of the Emetics of reactions occurring in nonideal
systems requires a knowledge of the activity coefficients as well as the concentrations of reactants and
catalysts. The necessary thermodynamic data are
difficult to obtain, and are rarely available from the
literature. The exploitation of accurate activity data
in mechanistic studies of reactions in solution may
provide one of the few kinetic methods of determining
the role of the solvent in reactions (If), and should
provide a sounder theoretical basis for several empirical correlations between reaction mechanism and
the effect on reaction rates of solvent acidity, hasirity,
and ionizing power.
Much useful information regarding the mechanism
of a reaction can be obtained by studying the effects
of environmental changes on reaction rate. Changes
in reaction rate produced by changes in solvent polarity,
nucleophilicity, and ionizing power yield useful information on the role played by solvent molecules
in a reaction. The effects of solvent polarity and of
dissolved electrolytes on rates often yield information
regarding the separation and distribution of electrical
charge in the transition state of the rate-limiting step
in a reaction mechanism. Changes in rate caused
by changing the isotopic composition of the solvent
are also instructive. For example, the measurement
of rates of acid-catalyzed reactions in water and in
deuterium oxide provides a useful empirical tool for
studying the mechanism of acid catalysis (18).
Another widely used application of chemical kinetics
is the study of rate changes produced by structural
alterations in one or more of the reactants. A knowledge of the effects of such changes on reactivity and
on the rate equations of reactions is particularly useful
in the study of organic reactions. Rate variations
caused hy structural alterations in the reactants yield
information on the electronic and steric requirements
of the reaction which is ~ertinentto its mechanism
(18).
A special kmd of structural change which frequently
causes meaningful rate changes is isotopic suhstitution. For example, the effect on rate of replacing
hydrogen by deuterium a t or near t,he reaction site
in an organic molecule affords valuable information
on the mechanism of the reaction and on the structure
of the transition state (14).
One of the most important, and least exploited
factors determining reaction rat,e is temperature.
Most reactions are found to obey the .4rrhenius equation,
k = Ae-&/HT
quite well over limited temperature ranges. (A is
the "preexponential fartor," and Eo is the activat,ion
energy of the reaction.) It is easy to evaluate A
and En Cram experimental raate data. These quantities-and the enthalpy (AH*), entropy (AS*), and
free energy ( A F * ) of artivation, derived from them
by application of the transition state theory of chemical
kinetics (/?-are ext,remely useful in mechanisms
studies. They oftcn indicate whether a reaction is
unimolecular, himolecular, or intramolecular, and
frequently give hints on how the transition state is
assembled. The observed values of E,, and A are
often compatible with some of the possihle mechanisms
suggested by the rate equation, and incompatible with
other mechanisms. Also, a sharp departure from
linearity in the Arrhenius plot of log li versus l / T is
good evidence that a reartion involves two competing
mechanisms.
The effects of cat,alysts and inhibit,ors on reaction
rates are of fundamental importanre in mechanisms
studies. A knowledge of the kinds of things which
catalyze or inhibit a react,ion usually enables one to
decide whether the reaction proceeds by a radical or
a heterolytic mechanism. The influenre of light and
of solid surfaces on the rat,e of a react.ion is also pertinent to its mechanism. The detailed nature of
the catalysis is also important. For example, whether
a reaction is general or specific acid catalyzed tells
something about the proton transfers responsible for
the catalysis, and the way in which the rat,c of an
acid catalyzed reaction varies with solvent aridity
gives import,ant hints on the nature of t,he rate-determining step of the reaction (16).
And finally, measurement of the variation of reaction
rate with pressure a t high pressures is becoming a
useful tool in the study of reactions taking place in
solution. The volume of act,ivation of a reaction
occurring in the liquid phase yields information about
the structure of its transition state, and hence about
its mechanism (16).
There are, of course, many kinds of information other
t,han rate data which are useful in the study of mechanisms. Physical measurements involving absorption
spect,roscopy,nuclear magnetic resonanre spectroscopy
( l 7 ) , electron paramagnetic resonance spectroscopy,
and cryoscopy have been valuabk in establishing t,he
existence and structures of reartive intermediates
(18). Isotopic labeling often makes it possihle to
determine the role of individual atoms in reactions,
and has been extensively used in establishing the
positions of bond cleavages (19). Isotopic exchange
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experiments have served to establish the existence of
several reactive intermediates (go). A knowledge
of the structures of all of the products of a reaction,
and of its stereochemistry, frequently supports some
mechanisms and eliminates others from consideration.
Competition and crossover experiments may furnish
valuable mechanistic clues.
It is fairly easy, after a little practice, to derive a
rate equation from a postulated reaction mechanism,
and to predict the effects of structural and environmental changes on the reaction rate which should be
observed if the mechanism is correct. Comparison
of these predictions with experimental observations
is a necessary step in checkmg the reasonableness of
a proposed mechanism. The reverse of this process,
arriving a t a reasonable mechanism consistent with
all of the experimental facts, is more difficult. Skill
a t this kmd of indurtive reasoning requires intuition,
imagination, and chemical sophistication.
Chemists-partirularly organic chemists-frequently
publish reaction mechanisms without offering evidence
to support them. Speculation is fun, and serves the
purpose of stimulating thought and suggesting new
experimentation. But it should always be recognized
for what it is. The minimum evidence required to
give credibility to a mechanism in most cases is the
stoichiometric equation of the reaction, its rate equation, and its energy and entropy of activation. The
more kinetic and non-kietic data the mechanism
accounts for, the greater the probability that it is
essentially correct.
Mechanisms-like other scientific hypotheses-are
extremely useful even though inherently unprovable.
As Hammett pointed out (6), "A mechanism . . . . is
a scientific tool by which to obtain verifiable relationships between measurable quantities; it is to he
judged by its utility in correlating known facts and
predicting new ones, not by its agreement with some
absolute, unknowable truth."
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Journal o f Chemical Education
Acknowledgment
The author is grateful to Dr. G. 0.Pritchard for helpful criticisms of an earlier version of this article.
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