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Richard M. Noyes University
of Oregon Eugene
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A Course in Kinetics Based on Elementary Processes
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hem~calkinetics is of importance as a scientific discipline primarily because kinetic data are of major importance in elucidating the detailed mechanisms of chemical reactions and other molecular processes. These mechanisms are often fairly complex, hut they are generally described in terms of elementaq processes that are unimolecular, bimolecular, or (occasionally) termolecular and that take place in single steps. During the past few years, I have been teaching a course on Emetics in solution, giving three lectures a week during the ten weeks of the spring term. The students are mostly seniors and first year graduate students who have had physical chemistry. The course has been aimed a t giving the students an understanding of present theories of chemical reactions and of how exoerimental observations can be used to obtain information of mechanistic utility. The understanding of elementary processes has seemed to offer the best foundation on which to build the subsequent details. The course first considers the theoretical treatment of elementary processes and the ways in which rates of these processes are affected by altering such facton as temperature, pressure, solvent, etc. This detailed discussion of elementary processes provides a foundation for the subsequent consideration of the rates to be anticipated when reactions take place by complex combinations of such processes. The treatment is aided by keeping attention iixed on the instantaneous rate of reaction under specified conditions rather than considering integrated extents of reaction. Although integrated rate equations for simple empirical orders often play a considerable part in the teaching of kinetics, they are applicable to a fairly limited number of real reactions and give a rather restricted idea of the problems encountered by a practicing kineticist. The course then leaves consideration of what the rate of reaction will he for different mechanisms and considers the reverse problem of gathering kinetic data and using them to draw mechanistic inferences. Although this arrangement delays consideration of the type of material with which an experimental kmeticist actually deals, it provides a background that permits a more thorough discussion than is possible if treatment of data is introduced before the students appreciate the mechanistic complexities that can arise in practice. The following outline does not develop the treatment in detail, but it will illustrate a few points and provide an idea of the type of argument. It is hoped that a Presented 8s part of the S p p m i u m on Kinetics in the Undergraduate Currioulum before the Division of Chemical Education Los at the 144th Meeting the American Chenlieal Angeles, California,April, 1963.
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book covering this material will be ready for publication in the not too distant future. Introduction ond Definitions
A chemical reaction can be represented by the balanced equation aA+bB-eC+dD
(1)
where the capital letters are chemical species and the lower case letters are stoichiometric coefficients. The rate of reaction, v, is defined to refer to the equation as written. Thus, for equation (1)
For some reactions, the rate can he described over a range of concentrations by an equation of the form where the exponents are empirical orders that may be positive, negative, zero, integral, or non-integral and may or may not bear any relation to the stoichiometric coefficients of equation (1). The species P in equation 3 does not enter equation (1) at all. The experimental rate constant, ice,, is an empirical quantity to be distinguished from the rate constants of elementary processes that are inferred from experimental data by assuming a mechanism for the overall process. Any experimental rate constant should always refer to the v for a specified chemical equation like (1) and not to a multiple or fraction of that v. Failure of some polymer chemists to relate termination rate constants to the rates of the assumed elementary processes has seriously confused the literature of radical polymerization. Theoreticol Treatment o f Elementary Processes
Collisional theories assuming equilibrium distributions. The usual kinetic equations can be derived from equilibrium radial distribution functions and rates of relative motion of molecules. The treatment can he extended to the situation in which the energy of several equilibrium energy states provide a basis for deriving the equations originally developed by Glasstone, Laidler and Eyring (Ij. Theories for very fast reactions. Both collisional and statistical thermodynamic treatments assume that distributions of molecules in space satisfy functions derived for eauilibrium. These assumutions fail for very reactive species in solution. The treatment employed has heen developed elsewhere (2). If thecourse were not specifically restricted t o solution kinetics, it might be appropriate a t this point to discuss unimolec-
ular gas reactions in which the equilibrium populations of internal energy levels are not maintained. Effects of Confrolloble Focfors on Rates of Elementory Processes
Concentration. Rates in ideal solutions can be treated easily. Statistical thermodynamic theories can be used to derive the equation where ko is the rate constant in ideal solution and the 7's are activity coefficients if species A and B r&ct to form a transition state. Temperature. Standard equations are easily derivable for activation energy and related quantities. Pressure. Volume of activation is defined and discussed. Inert electrolyte. Debye-Hiickel expressions for activity coefficientsare used to predict effectsof changes in ionic strength on rates of elementary processes involving ions. Dielectric constant. Easily deiivable equations predict effects of varying dielectric constant on ion-ion and dipoledipole reactions. Students are warned that dielectric saturation effects make these equations of marginal value if macroscopic dielectric constants are employed. They are also warned against the dangers of using these equations to interpret effects when dielectric constants are changed by varying the relative amounts of solvent components. Viscosity. This property has direct influence only on the rates of reactions so fast that equilibrium spatial distributions are not maintained. Other solvent effects. Solvent media influende rates in many ways that are not yet satisfactorily characterized. Attempts have been made to define properties like nucleophilicity, ionizing power, etc. that have been proposed to characterize solvents. Isotopic substitution. Rate of reaction may be affected by isotopic substitution of a species that is transferred during the elementary process. Usually smaller effects follow substitution elsewhere in the reactant or in the solvent. Rigorous treatment requires detailed understanding of molecular vibrations. Molecular Structure. The subject is too broad for general treatment. The brief discussion in this course includes effects of substituents on rates of reactions in aromatic systems. Kinetics of Consecutive Processes
A consecutive process is defined to be of the form
Steps are said to be locally equilibrated when their forward and reverse rates are almost equal and to he irreversible when the reverse rate is negligible compared to the forward rate. A step pre-determines subsequent steps if those steps are virtually sure to follow the occurrence of the pre-determining step. Conditions are then developed for application of the rate-determining step approximation and of the uniform flux sequence of Christiansen (3). When neither approximation is applicable, the reaction can sometimes be separated into sequences for which these approximations are valid. The argument is presented in detail in a forthcoming paper (4). Kinetics of Parallel Processes
Parallel processes provide different mechanisms by which the same reactants can go to the same products. A typical example is the oxidation of oxalate ion by manganese(II1); transition states having empirical formulas MnC20*+, Mn(CpOa)z-, and Mn(C20,)P can all contribute to the reaction. The total rate in such a system is the sum of the rates due to the individual parallel processes. Kinetics of Competitive Processes
Competitive processes occur when the same species may react in two or more different ways giving different products. Competition may be for different positions in the same molecule as in reactions of substituted benzene derivatives, it may involve two species attacking the same initial reactant so that the rate of disappearance of the reactant is the sum of the rates of the two reactions, or it may involve competition for an unstable intermediate so that changing concentrations of competing reagents affect the final composition of the products but not the overall rate of reaction. The discussion of competitive processes provides a good point for presenting the distinction between k'metic and thermodynamic control of reaction product composition. Kinetics of Repetitive Processes
Repetitive processes are those in which a n intermediate can undergo a sequence in which the intermediate is regenerated. This sequence is usually in competition with some other reaction that consumes the intermedintc. llnny examples in\wlve free mdic:~lvl.ains. Topics di.,cusuml it~cludcelTcctsot~the overdll kinrtir-: from change in radicals undergoing termination and competition of termination reactions that are first and second order in radicals. Branched chain reactions are discussed briefly. Kinetics of Catalytic Processes
where A and the R's are reactants, Q and the P's are products, and the 1's are intermediates. The species A, Q, and each of the 1's must be chemically distinct from each other and from all of the other species in these equations. If any species occurs as both R and P, it does so only once for each.
I n principle, catalytic processes usually belong in the class of consecutive processes already considered. They offer the interesting kinetic feature that some species that appeam as both R and P i n equation (5) is usually in much smaller concentration than are the chief reacting species. The discussion offers examples, distinguishes specific and general acid catalysis, and mentions a little about enzymes. Autocatalysis presents a special problem because catalyst is produced as the catalyzed reaction proceeds. Volume 40, Number 1 1 , November 1963
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Kinetics o f induced Reodions
A slow reaction having a favorable free energy change can be induced to go more rapidly by the simultaneous occurrence of another irreversible reaction in the same system. Examples discussed include some of the chemistry of chromium and manganese and the use of initiators in free radical polymerization. Kinetics of Reversible Reactions
When the final position of equilibrium involves measurable concentrations of the initial reactants, the kinetics of forward and reverse processes are related. The relationship does not permit the kinetics in one direction to be uniquely determined from the kinetics in the other, but certain conclusions can be drawn. The principle of microscopic reversibility also provides a useful touchstone for rejecting certain mechanisms that would otherwise appear plausible. Experiment01 Techniques
Conventional kinetic studies in batch systems require temperature control, measurement of time, and a precise and rapid analytical method. When the time scale gets shorter than a few seconds, techniques can involve mixing in continuous flow, stopped flow, or stirred reactors. When the times of interest become too short even for mixing techniques, a system initially a t equilibrium can he perturbed by a periodic method such as ultrasonic sound absorption or by a discontinuous change such as temperature jump or flash photolysis (5). Mothemoticol Treatment of Data
Since most experimental techniques measure concentrations at specific times, and since rate of reaction is a derivative quantity, many mathematical treatments involve integration of rate equations for comparison with experiment. Other techniques involve getting derivatives of continuous curves approximating experimental observations. Some specific methods have also been developed. Mechanistic lnterpretotion of Kinetic Data
Information from concentration dependence. If all subsidiary equilibria are known and if a single rate
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determining step exists, the concentration dependence can be used to determine the empirical formula of the transition state for that step. Separate terms in the numerator of the rate expression and increase of apparent order with increasing concentration of reactant indicate parallel mechanistic paths for obtaining product. Separate terms in the denominator and decrease of apparent order with increasing concentration of reactant indicate contributions from consecutive steps or unidentified intermediates formed in significant concentration. Fractional orders frequently but not invariably accompany radical chain processes. Much of modern kinetic work is concerned with demonstrating the existence of intermediates and determining their properties. Although unequivocal evidence for an intermediate can often be obtained by some competitive technique, lack of evidence can only shorten the permissible lifetime of the intermediate but cannot prove its non-existence. Information from temperature dependence. Activation energies and similar quantities can ofteh be combined with thermochemical information such as bond energies to draw useful mechanistic conclusions. Information from other factors. Many factors such as pressure, ionic strength, dielectric constant, etc. have been shown above to influence rates of elementary processes. When the rate of a real process is found to be influenced by these factors, mechanistic inferences can often be drawn. They must be drawn carefully as illustrated by the fact that different investigators have reported (apparently correctly in each case) that increasing ionic strength strongly accelerates, strongly decelerates, or scarcely affects the rate of decomposition of oxalate complexes of manganese(II1) (6). Literature Cited
(1) GMSSTONE, S., LAIDLER, K. J., AND EYEING,H., "The Theory of Rat&Processes," MeGraw-Hill Book Co., New York, 1 9 4 1 , ~185ff. . R. M., Prog. Reaetion Kinetics, 1,129 (1961). (2) NOYES, J. A., Z. ph&. Chem., 288,303 (1935). (3) CBRISTIANSEN, R. M., P~og.Reation Kinetics, 2 , (in pms). (4) NOYES, (5) EIGEN,M., "Technique of Organic Chemistry, Vol. VIII, Part 11, 2nd ed., Investigation of Rates and M e c h a ~ s m ~ of Reactions, Very Fast Reactions in Solution,'' edited by S. L. FKIESS,E. S. LEWIS,AND A. WEISSBERGER, Interscience Publishers, New I'ork, 1963, p. 895ff. J. M., A N D NOYES, R. M.. J . Am. Cham.. Soc.. 74. (6) MALCOLM, 2769 (1952).
