Reaction Kinetics Volume 1

A Review of the Recent Literature Published Up to December 1973

By P. G. Ashmore

The Royal Society of Chemistry

Copyright © 1975 The Chemical Society
All rights reserved.
ISBN: 978-0-85186-756-4

Contents

Chapter 1 Chemical Kinetics — Retrospect and Prospects By S. W. Benson, 1,
Chapter 2 Reactions of Atoms in Ground and Electronically Excited States By R. J. Donovan and H. M. Gillespie, 14,
Chapter 3 Unimolecular Reactions By P. J. Robinson, 93,
Chapter 4 A Critical Survey of Rate Constants for Reactions in Gas-phase Hydrocarbon Oxidation By R. W. Walker, 161,
Chapter 5 Kinetic Studies in Silicon Chemistry By I. M. T. Davidson, 212,
Chapter 6 Network Effects in the Dissociation and Recombination of a Diatomic Gas By H.O. Pritchard, 243,
Chapter 7 Recent Advances in the Analysis of Kinetic Data By A. Jones, 291,
Chapter 8 Kinetics of Oscillating Reactions By B. F. Gray, 309,
Author Index, 387,

CHAPTER 1

Chemical Kinetics – Retrospect and Prospects

BY S. W. BENSON

1 Introduction

From time to time my now 16-year-old son, repeating a time-honoured but half-forgotten ritual, will ask me what I do for a living and as I absentmindedly chant in reply the litany – ‘… chemistry … physical chemistry … chemical kinetics … speed of chemical reactions …,’ I can see the expression of curiosity changing slowly and familiarly to one of resigned bafflement. The situation is quickly recovered with another set of words, ‘… rocket engines … fires … explosions … atomic bombs … digestion …,’ but neither of us has yet had the courage to explore the gulf between these languages.

Chemical kinetics as a formal science can be today reckoned to be about a hundred years old, but, despite its pervasive involvement with nearly every branch of science and technology, it has never stirred many sparks in the public imagination. Probably, it is too far behind the front lines. This is, I believe, an unfortunate situation since the demands of our growing, complex, industrial–technological society will place an increasing burden of responsibility on chemical kinetics to provide answers to problems which seem to grow exponentially in their molecular complexity. In the present Report I would like to review some of the changes and involvements which have occurred in chemical kinetics, and then, hopefully, to look into the crystal ball and try to make some educated guesses about what the future is likely to hold.

Any special field of knowledge starts in the observer mode with an assembly of described experiences. These may become categorized if common variables can be discerned, and the final stage sees the emergence of quantitative relations which completely describe the observations and permit their expression in mathematical form. The variables in a kinetic system are basically chemical composition (reactants, products, catalysts), pressure, and temperature, ignoring for the moment physical state and external fields. Chemical kinetics emerged as a quantitative science with the statement of the law of mass action by Guldberg and Waage and attained some form of adolescence with Arrhenius’ expression for the temperature dependence of the rate of chemical reactions. If one delves into the history of this early period one cannot help but be struck by the incredibly small data base which served to inspire both of these fundamental generalizations.

In the next 50 years (roughly 1870 — 1920) there followed a period of very slow growth. Very few scientists were attracted to study kinetic phenomena. On the other hand the same could probably be said of most fields of chemistry during this period. Chemistry had not yet made a great social impact. As a hobby, however, chemistry was still relatively inexpensive and any enthusiast with a stopwatch and the patience to perform many repetitive chemical analyses could engage in the action in kinetics. Adequate tools had not yet been developed to explore many of the most interesting phenomena such as combustion and explosion. However, the real flowering of physical chemistry during this period gave an early inspiration to the application of physico-chemical methods of analysis to the study of kinetic processes. Optical and electrical properties were used to follow the course of reactions in solutions while gas reactions could frequently be followed simply by observing pressure changes.

World War I gave a large impetus to the acceleration of scientific research and witnessed the extensive involvement of both industry and government in the support of science. The period between World War I and World War II also witnessed the development of the conceptual basis for chemical kinetics. The methods of describing molecular behaviour, using the tools of statistical mechanics, were outlined in useful detail for gas reactions by the important contributions of Lindemann, Rice, Ramsperger, Kassel, Evans, Polanyi, and Eyring, leading to the most recent expressions for unimolecular reactions in the RRKM (Rice–Ramsperger–Kassel–Marcus) formulation of Transition State Theory. Transition State Theory itself has blossomed into a primary underpinning of all ‘equilibrium’ kinetic theory for both gases and liquids.

World War II gave a further enormous impetus to the development of both science and technology. The status of science in various countries is measured today in terms of the fraction of the total national effort (G NP) expended on science (more properly, technology). The very concept of such a measure would have been the occasion of great humour in scientific circles prior to 1930. Perhaps an even greater impact introduced by World War II was the development of electronic tools for measurement. The unbelievable rate of growth and sophistication of electronic devices, particularly solid-state devices, since 1940 is probably the single biggest common feature in the research activity of the past three decades. In a very profound sense we, meaning all scientists, may be said to be in the ‘Electronic Age’.

What this has done primarily has been to give us the ability to explore the details of chemical interactions on a molecular level and to answer questions which would have been considered moot or meaningless just a short time ago. It has not changed our conceptual understanding of chemical kinetics (which was basically complete with the Dirac Equation) but it has made it possible to use quantum theory to explore the rich and complex phenomena of many-body interactions both in space and in time.

One eloquent testimony to this rich development in chemical kinetics has been the growth of specialities. We have today specialists in gas kinetics, solution kinetics, and catalysis, and in these areas we have sub-specialities of ion–molecule reactions, atom–electron reactions, free-radical reactions, and unimolecular reactions. There are kineticists today who have devoted almost their entire professional lives to the kinetics of energy-transfer processes. In the areas of solution kinetics, scientists who study ionic reactions or ‘redox’ reactions rarely talk to kineticists who deal with enzyme kinetics or ‘concerted’ reactions. Finally, there are ‘mission-oriented’ kineticists whose field of application may cut diagonally across many of these specialities. Lasers, space travel, rocket engines, automobile exhausts, photochemical smog, electrical discharges, and most recently the spectroscopy of interstellar dust have all generated communities of scientists with much applied but little basic interest in the results of chemical kinetics. Let us look at some of these specialities in some greater detail.

2 Gas-phase Kinetics – Neutral Species

Studies of gas-phase reactions have always been technically the most difficult and expensive of kinetic researches. Their results, however, have also been the simplest to interpret at the molecular level and so they have been, and will probably continue to be, at the forefront of our ‘basic researches’ in chemical kinetics. They have been the traditional testing ground of molecular theories of kinetic processes. All chemical reactions in dilute (i.e.<1 atmosphere pressure) gases can be looked upon as sequences of elementary steps involving either one or two molecules at a time. Thus an overall termolecular event such as atom recombination can be considered to be a sequence of two bimolecular collision events in the first of which a short-lived collision complex is formed. If an isolated molecule has a sufficient amount of internal energy, it may localize this in such a way as to rearrange its atomic structure (i.e. isomerize) or break a bond, and this becomes a unimolecular process.

Unimolecular reactions are perhaps one of the best understood processes in chemical kinetics. We have a quantitative theory, the transition state theory, which permits us, with some physically reasonable, empirical assumptions, to evaluate the Arrhenius A-factor for the unimolecular reaction of a Maxwell-Boltzmann, thermalized population of reactant molecules. The accuracy with which we can do this is probably in most cases as good as or better than that with which the A-factors can be measured.

In simple bond-breaking reactions (e.g. C2H6 -> 2CH3) and a limited number of 1,2-elimination reactions (e.g. CH3CH2Cl -> C2H4 + HCl) we can also predict the activation energies, and so predict quantitatively how the rate constants vary with temperature.

For the numerous other categories of unimolecular reactions, e.g. complex rearrangements (cyclopropane -> propylene), we have no theoretical model which allows us to predict activation energies. The best we can do in such cases is to predict the effects of substituents on changes in the activation energy and hence to predict, empirically, activation energies in homologous series, knowing one of the members of the series. The extension of such methods to highly branched compounds and ‘unusually’ strained compounds still remains an incomplete task and one which will await a much more basic understanding of both non-bonded interactions and ‘poly-centre’ valency. Thus we have no reliable method for predicting the activation energy of a 1,2 atom or group transfer which can in principle occur in ions, in free radicals, and in molecules:

[FORMULA OMITTED]

Electronic techniques when applied to the measurement of physical properties have given us an extraordinary facility in exploring events occurring in ever shorter intervals of time. Mass spectrometric methods of analysis have given us the possibility of sampling gas systems in times of the order of 10-4 s. Molecular spectroscopy together with ultrasensitive, rapid-response detectors can resolve times of 10-6 s and has been thus used to follow reactions behind shock waves. Recent developments in nano- and pico-second pulse laser spectroscopy give promise of following chemical events down to times of the order of 10-12 s. Such techniques have made it possible to identify, study, and measure the production and subsequent reactions of unstable intermediates produced in chemical reactions. Free radicals and vibrationally and electronically excited species have by these means been ‘seen’ in rapid chemical reactions and we today have a good deal of data on their reactivity.

One of the very exciting recent developments in this area has been the use of resonance absorption to measure, in situ, very small (~ 10-10 mol dm-3) concentrations of atoms and small molecule sand radicals. The companion technique of resonance fluorescence is simpler to use and even more sensitive. The development of tuneable lasers for the wavelength region 200 — 400 nm, which seems imminent, would trigger an avalanche of interesting kinetic investigations in gas-phase reactions probably comparable to that which followed the introduction of flash photolysis techniques.

With so much of the basic creative urge in kinetic circles being devoted to exploring ever smaller intervals on the time scale it is rarely appreciated that a quite considerable scientific market exists for understanding kinetic phenomena over very long time periods. A reliable knowledge of very, very slow rate phenomena is of considerable interest to geologists trying to understand the evolution of the earth’s crust over the past 109[plus or minus]1 years and also to geochemists anxious to retrace the evolution of our planetary system from the presumed Laplacian dust clouds of 1010[plus or minus]1 years ago. Although these problems do not seem to pose challenges of appreciable urgency now, the future (i.e. >106[plus or minus]1 years) of life in this solar system may well rest on the success of distant generations in deciphering the cosmic record.

More contemporary interest in such slow reactions is to be found among bridge builders trying to make more enduring structures, among communications engineers trying to plant more permanent telephone poles, and among biologists trying to estimate the cumulative effects of our now rapidly changing chemical environment on various physiological functions and structures. The measurement of very small rate constants in a ‘short’ time is a real challenge.

The RRKM theory of unimolecular reactions gives us a theoretical handle for exploring unimolecular reactions of non-Maxwellian populations of energized molecules. This had been a popular subject for many years but had been restricted to either reactions of small molecules at moderate pressures (e.g. NO2Cl -> NO2 + Cl) or else large molecules at very low pressure (l0-1 — 10-2 torr). By working at much higher temperatures and much lower pressures (10-3 — 10-4 torr) the Reporter and his colleagues have been able to extend such studies to larger molecules with as many as 20 — 40 atoms. The technique is called ‘Very Low-pressure Pyrolysis’ (V.L.P.P.) and it has been very valuable in demonstrating the validity of applying RRKM theory to such extreme conditions. In the same period another technique of preparing populations of very excited molecules in narrow energy ranges (chemical activation) has been exploited by Rabinovitch and his co-workers in testing various details of unimolecular rate theory such as energy transfer between molecules in gas-phase collisions and the rates at which energy is redistributed among the internal degrees of freedom of a large molecule.

Infrared spectroscopy together with laser techniques have both inspired and made possible very extensive investigations of the exchanges of rotational and/or vibrational energy in collisions between small molecules. In the past, such processes had been studied indirectly via measurement of sound dispersion or shock propagation through gases. The laser techniques have made it possible to pinpoint the histories of individual vibronic states in diatomic and linear triatomic molecules. No one appears to have attempted to extend such techniques to larger molecules. The theory of such energy-transfer processes seems to be reasonably well understood and when extended to include the appreciable dipole forces which exist in the collisions of polar molecules, such as HF or H2O, seems to be able to account quantitatively for the rates observed. A comparable theory of energy transfer in larger molecules neither exists nor currently seems capable of quantitative testing. Picosecond laser technology may soon change this.

Bimolecular events in the gas phase fall in the category either of an energy-transfer process such as we have discussed or of an association reaction (complex formation) or finally, and perhaps the sole chemical event, a metathesis reaction in which an atom or group is transferred from one species to the other:

H + F2 [??] HF + F

Me + EtBr [??] MeBr + Et

These metathesis reactions are among the oldest categories of bimolecular reaction studied by gas-phase kineticists and are in part reasonably well described by transition state theory. Their A-factor corresponds to what are called ‘tight’ transition states and can be estimated to within a factor of three, which is as good as most experimental uncertainties. The activation energies for these processes, however, continue to be elusive. A number of empirical techniques exist for either estimating or calculating these activation energies to within ca. [+ or -] 8 kJ mol-1 uncertainty. Although this seems quite good it must be reckoned against the observation that ‘intrinsic’ activation energies (i.e. in the exothermic direction) for metathesis fall in a very narrow range of ca. 30 [+ or -] 10 kJ mol-1 for most examples and 0 — 65 kJ mol-1 for all known examples. This is a theoretical vacuum which up to now has attracted relatively few prophets. Recent progress in our ability to predict heats of formation of ions, molecules, and free radicals suggests that this situation is overdue for remedy.

One of the most fascinating areas on the bimolecular scene has been the four-centre double metathesis reactions:

AB + CD [??] AC + BD

Considered once the prototype par excellence of the collision theory of chemical reaction rates, it is today more aptly dubbed the ‘abominable snowman’ of chemical kinetics, with no extant authentic examples for covalently bound molecules. When Sullivan demonstrated that the reversible reaction

H2 + I2 [??] 2HI

could be completely accounted for by the termolecular mechanism

I + H2 + I [??] IH + HI

he made illegitimate the last member of the royal line which had, in fact, inaugurated the modern study of gas reactions.

A number of suggestions have been made to account for the fact that such reactions have very high activation energies. In the absence of valid examples it is difficult to decide which of these properly accounts for the remarkable coincidence that, in all of these reactions, the free-radical pathway is always at least 10 — 100-fold faster than the possible bimolecular pathway.

(Continues…)Excerpted from Reaction Kinetics Volume 1 by P. G. Ashmore. Copyright © 1975 The Chemical Society. Excerpted by permission of The Royal Society of Chemistry.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.