Probing
M
the
Chemical Kinetics of When used with care, kinetic studies can produce valuable results despite data uncertainties and mechanistic surprises.
S I D N E Y W. B E N S O N
he world’s atmosphere is a complex chemical reactor, whose behavior is gradually being understood through the combined application of many scientific disciplines. Over the past 20 years, chemical kinetics has increasingly played a pivotal role in this research effort. Among other roles, it has been key to understanding smog formation and the chemistry behind creation of the ozone hole. Yet, chemical kinetics can also be “fragile” in its utility, a consequence of the sheer complexity of the many atmospheric reactions that can occur and the data uncertainties that can arise when studying large reaction ensembles. It remains a tool that, despite technological advances, must be used with care, and strengths and weaknesses must be understood so that interpretations of findings are inherently reasonable. Failure to observe necessary cautions can lead to incorrect assumptions about the nature of reactive chemical processes and about what information can
TONY FERNANDEZ AND SEAN KENNEDY
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© 2002 American Chemical Society
be obtained from collected data. A review of the evolution of this discipline provides some useful insights concerning the promises and pitfalls of applying chemical kinetics to environmental problems.
Early beginnings Chemical kinetics, today considered a mature science, began with the publication of Bodenstein’s classic 1894 study of the homogeneous gas phase, reversible decomposition of hydrogen iodide (HI) into molecular hydrogen (H2) and iodine (I2) (1). From then until the beginning of World War II, enormous strides were made, including the discovery of unimolecular, free-radical, chain, and branching chain reactions. A strong theoretical base of statistical mechanics and transition state theory supported these findings. Progress in the field proved fortunate for environmental chemists, as it provided needed research tools when Los Angeles smog and air pollution were “discovered” in 1946. JANUARY 1, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY I 29 A
In the half century since then, experimental kinetics has undergone tremendous development. Flash photolysis, modern electronics, mass spectroscopy, gas–liquid chromatography, and other tools have made it possible to analyze increasingly smaller amounts of chemical changes in increasingly shorter time intervals—now down to about 50 femtoseconds (5 × 10−14 s), a time so short that the average gas-phase molecule of N2 at 300 oK moves only ~0.25 Å, or ~10% of its van der Waals’s radius.
Lessons learned An important observation obtained from a review of past research is how many early studies were misinterpreted. One example is the study of HI decomposition, first modeled as a simple bimolecular reaction between two HI molecules with a cyclic transition state (1). In contrast to these early findings, subsequent studies showed that the HI reaction proceeded in part by a chain similar to that for the reaction RI + HI (R is a methyl, ethyl, or n-propyl group) and in part by a termolecular reaction between two I atoms and H2, having an open (noncyclic) transition state (2, 3). Still further study showed that the reaction between RI and HI proceeded entirely as a chain reaction (4, 5). In short, there were no examples of bimolecular 4-center metathesis reactions, and all of those proposed turned out to be chain reactions. Other examples of early miscues come from the many kinetic studies of gas-phase hydrocarbon pyrolysis of compounds such as ethane, propane, and butane carried out between about ~1925 and 1950. Initially, it was believed that these decompositions proceeded by one rate-determining step followed by faster steps. The rate-determining step was generally assumed to involve the parent molecule, yielding an overall reaction first-order rate in hydrocarbon concentration. When it was found that the supposed first-order rate constant increased at higher pressures, this was interpreted as a theoretically foreseen con-
sequence of the rate-determining step not being at its high-pressure limit. Although the Rice−Herzfeld mechanisms that were proposed in 1934 suggested that all these pyrolyses were in fact complex, freeradical, chain reactions having no single, rate-determining step (6), it took almost 20 years to convince the most reluctant, gas-phase kineticists of this interpretation. Consequently, during this time, a large number of “unimolecular” rates were described in the literature (7, 8). In addition to these complexities, other issues persist such as the great problem with all gas-phase kinetic data: how to cope with contributions from heterogeneous or “wall” reactions. Two methods that are generally used for doing this are changing the surface-to-volume ratio of the reaction vessel by packing the vessel with glass tubing and modifying the walls by coating them with materials, such as gold, teflon, AgCl, KCl, or B2O3. If the observed reaction rate is not perturbed by such changes, it is surmised that a true homogeneous reaction has been observed. Such conclusions may not always be justified, however; and wall reactions continue to haunt kinetic studies, even though in the past few decades, teflon and halocarbon waxes have been shown to be inert to free radicals and that coating them on glass or metal can decrease wall reactions to below measurable levels (7, 8). This problem arises because such coatings cannot be used in many cases, such as with reactions studied at above 250 °C. The message of this historical perspective is that although we may be able to demonstrate that a model may account for a given set of data, it is seldom if ever possible to prove that this interpretation is unique. Sometimes, the ambiguity lies in the data uncertainties, and sometimes, the difficulty is that the parameter range studied is too narrow to reveal important deviations from a proposed mechanism.
How certain are we? Given all the improvements in analytical techniques, how good are the results? In simple unimolecular reactions, such as the isomerization of cyclopropane
TA B L E 1
Variations in reported bimolecular reaction rate constants at 298 Ka Establishing rate constants for fast reactions still poses a difficult challenge.
Reaction
Cl + C2H6 → HCl + C2H5 Cl + CH4 → HCl + CH3
2CH3 → C2H6
Cl + C2H5 → HCl + C2H4
CH3 + C2H5 → C3H8
Rate constant range × 1011 (cm3/molecule-s)
Average rate constant × 1011 (cm3/molecule-s)
Number of measurementsb
References
5.46–6.70
5.99 ± 0.37
8
(11)
0.0029–0.0150c
0.0086 ± 0.0034
12
(10, 11)
2.0–10.0
5.6 ± 2.3
8
(11)
1.21–45.1
21.8 ± 17.4
6
(11)
2.12–9.29d
5.29 ± 2.1.
8
(11)
aThe
rate constants l isted are derived from representative sets of values. Additi onal data are cited in the li terature. of measurements from which average val ues are calculated. rates that fal l w ithin the indicated range are calculated, not ex perimental values. d Some measured rates i n the range i ncl ude contri buti ons from di sproporti onati on and recombi nati on reacti ons. b Number cSome
30 A I ENVIRONMENTAL SCIENCE & TECHNOLOGY / JANUARY 1, 2002
to propylene or the decomposition of alkyl halides into olefins and hydrogen halides, results are in good agreement when measured in different laboratories— accord is generally within 10–20% (9). For faster bimolecular reactions such as those between atoms or radicals and molecules, the range of values is somewhat larger, usually within a factor of 1.2–2.0 (10–12). Table 1 shows one of the best examples of fast bimolecular reactions, the rate of reaction of Cl atoms with ethane, and also indicates rate constants for the comparable but slower reaction of Cl atoms with methane. Difficulties increase considerably when attempting to measure very rapid bimolecular reactions, such as radical–radical or atom–radical reactions. Here, rate constants can be close to collision frequencies, and it is difficult to obtain pseudo-unimolecular conditions. Consequently, the absolute initial concentration of one or both radicals must be known. Table 1 includes data for perhaps the simplest reaction of this type, the recombination of methyl radicals. The spread of experimental results is much greater than for the preceding cases, and the pressure dependence of the rate constant introduces added complexity. A more difficult example involving two different radicals is the reaction of Cl atoms with ethyl radicals. The reaction is actually a recombination to form vibrationally excited C2H5Cl*, which rapidly (half-life
