Collision theory termolecular collisions

Termolecular Reactions. If one attempts to extend the collision theory from the treatment of bimolecular gas phase reactions to termolecular processes, the problem of how to define a termolecular collision immediately arises. If such a collision is defined as the simultaneous contact of the spherical surfaces of all three molecules, one must recognize that two hard spheres will be in contact for only a very short time and that the probability that a third molecule would strike the other two during this period is vanishingly small. 

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. 

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... 

In this last expression, the preexponential factors are all similar in containing a product of two collision frequencies, a steric factor, and a mean lifetime. The latter may be approximated in a number of ways, each of which yields about 10 sec. Since bimolecular collision frequencies are about 10 liters/mole-sec, this would make Z V about 10 liters /mole -sec. The collision theory thus leads to a frequency of termolecular collisions of about 10 liters /mole -sec, which as we shall see from Table XII.9, is about the order of magnitude observed for the fastest reactions. 

The kinetic molecular theory of gases predicts that an increase in temperature increases molecular velocities and so increases the frequency of in-termolecular collisions. This agrees with the observation that reaction rates are greater at higher temperatures. Thus there is qualitative agreement between the collision model and experimental observations. However, it is found that the rate of reaction is much smaller than the calculated collision frequency in a given collection of gas particles. This must mean that only a small fraction of the collisions produces a reaction. Why ... 

In its simplest form the collision theory is applicable only to bimolecular elementary reactions. With additional assumptions it can be applied to first-order reactions, and with some elaboration it is applicable to termolecular elementary reactions. As an example, we choose an elementary reaction of the type... 

The problem of termolecular reactions can be treated by collision theory also. A number of such reactions are known reactions of NO with H2, O2, CI2 are famous examples. If we choose the reaction with oxygen. 

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 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. 

This problem was resolved in 1922 when Lindemann and Christiansen proposed their hypothesis of time lags, and this mechanistic framework has been used in all the more sophisticated unimolecular theories. It is also common to the theoretical framework of bimolecular and termolecular reactions. The crucial argument is that molecules which are activated and have acquired the necessary critical minimum energy do not have to react immediately they receive this energy by collision. There is sufficient time after the final activating collision for the molecule to lose its critical energy by being deactivated in another collision, or to react in a unimolecular step. 

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... 

An alternative method of treating termolecular reactions which avoids the formal difficulty of defining the conditions for ternary collisions is that of estimating the partition functions for the transition state. The procedure has already been illustrated (p. 382). The formal superiority of the theory is, however, counterbalanced by the arbitrariness of the molecular constants assigned to the transition complex. 

O. Termolecular processes and sticky colhsions. Third-atom-assisted processes are often assumed in chemical kinetics. A notable example is in recombination processes, e.g., O + O2 + M -> O3 + M, where the fimction of the third body, M in the example, is to take away energy and thereby stabilize the new ozone molecule. It is reasonable to conjecture that the reaction proceeds by a two-step process where, in the first step, O + O2 (or O2 + M) imder-goes a collision where a long-living complex is formed and it lives for long enough to collide with M (or with O). (a) Use RRKM theory to estimate the lifetime of the unrelaxed O3 complexes formed from thermal O + O2. (Go for, or estimate, the data that you need.) (b) The complex needs to collide with M before it dissociates. Is the estimated lifetime sufficient if the pressure is, say, an atmosphere ... 

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