Three-body reaction rate constants

Table 1 Three-Body Attachment Rate Constants /cm for the Reaction e Room Temperature (From Refs. 10 and 11.)...

A rather striking correlation of three-body association rate constants and D has been obtained in the recent work of Adams et From the occurrence of reactions of the type... 

In Table I, the bimolecular rate constants for C2 X3Eg and a3II which we measured are tabulated. The experiments were carried out over a wide range of laser powers, buffer gas pressures, and precursor molecule pressures to assure that the experimental data does not contain artifacts due to three body reactions, vibrational quenching, fragment diffusion, or other fragment reaction. 

Clerc and Barat " flash-photolyzed CO2 in the vacuum ultraviolet and watched CO formation by kinetic spectroscopy. They found [CO] to increase rapidly to a maximum (at about 25 i sec when [CO2] = 3 torr, [Ar] = 300 torr) and then remain constant. They attributed the observation to the reaction of excess 0( /)) with the CO produced. They calculated a rate coefficient for 0( Z)) + CO recombination of 10 l. mole . sec or 2x 10 l.mole sec depending whether or not the reaction required a third body. They noted that the third-order rate coefficient was too large for a normal three-body reaction, and suggested a long-lived intermediate complex. In two later papers " ° ° they reported the value of the second-order rate coefficient to be first 6x 10 and then 1.2 x 10 ° l.mole" sec As mentioned above, Clerc and Reiffsteck " recently reassessed the relative rates of addition of 0( J9) to CO2 and CO, and found the latter reaction to be approximately 55 times faster than the former. 

X lo cm molecule s has been reached where three-body recombination by M and quenching by M is balanced. From the slope of the plot of Icm vs. total pressure a three-body rate constant of 7 x 10 cm molecule s was determined. As a consequence, the air glowreaction proceeds by a two-body as well as by a three-body reaction. When the air glow rate constant is compared with the total recombination rate of NO + O + M, which also was measured in the chamber, it can be concluded that the air glow rate constant represents within the error limits the total recombination rate constant. Further details are given in the publications Becker et al. (1972c) and (1973). 

The present compilation of kinetic data represents the 12th evaluation prepared by the NASA Panel for Data Evaluation. The Panel was established in 1977 by the NASA Upper Atmosphere Research Program Office for the purpose of providing a critical tabulation of the latest kinetic and photochemical data for use by modelers in computer simulations of stratospheric chemistry. The recommended rate data and cross sections are based on laboratory measurements. The major use of theoretical extrapolation of data is in connection with three-body reactions, in which the required pressure or temperature dependence is sometimes unavailable from laboratory measurements, and can be estimated by use of appropriate theoretical treatment. In the case of important rate constants for which no experimental data are available, the panel may provide estimates of rate constant parameters based on analogy to similar reactions for which data are available. 

In writing rate equations for reactions of the type A + B + M AB + M, for example, reaction 5.26. one must decide whether to express the rate of the reaction as A [A][B][M] or it[A][B]. This is simply an issue of notation, since the value of the rate constant k will depend on the concentration of the third body M through its appropriate formula, as given in Appendix B. We will often choose not to explicitly indicate (M) in the rate equation for such three-body reactions, keeping in mind that the value of the rate constant will depend on [M] through its appropriate formula. 

The ny, ng, and nx are the number densities of species of A, B, and X in cm" . The rate constants are known and fixed (at least for the purposes of the computation ). The positive terms in the equation above represent formation routes to species X the negative ones represent the destruction pathways. We have assumed that the density is sufficiently low that three body reactions can be ignored. This is not always the case in astrophysical circumstances (e.g. Rawlings, 1986), but we can, of course, modify the equations accordingly. For each element included in the model we also have a conservation equation, each of which we may used to replace one equation of the form given above. 

The reactions of the bare sodium ion with all neutrals were determined to proceed via a three-body association mechanism and the rate constants measured cover a large range from a slow association reaction with NH3 to a near-collision rate with CH3OC2H4OCH3 (DMOE). The lifetimes of the intermediate complexes obtained using parameterized trajectory results and the experimental rates compare fairly well with predictions based on RRKM theory. The calculations also accounted for the large isotope effect observed for the more rapid clustering of ND3 than NH3 to Na+. 

Using laser fluorescence measurements on fuel-rich H2/02/N2 flames seeded with H2S, Muller et al. [43] determined the concentrations of SH, S2, SO, S02, and OH in the post-flame gases. From their results and an evaluation of rate constants, they postulated that the flame chemistry of sulfur under rich conditions could be described by the eight fast bimolecular reactions and the two three-body recombination reactions given in Table 8.4. 

Reaction 2-6 is sufficiently fast to be important in the atmosphere. For a carbon monoxide concentration of 5 ppm, the average lifetime of a hydroxyl radical is about 0.01 s (see Reaction 2-6 other reactions may decrease the lifetime even further). Reaction 2-7 is a three-body recombination and is known to be fast at atmospheric pressures. The rate constant for Reaction 2-8 is not well established, although several experimental studies support its occurrence. On the basis of the most recently reported value for the rate constant of Reaction 2-8, which is an indirect determination, the average lifetime of a hydroperoxy radical is about 2 s for a nitric oxide concentration of 0.05 ppm. Reaction 2-8 is the pivotal reaction for this cycle, and it deserves more direct experimental study. 

However, if it occurs, it appears to be minor. Thus, based on a review of the relevant studies reported in the literature, DeMore et al. (1997) suggest that k l0 = 4.5 X 10-l4e-1260/7 = 6.6 X 10 16 cm3 molecule 1 s 1 at 298 K. This can be compared to an effective second-order rate constant for reaction (9) at 1 atm of 1.3 X 10 12 cm3 molecule-1 s-1. In short, the two-body reaction is more than three orders of magnitude slower than the termolecular process at 1 atm pressure. 

Young and Black [184] found the three-body rate constant k = 1.5 X 10 84 cm6/sec, which is consistent with the value required by Chapman s theory. They also found the rate constant k= 3 x 10 33cm8/sec for the reaction... 

Some of the continuing approaches to reaction-rate theory that differ from either the simple collisional theory or the transition-state theory discussed here are cited on pages 98-112 of [4]. Examples of differing approaches may be found in particular in theories for rates of three-body radical-recombination processes [61]. Advances in methods for calculating rate constants relevant to the Lindemann view of unimolecular processes also are providing new information relevant unimolecular and bimolecular rates. Future work may be expected to produce further results of use in combustion problems. 

Most elementary reactions involve either one or two reactants. Elementaiy reactions involving three species are infrequent, because the likelihood of simultaneous three-body encounter is small. In closed, well-mixed chemical systems, the integration of rate equations is straightforward. Results of integration for some important rate laws are listed in Table 2.7, which gives the concentration of reactant A as a function of time. First-order reactions are particularly simple the rate constant k has units of s , and its reciprocal value (1/k) provides a measure of a characteristic time for reaction. It is common to speak in terms of the half-life ( 1/2) for reaction, the time required for 50% of the reactant to be consumed. When... 

These strong non-adiabatic effects observed in the cone-states of the upper sheet contrast with the absence of any significant effect in the H-I-H2 reactive collision. Eor instance, Mahapatra et al. [69] examined the role of these effects in the H -f H2 (v = 0, = 0) reaction probability for / = 0 and found negligible nonadiabatic coupling effects in the initial state selected probability. Subsequently, Mahapatra and co-workers [70] reported initial state-selected ICS and thermal rate constants of H -I- H2(HD) for total energies up to the three body dissociation. Again, they... 

---