Richard Wolfgang Universitv of Colorado
Boulder
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The Revolution in Elementary Kinetics and Freshman Chemistry
The last decade has seen a revolution in our understanding of the nature of elementary chemical change. The use of beam methods has made it possible to follow in detail just what occurs in a single collision that causes it t o result in reaction ( I ) . Hot atom techniques have led to the exploration of the rich new field of what happens in chemistry above threshold or activation energies ( 2 ) . Ionic reactions in the gas phase have been intensively studied and the importance of these processes for elementary kinetics in general recognized (3). Progress in the theory of both bimolecular and unimolecular processes has started to keep pace with these developments. Normally, advances in a field are first reported to the student in graduate courses. But these new developments in kinetics so fundamentally affect our most elementary conception of the nature of chemical change that they must inevitably he reflected in beginning courses in chemistry. Fortunately, this is not difficult to do. The new techniques in chemical dynamics may be technically difficult, hut they are conceptually simpler to grasp than much of kinetics that is now presented to the freshman. Studying reactions in a beam apparatus is experimentally more complex than mixing two reagents and observing a change in color. But it is easier for the student to understand what happens in a single well-defined collision in a beam apparatus than to comprehend the "ordinary" reactions which may involve several steps, each one of which involves reagents in a wide distribution of translational and internal energy states. The objection may be raised that since the modern techniaues are bevond the ca~abilitiesof the beginning student, their results shouldnot he presented & him: But this is like saying that nuclear reactions should not be mentioned in elementary physics since the student cannot he expected to build and operate a cyclotrou; that instead, he should he plunged into the incredible complexity of gaseous discharges since they are something that he himself can produce in the laboratory. The point is, of course, that the elementary student should learn first about elementary processes, even if the understanding of these comes later in the history of the science. Iinowing what happens in individual collision and decay events thus prepares the student of kinetics to understand the richness and complexity of "ordinary" chemical reactions. It is my belief that the time is ripe to deviate from the customary historical approach to elementary kinetics to one that presents concepts in a more logical order. This means some reorganization of the time-honored sequence of topics in order to give the student a fresh and larger perspective of the subject. For instance, it seems appropriate to de-emphasize the algebraic analy-
sis of rate laws as a first suhject. Rate laws can provide an enormous amount of information for the experienced lcineticist. But to the elementary student, they more frequently serve to hide this very richness. The rate law often appears to him as an end in itself: He may grasp that it could reveal that sequence of steps in a reaction, hut it frequently does not occur to him to wonder just how and why each of these steps occur. An approach based in part on modern elementary concepts should not, however, denigrate the importance of rate laws: On the contrary, it can put them in perspective as one vital technique for study of both simple and complex rate processes. The ways in which the new approach to elementary chemical dynamics can he presented are, of course, infinite in number. As an example, I will outline what has been done in a short course on chemical kinetics which I recently gave a t the University of Colorado. This was presented to a mixed class with students at a variety of levels and with a wide range of abilities. No prerequisite other than a knowledge of calculus was expected. The course seemed to be well received, judging by the rather sensitive criterion of the number of auditors who remained loyal. The content of the first part of this course (dealing with elementary processes) took about five weeks to cover, hut for the purposes of a freshman course, much would be eliminated to shorten the time required t o three or even two weeks without putting undue demands on the student. The presentation of these fundamentals is then followed by a consideration of more complex processes: reaction in solution, organic reactions, enzyme kinetics, etc. A course outline is given below, together with some comments. Depending on the level of the class, more or less of the detailed material can, of course, he eliminated. References are given to background material not readily available in standard references, such as King (4), Laidler (5), and Frost and Pearson (6). This material is unfortunately quite scattered, possibly indicating the need for a new generation of textbooks on elementary chemical dynamics. Outline of Lectures for Freshmen on Elementary Chemical Dynamics 1. Introduction (One lecture or less) Relation of chemical dynamics to the "static" branches of chemistry: thermodymrnics (dealing with energy balance) and struetuve. Synthesis as applied kinetics. Examples of familiar reactions, e.g., frying of eggs and rusting of iron. Thoughfamiliar, most of these processes areactually very complex. Therefore, start consideration of kinetics with much simpler processes. Basic problem in d l kinetics is to find out the nature of the barrier to the reaction. How the system overcomes this bar-
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rier is called the mechanism. Barrier can be energeticsystem must go through some intermediate of high potential energy. It can also be "configumtional" or statistical-system cannot find the law energy pass in barrier-introduce qualitatively concept of entropy of activation. Study of kinetics generally involves two kinds of problemsdetermining the individual sleps in a reaction sequence and investigatingnature of individual step. ( ~ x a m p l eof chain mechanism for I t Br%reaction) Gas phase is simplest. All individual reaction steps are of two HBr -r HS Br) or decay kinds: collision (Example H (Examples: u decay of 2aW,isomeriaation of cyclopropane). Collision (bimolecular) usually precedes any decay (unimolecular) hecause it is necessary to form or activate the decaying ~pe~ier. F u ~ t d n ~ n c n qwrnririrs r~I dprrrilinr, r3tC arc: rror,-9rrlion for - f 3 . Ikfine .,lad give mrwlwr sigo l l i h nifiruce. r \ V ~ l lrhow l:,ter hna thr;r urr related ro .inother convenient quantity: the rale conslant). 2. Some Methods i n Chemical Dynamics (Not a complete, encyclopedic survey) I n principle, simplest method is to bring two molecules close together and see whether they react. This is what is done in beam techniques which are briefly described (I). Cross-section as the fundamental measure of reaction probability. How cross-section is determined: Change in beam intensity = beam intensity X number target molecules per square centimeter X cross-section What is expected to happen when energy of collision changes? Concept of energy dependence of cross-section (3).
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CROSS SECTION
Discussion of energy threshold of reaction. Why cross-section rises beyond threshold, then declines (2). Present practical limitations of beam techniques. Thermal techniques: Experimentally simple and widely applicable for reactions a t low energy (lOOOaK = only 0.1 ev). Heat svstem until hieh enerw -" "tail" of Boltzmann distribution overlaps threshold energy. At higher temperatures, more systems exceed threshold rtt any time and reaction is faster. Discuss thermal rate methods. (Mix reactants and measure change in concentration, pressure, etc.) Possibly discuss methods of measuring fast reaction. Rate equations Emphasis on showing that rate law does not prove any mech* nism. Present typical rate laws and show which mechanism consistent with these. Relation to eauilibrium constant: introduce subieot of reverse reaction. Discuss strictures on not a t great length. Temperature dependenceThe Arrhenius Law is presented as an empirical finding and used to define the "activation energy." Other m e t h a d ~ P a i n tout that chemical methods discussed above are useful only for reactions occurring near threshold. Briefly mention methods which overcome these limitations: photalytic methods, electron impact ( S ) , chemistry of hot atoms produced by nuclear recoil (d). 3. Theories of Simple Bimolecular Reactions (At this point, the students should bave acquired enoughfeeling for what happens to make some theory palatable.) The collision theory is treated in some detail. The improbable nature of the asumptions made are emphasized: hard sphere collisions, restrictions on energy transferred, and the fact that a certain arbitrary dependence of energy on crosssection is implicity assumed. The latter assumption in particular makes it obvious to the student why the steric "fudge" factor (p) is needed. The nature of the "activation energy" is discussed, and it is
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pointed out that this is not identical with the threshold but lies a little above it. At this point, it is possible to relate the average reaction cross-section and bimolecular rate constant by simply taking the appropriate collision theory expression and replacing the total collision cross-section by the mean reaction crosssection. Potential energy surfaces are introduced as a simple way of looking a t passage from reactant to product, which forms the basis of more sophisticated theories. If the student has already had the IIeltler-London treatment of H2, the London equation for Ha can be introduced. M. Polanyi's (7) simple interpretationof this, whichshows why end-onattaek of 1%on H. is energetically more favorable than sideways attack, can then provide a valuable bit of quabtative insight into the nature of the %teric" factor, and why the cross-section dependence on energy rises gradually rather than step-wise. The student can then be shown how solving the equations for a particle sliding across a potenlid energfiurface can provide a complete model of bimolecular reactions a t any energy. This theorv is analomus to the Schroedineer eanation in that it is practical to work it out only far the simplest cases. Transition state theory can be int,roduced (for advanced students if there is time) as a special case theory dealing only with systems a t thermal equilibrium passing across the saddle point in the potential energy surface. A full derivation is inappropriate a t the freshman level, but the presentations of the expression in terms of AH' and AS{ with discussion of the latter, will interest the best students. 4. Some Simple Bimoleeula~Readions BC are obviously simpler Atomic reaet,ions of the type A than any reaction between molecules and should be discussed first. Michael Polanyi's old book, "Atomic Reactions" (7), still appears to be the best treatment of this subjectbeautiful in its simplicity and impressive for its insight. Freshmen, however, will find it easier to understand beam work than t,he equivalent diffusion flame results a n the same systems. Alkali atom-halide systems are discussed as an example. Emohmis is olaced on the "direct" nature of these reactions (no long-lived intermediate). The "harpooning" mechanism is discussed as an elegantly simple example of really understanding the natureof a reaction (I). The Hz-Bb reaetion provides 8. good way of introducing chain reactions and the steady state assumption. The H,-L reaction provides another good example of a "simple" reaction-particularly in view of recent work which shows that its apparent simplicity is deceptive (8). 5. Unimolecular Decay This section introduces the concept of the activated complex which has s. hfetime of menv moleeulllsr vibration oeriods. Examples of unimoleculer decay are discussed in order of increasing conceptual complexity: Decay of a, radioisotope Fluorescence Decay of an entity formed by chemical reaction
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Decay of an entity formed by collisional excitation This provides a basis for as much theory as one then cares to give. Simple Rice-Ramsperger-Kassel theory leading to an expression of the type
is within the grasp of the elementary students and helps consolidate important concepts.
Having given this presentation of elementary concepts and theory, one can then proceed to other more traditional topics in chemical kinetics which are important to the freshman. Literature Cited (1) HERSCHBACH, D. R., Ads. C h m . Phys., 10,319 (1966).
(2) WOLFGANG, R., Ann. Reus. Phys. Chem., 16, 15 (1965); Scientific American, 214, No. 1,82 (1966). M., Ann. Reports, 62,39 (1965). (3) HENCHMAN,
(4) KING,E. L.,"HOWChemical Reactions Occur," W. A. Benjamin & Co., Inc., New York, 1964.
(6) FROST, A. A,, AND PEARSON, R. G., "Kinetics and Mechanism," John Wiley & Sons, Inc., New York, 1961. (7) POLANYI, M., "Atomic Reactions," William & Norgate, London, 1932. (8) SULIJVAN, J. H., J. Chem. Phya., 46,73 (1967).
(5) LAIDLER, K. J., "Chemical Kinetics," McGraw-Hill Book Co. 1965.
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