Termolecular Reaction Kinetics

Let us take the reaction (10) of OH with S02 as an example of a termolecular reaction of atmospheric interest and examine how its pressure dependence is established. It is common in kinetic studies to follow the decay of one reactant in an excess of the second reactant. In the case of reaction (10), the decay of OH is followed in the presence of excess SOz and the third body M, where M is an inert bath gas such as He,... 

TABLE 5.8 Some Kinetic Parameters for Some Termolecular Reactions"... 

This result is of a very rough character, but it shows that termolecular reactions can reasonably be interpreted in terms of simple kinetic mechanisms. 

The first mechanism implies k19 = k5AK11A 11A the second leads to ki9 = k2iKlm- . Independent evidence suggests the existence of both intermediate species in the nitric oxide-oxygen system, and both mechanisms involve entirely reasonable collision complexes. In both, the equilibrium step is rapid, and the overall kinetics are third order. Theoretical calculations based on the activated complex theory were made by assuming a true termolecular reaction the predicted rates agree well with experiment.161 The experimental rate constants are summarized in Tables 4-3 and 4-4. 

The first studies of the kinetics of the NO-F2 reaction were reported by Johnston and Herschbach229 at the 1954 American Chemical Society (ACS) meeting. Rapp and Johnston355 examined the reaction by Polanyi s dilute diffusion flame technique. They found the free-radical mechanism, reactions (4)-(7), predominated assuming reaction (4) to be rate determining, they found logfc4 = 8.78 — 1.5/0. From semi-quantitative estimates of the emission intensity, they estimated 6//t7[M] to be 10-5 with [M] = [N2] = 10 4M. Using the method of Herschbach, Johnston, and Rapp,200 they calculated the preexponential factors for the bimolecular and termolecular reactions with activated complexes... 

This is a general fact. For monomolecular (or pseudo-monomolecular) reactions the graphs corresponding to compartments are acyclic. A similar property for the systems having either bi- or termolecular reactions is more complex. It can be formulated as follows. If every edge in the graph of predominant reaction directions for some compartment is ascribed to a positive "rate constant k and chemical kinetic equations are written with... 

Patrick, R. and Golden, D.M. (1984) Termolecular reactions of alkali metal atoms with oxygen and hydroxyl. Int. J. Chem. Kinet., 16, 1567. 

Because the general principles of chemical kinetics apply to enzyme-catalyzed reactions, a brief discussion of basic chemical kinetics is useful at this point. Chemical reactions may be classified on the basis of the number of molecules that react to form the products. Monomolecular, bimolecular, and termolecular reactions are reactions involving one, two, or three molecules, respectively. 

We can define a termolecular reaction as one that requires the participation of three individual particles in a single kinetic process. Thus we might think of the reaction of NO with CI2 as proceeding through the simultaneous interaction of two NO molecules with CI2 to form the transient reaction complex (NO)2Cl2, which then decomposes in a single step into two molecules of NOCl. Or in more general terms, for the reaction of A + B + C —> products we may write... 

An important concept in chemical kinetics is molecularity of a reaction or the number of particles (molecules, atoms, ions, radicals) participating in it. Most common are bimolecular reactions, unimolecular reactions being also encountered. In very rare cases termolecular reactions may be observed as well. Reactions of higher molecularity are unknown, which is due to a very low probability of a simultaneous interaction of a larger number of molecules. Consequently, our further considerations will be confined to the examination of uni- and bimolecular reactions. On the other hand, the reactions of a termolecular character, whose kinetic equations have a number of interesting properties, are sometimes considered. As will appear, a termolecular reaction may be approximately modelled by means of a few bimolecular reactions. For an elementary reaction its molecularity is by definition equal to the order whereas for a complex reaction the molecularity generally has no relation whatsoever to the reaction order or the stoichiometry. 

Olbregts, J. (1985). Termolecular reactions of nitrogen monoxide and oxygen A still unsolved problem. Int.. Chem. Kinet. 17, 835-848. 

While termolecular reactions are relatively uncommon, at the other end of the scale, unimolecular reactions are often encountered. The theory of the kinetics of such reactions is important for the detail it provides on the individual events that must occur in those reactions, which we have termed elementary steps, and we will treat it separately in the following section. First, however, let us take some time here for an example illustrating some additional aspects of binary collision theory via numerical calculations. 

The primary emphasis in shock tube interferometric studies of the hydrogen-oxygen reaction has been on induction period phenomena. Recently, however, the entire postshock density profiles of a selection of rich, lean and near stoichiometric Ha-Oa-Ar mixtures have been studied by numerical integration of an assumed reaction mechanism. In this manner it was shown that the characteristic features of the profile prior to the end of the density plateau are essentially independent of the recombination kinetics. Thereafter, however, the shape of the profile is largely accounted for by termolecular reactions (e)-(g). Systematic variation of the termolecular rate coefficient values in experimental regimes where recombination is most sensitive to reactions if) or ig)> respectively, has yielded temperature-dependent expressions of the form kf< = AT for kf and kf believed valid over the range 1400-3000 K. The expression of Jacobs et al. was found satisfactory for kf. In all three cases, variation with temperature is small (1-0 m 0-5). Values at 1700 K, kf = 5-9 x 10 (cited above), kf z= 1-9 X 10 , and kf = 3-6 x 10 cm mole sec, are in excellent accord with those listed in Table 2.2. 

Modern theoretical and experimental studies have revealed additional details of the reaction kinetics. The results of these studies surest that the low temperature thermal reaction proceeds by both the direct bimolecular reaction of hydrogen molecules with vibrationally excited iodine molecules H2 + l2(hi v) —> HI + HI and the termolecular reaction of hydrogen molecules with iodine atoms H2 + I + I—>HI- - HI. The direct bimolecular reaction mechanism and the termolecular reaction mechanism were among those suggested by Bodenstein one hundred years ago. 

In 1967 Sullivan [14] reported experimental measurements of the rate of the overall reaction H2 +1 4-1 HI -I- HI. Using a low-temperature photochemical source to produce I atoms Sullivan measured their reaction rate with H2 and determined the (apparent) rate constant for the termolecular reaction and its temperature dependence. Extrapolation of the rate constant to the higher temperature range of the thermal reaction data showed that the former could accoimt for the entire thermal rate. It was thus shown that the dominant mechanism for the thermal reaction of H2 with I2 at temperatures below about 700 K is either the termolecular reaction H2 + I + I HI + HI or another mechanism which is kinetically indistinguishable from it. 

The techniques for measuring rate constants and prodnct distribntion (branching ratios) for ion-molecule reactions are varied, but the majority of the data have been determined using the FA, drift-tube (DT), selected ion flow tube (SIFT), high-pressure mass spectrometric techniques, or ICR. These methods are detailed in Chap. 4. A number of surveys of all classes of ion-molecule reactions have appeared in the literature Ferguson [16], Sieck et al. [17], Albritton [18], Anicichet al. [19], Ikezoe et al. [20], some of which include termolecular reactions or are limited to selected methods. Anicich listed [21] an index to the hterature for gas phase bimolecular positive ion-molecule reactions as a comprehensive survey of ion-molecule reaction kinetics and product distribution of the reactions. Over 2300 references are cited. This index covers the hterature from 1936 to 2003. It was limited to selected reactions, listed by reactant ion, that were important for chemical modehng ionic processes in planetary atmospheres, cometary comas, and intersteUar clouds. 

Nickolaisen, S.L., Friedl, R.R., Sander, S.P. Kinetics and mechanism of the chlorine oxide CIO -I-CIO reaction pressure and temperature dependences of the bimolecular and termolecular channels and thermal decomposition of chlorine peroxide. J. Phys. Chem. 98, 155-169 (1994) Nickolaisen, S.L., Roehl, C.M., Blakeley, L.K., Friedl, R.R., Francisco, J.S., Liu, R.F., Sander, S. P. Temperature dependence of the HO2-1-CIO reaction. 1. Reaction kinetics by pulsed photolysis-ultraviolet absorption and ab initio studies of the potential surface. J. Phys. Chem. A 104, 308-319 (2000)... 

The kinetics of such termolecular reactions are well understood, and many have been studied using the SIFT. However, they cannot occur in ISC because the pressures in these regions are very low. Instead, the analogous process of radiative association occurs. Continuing with the above example, the bi-molecular reactions [13] can occur in ISC, and indeed it is promoted by the low ambient temperatures (as low as 10 K in some clouds), and if the dissociation lifetime of the excited (CH )" ion is long enough, then it may emit a photon which will stabilize it against dissociation ... 

The reaction steps in the mechanism of a homogeneous gas-phase reaction are usually elementary reactions, that is, the stoichiometric equation of the reaction step corresponds to real molecular changes. The molecularity of an elementary reaction is the number of molecular entities involved in the molecular encounter. Thus, an elementary reaction can be unimolecular or bimolecular. Some books on chemical kinetics also discuss termolecular reactions (Raj 2010), but three molecular entities colliding at the same time is highly improbable (Drake 2005). What are often referred to as termolecular reactions actually involve the formation of an energetically excited reaction intermediate in a bimolecular reaction which can then collide with a third molecular entity (e.g. a molecule or radical). 

Some reactions can only proceed via a termolecular mechanism. The recombination of two gas-phase hydrogen free radicals, H + H — H2, does not occur on a molecular level. Collisions can take place between two hydrogen free radicals. However, if an H-H bond formed, it would have to contain a great deal of the kinetic energy that the two H free radicals had before the collision. This would make the bond unstable, and it would break essentially as soon as it was formed. Recombination reactions, including the recombination of two H radicals, are believed to proceed according to a termolecular reaction, e.g.,... 

H30+(H20) clusters form by termolecular reactions of the type H30 (H20) .i + H2O + X H30 (H20) + X, where X is some tiiird body. In addition to increased fragmentation of H30 (H20)n clusters at an elevated kinetic energy, the rate of formation of diese cluster ions is reduced because the rate coefficient has a strongly negative energy dependence. 

Even though the rearrangements suggest that discrete carbocation intermediates are involved, these reactions frequently show kinetics consistent with the presence of at least two hydrogen chloride molecules in the rate-determining transition state. A termolecular mechanism in which the second Itydrogen chloride molecule assists in the ionization of the electrophile has been suggested. ... 

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