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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 / 95 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. 96 / 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 Volume 40, Number 2, February 1963 / 97 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." 98 / 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. Literature Cited (1) GOULD,E. S., "Mechanism and Structure in Organic Chemistry," Henry Holt and Co., New York, 1959, p. 127. R. G., "Kinetics and Mecha(2) FROST,A. A,, AND PEARBON, nism." 2nd ed., John Wilev and Sans, Inc., New York. 1961, p. 2. (3) LIVINGSTON,R., "Technique of Organic Chemistry," Weissberger, A,, Editor, Interscience Publishers, Ine., New Yark, 1953, 1st ed. vol. 8, p. 208. R. G., "Mechanisms of Inorganic (4) Basow, F., AND PEARSON, Reactions," John Wiley and Sons, h e . , New York, 1958. S. W., "The Foundations of Chemical Kinetics," (5) BENSON, McGraw-Hill Book Co., Inc., New York, 1960. L. P., " P h y k d Organic Chemistry," McGraw(6) HAMMETT, Hill Book Co., Inc., New York, 1940. (7) HINE, J., "Physical Organic Chemistry," McGrew-Hill Book Co., Inc., New Yark, 1956. (8) INGOLD, C. K., "Structure and Mechanism in Organic Chemistry," Cornell University Press, Itham, New York, 1053 (9) WEISSBERGER, A,, edit.," Technique of Organic Chemistry," 2nd ed. Interscience Publishers, Inc., New York, 1961, vol. 8. H., J. CHEM.EDUC., 36,451 (1959). (10) TAUBE, J. F.. J. Am. Chem. Soc... 83.4956(1961) 111) , , BUNNETT. . (12) LONG,F. A,, A N D BIGELEISEN, J., Trans. Paraday Soe., 55, 2077 (1959). (13) TAFT, R. W., "Steric Effects in Organic Chemistry," Newman, M. S., edit., John Wiley and Sonu, Inc., New York, 1956, p. 558. K. B., Chem. rev.^., 55,713 (1955). (14) WIBERG, (15) I,ON(I,F. A., ANDPAuL,M. A,, Chem. Reus., 57,942(1957). (16) O s a o ~A. ~ ,R., AND WHALLEY, E., Can. J . Chem., 39, 1094 (1961). J. D., J . Chem. Educ., 37,581 (1961). (17) ROBERTS, (18) LEFFLER,J. E., "The Reactive Intermediates of Organic Chemistry," Interscience Publishers, Inc., New Yark, 1956. D. A,, A N D ROBERTS,J. D., J . Chem.Educ., 33, (19) SEMENOW, 2(1956). R. J.. AND TOBEY, (20) BENDER,M. L., MATSUI,H., THOMAS, S. W., J . Am. Chem. Soe., 83, 4193 (1981).