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. Volume 40, Number 2, February 1963
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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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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 ~
