Termolecular reaction rates

A termolecular reaction rate is proportional to the frequency of the collision of three bodies. These reactions are proportional to [A]3, [A]2[B], or [A][B][C], depending on whether the molecules taking part in the reaction are of one, two, or three species. If these species are the starting materials, the reaction is third-order however, termolecular reactions are rare because of the low probability that three species will come together. 

The phase-space model has been applied to triple collisions by F. T. Smith (1969) in a detailed study of termolecular reaction rates. He classified 3-body entry or exit channels into two classes, of pure and indirect triple collisions, and introduced kinematic variables appropriate to each class. These variables were then used to develop a statistical theory of break-up cross-sections. A recent contribution (Rebick and Levine, 1973) has dealt with collision induced dissociation (C1D) along similar lines. Two mechanisms were distinguished in the process A + BC->A + B + C. Direct CID, where the three particles are unbound in the final state, and indirect CID, where two of the particles emerge in a quasi-bound state. Furthermore, a distinction was made in indirect CID, depending on whether the quasi-bound pair is the initial BC or not. Enumeration of the product (three-body) states was made in terms of quantum numbers appropriate to three free bodies (see e.g. Delves and Phillips, 1969) the vibrational quantum number of a product... 

From these equations, the termolecular reaction rate constant kter is derived as... 

F. 2.9 Pressiffe dependence of termolecular reaction rate constant for (a) Hinshelwood-Lindeman mechanism and (b) Tree s formula... 

The curve (a) in Fig. 2.9 is the schematic graph of the pressure dependence of a termolecular reaction rate constant according to the Lindemann mechanism. From the figure, it can be seen that the reaction rate constant is proportional to [M] (pressure) in the low-pressure limit, and gets nearly constant independent on the pressure in the high-pressure limit. The intermediate region between these two limits is called the fall-off region. 

Is best used for representing the pressure dependence of the termolecular reaction rate constant. This equation is based on the curve fitting to the pressure dependence of the unimolecular decomposition rate by the Kassel theory. In Eq. (2.54), is called a broadening factor, and it is a good experimental fitting for many termolecular reactions in atmospheric chemistry has been obtained by taking e.g. Fp = 0.6. The curve (b) in Fig. 2.9 shows the schematic pressure dependence... 

From these relationships, unimolecular decomposition rate constants can be calculated from termolecular reaction rate constants and equilibrium cmistants (see Table 5.3). 

Like other metal reactions studied previously in our laboratory, H2 elimination is initiated by insertion into one of the C-H bonds forming HMC3H5. The reaction rate constant for Y + cyclopropane was found to be very small at room temperature, 0.7 x 10 12 cm3 s 1, and it was suggested that the reaction most likely involved termolecular stabilization of C-H or C-C insertion complexes, rather than molecular elimination.22 By analogy with other systems studied, the dynamically most favorable route to H2 loss in this case is likely via H atom migration to the Y-H moiety, with concerted... 

Intramolecular general base catalysed reactions (Section II, Tables E-G) present less difficulty. A classification similar to that of Table I is used, but since the electrophilic centre of interest is always a proton substantial differences between different general bases are not expected. This section (unlike Section I, which contains exclusively unimolecular reactions) contains mostly bimolecular reactions (e.g. the hydrolysis of aspirin [4]). Where these are hydrolysis reactions, calculation of the EM still involves comparison of a first order with a second order rate constant, because the order with respect to solvent is not measurable. The intermolecular processes involved are in fact termolecular reactions (e.g. [5]), and in those cases where solvent is not involved directly in the reaction, as in the general base catalysed aminolysis of esters, the calculation of the EM requires the comparison of second and third order rate constants. 

Of these four reactions (ii) and (iv) involve simple proton transfers to and from oxygen atoms, and experience shows that such equilibria will be set up very rapidly. The rate-limiting steps then become (i) and (iii), which involve greater structural changes and are likely to be slow. They are both formally termolecular reactions, and it is of interest to enquire whether either of them can be split up into consecutive bimolecular processes, one of which is rate-limiting. The only possibilities are as follows ... 

In Table 1 (pp. 251-254), IM rate constants for reaction systems that have been measured at both atmospheric pressure and in the HP or LP range are listed. Also provided are the expected IM collision rate constants calculated from either Langevin or ADO theory. (Note that the rate constants of several IM reactions that have been studied at atmospheric pressure" are not included in Table I because these systems have not been studied in the LP or HP ranges.) In general, it is noted that pressure-related differences in these data sets are not usually large. Where significant differences are noted, the suspected causes have been previously discussed in Section IIB. These include the reactions of Hcj and Ne with NO , for which pressure-enhanced reaction rates have been attributed to the onset of a termolecular collision mechanism at atmospheric pressure and the reactions of Atj with NO and Cl with CHjBr , for which pressure-enhanced rate constants have been attributed to the approach of the high-pressure limit of kinetic behavior for these reaction systems. 

Again, the molecularity of a reaction is always an integer and only applies to elementary reactions. Such is not always the case for the order of a reaction. The distinction between molecularity and order can also be stated as follows molecularity is the theoretical description of an elementary process reaction order refers to the entire empirically derived rate expression (which is a set of elementary reactions) for the complete reaction. Usually a bimolecular reaction is second order however, the converse need not always be true. Thus, unimolecular, bimolecular, and termolecular reactions refer to elementary reactions involving one, two, or three entities that combine to form an activated complex. 

The rate constant (sometimes called the specific reaction rate) is commonly designated by k. The SI unit of time is the second (symbolized by s). Thus, unimolecular rate constants are typically expressed in s and unimolecular processes are by definition concentration-independent reactions. A slight difficulty arises regarding SI units and bi- and termolecular rate constants. Concentrations in the SI system would be mol per cubic meter, but in chemistry concentrations are expressed in mobdm (or more commonly mol-L or simply M ). Thus, a bimolecular rate constant typically has units of M s whereas a termolecular rate constant is expressed with units of... 

Trimolecular reactions (also referred to as termolecular) involve elementary reactions where three distinct chemical entities combine to form an activated complex Trimolecular processes are usually third order, but the reverse relationship is not necessarily true. AU truly trior termolecular reactions studied so far have been gas-phase processes. Even so, these reactions are very rare in the gas-phase. They should be very unhkely in solution due, in part, to the relatively slow-rate of diffusion in solutions. See Molecularity Order Transition-State Theory Collision Theory Elementary Reactions... 

The termolecular reaction 2NO +H2 2NOH is found to be third-order obeying the rate law r = K[NO]2 [H]... 

Termolecular Reactions and Pressure Dependence of Rate Constants... 

This approximate treatment of termolecular reactions can also be used to examine how the third-order, low-pressure rate constant A111 relates to the rate constants k.d, kh, and Ac. for the elementary reactions assumed to be involved. As [M] approaches zero, Aft approaches AaAc[M]/Ab, so that Aft1 is given by... 

While most reactions with which we deal in atmospheric chemistry increase in rate as the temperature increases, there are several notable exceptions. The first is the case of termolecular reactions, which generally slow down as the temperature increases. This can be rationalized qualitatively on the basis that the lifetime of the excited bimolecular complex formed by two of the reactants with respect to decomposition back to reactants decreases as the temperature increases, so that the probability of the excited complex being stabilized by a collision with a third body falls with increasing temperature. 

An alternate explanation can be seen by treating termolecular reactions as the sum of bimolecular reactions, as was illustrated in Section A.2 for the OH + SOz + M reaction. Recall that the third-order, low-pressure rate constant A 111 can be expressed as the product of the three rate constants A., Ab, and Ac for the three individual reaction steps (12), ( — 12), and (13) ... 

The 1997 recommendations for the OH + N02 rate constants (DeMore et al., 1997 Atkinson et al., 1997a, 1997b) may be systematically high (e.g., Donahue et al., 1997) at temperatures below 240 K. Thus, recent measurements at temperatures characteristic of the upper troposphere give rate constants that are smaller than the recommendations by 10-30% (Brown et al., 1999a Dransfield et al., 1999). In addition, 02 appears to be only about 70% as efficient a third body as N2 in the termolecular reaction. Using a modified form of the semiempirical equation for the rate constant in the falloff region (Chapter 5, Eq. (C)), which takes into account the variable collision efficiency /3,... 

However, the formation of the dimer in the ter-molecular reaction is sufficiently fast under stratospheric conditions that the bimolecular reactions are not important. For example, using the recommended termolecular values (DeMore et al., 1997) for the low-pressure-limiting rate constant of /c,3()0 = 2.2 X 10-32 cm6 molecule-2 s-1 and the high-pressure-limiting rate constant of k3()0 = 3.5 X 10-12 cm3 molecule-1 s-1 with temperature-dependent coefficients n = 3.1 and m = 1.0 (see Chapter 5), the effective rate constant at 25 Torr pressure and 300 K is 1.6 X 10-14 cm3 molecule-1 s-1, equal to the sum of the bimolecular channels (Nickolaisen et al., 1994). At a more typical stratospheric temperature of 220 K and only 1 Torr pressure, the effective second-order rate constant for the termolecular reaction already exceeds that for the sum of the bimolecular channels, 2.4 X 10-15 versus 1.9 X 10-15 cm3 molecule-1 s-1. 

The rate constant for paths a and b have been determined to be /q,u = 5.3 X 10-I2 i-2II// and k(llb = 1.1 X 10 l4e m/1 cm3 molecule-1 s-1, respectively (Harwood et al., 1998). At temperatures below 250 K, the termolecular reaction forming the dimer becomes relatively more important (Harwood et al., 1998). However, this self-reaction is not important because of the relatively small concentrations of BrO in the stratosphere. Reactions with CIO and HOz are much more important. 

A bimolecular reaction which would proceed with comparable velocity at the same temperature as this reaction would have a heat of activation of about 60,000 calories, as may be inferred from the table on page 96. Now termolecular collisions are about 1,000 times less frequent than bimolecular collisions at atmospheric pressure. Thus if we have a bimolecular reaction and a termolecular reaction with equal heats of activation, the rate of the latter should be at least 1,000 times smaller than that of the former at the same temperature. It will probably be more nearly 10,000 times slower, since a larger proportion of the ternary collisions are likely to be ineffective on account of unfavourable orientation of the molecules during impact. Conversely, if a termolecular reaction and a bimolecular reaction are to take place at equal rates at the same temperature, then the heat of activation of the termolecular reaction would need to be the smaller by an amount AE, such that e ElRT = 1,000 to 10,000. Thus, other things being equal, the heats of activation of termolecular reactions ought to be about 5,000 calories less at the ordinary temperature, and about 15,000 calories less at 1,000° abs., than those of bimolecular reactions. We have also to allow for the diminished duration of collisions at higher temperatures, which we can do by comparison with the nitric oxide oxidation. 

A bimolecular reaction which would take place at a rapid but measurable rate at the ordinary temperature would have a heat of activation of 12,000 to 15,000 calories, a termolecular reaction might therefore be expected to have one of 5,000 to 10,000 calories. This would mean a very small temperature coefficient. The effect of the diminishing duration of collisions is enough just to invert this. 

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... 

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