Fall-off region

The rate constants were determined at a series of pressures in the fall-off region, and the fall-off curve was very similar to that obtained for the structural isomerization to propylene. The similarity of the two sets of data suggests that both reactions may proceed through similar reaction paths. One obvious possibility is that once again the trimethylene biradical is formed, which can undergo internal rotation followed by recyclization. An alternative transition state has been suggested which involves, as an activated complex, a much expanded cyclopropane ring in which hindered internal rotation occurs (see also Smith, 1958). 

At 5 mm the rate constant has already begun to decrease from the high-pressure value, and at 0-15 mm it is only about 13 % of the high-pressure value. Addition of inert gases in the fall-off region increases the value of the rate constant towards the high pressure limiting value. 

Ethyl bromide, in a static system, was studied at 724.5-755.1 K103. The pressure dependence for the HBr elimination was observed in its fall-off region. Evaluation of the rate coefficients was performed by using the RRKM theory and the values were compared with the experimental observation. The work reported an activation energy of 216.3 kJ moT1 and an Arrhenius A factor of 1012 5. The low-frequency factor was rationalized in terms of the formation of a tight activated complex and a molecular elimination as a prevalent reaction mode. 

These models were used to evaluate the necessary sums, densities, and moments of inertia, and eqs. (22) and (27) were integrated numerically to give k, (Fig. 12) and the calculated values of Table XVI. As was mentioned earlier in connection with ethane decomposition, we believe the thermally activated ethyl radical decomposition at 600°C. to be well into the fall-off region at pressures below atmospheric. In fact, comparison of Tables XII and XVI indicates that the fall-off behavior at 600°C. is very similar in its pressure dependence for ethyl and ethane, i.e., k, is a closely similar function of energy in both cases as shown explicitly... 

The parametric representation of unimolecular rate coefficients, both at the low pressure limit and in the fall-off region has been the result of a monumental work by Troe and his coworkers [67-71]. This work is tremendously useful for applications of unimolecular reactions to complex systems, for example to combustion or to atmospheric chemistry, as it permits accurate representation of the fall-off without having to to a time-consuming and difficult Master Equation calculation. 

The decompositions of the formyl and acetyl radicals are certain to be in the fall-off region at the pressures used in the investigations of the acetaldehyde pyrolysis. However, the complexity of the mechanism impedes any conclusion to be drawn from this system. 

The first-order initiation and second-order termination steps suggested seem to be in agreement with this observation and, at the same time, also satisfy the kinetics observed experimentally. The decomposition of the formyl radical is, however, probably in its fall-off region at the pressures studied. 

We prefer to explain the results of Herr and Noyes as well as those of Anderson and Rollefson on the pressure effect by the pressure dependence of the decomposition of the CH3CO radical. According to the Benson equation , based on the detailed theory of unimolecular reactions, the acetyl radical is in the fall-off region below a few atmospheres. O Neal and Benson demonstrated that the results, obtained in the absence of added foreign gases at low light intensities - , are in accordance with the assumption of a pressure-dependent decomposition and a homogeneous recombination of the acetyl radicals. 

The fall-off region of the methyl radical recombination lies between 1 and 100 torr (see the figures). From these data, a minimum and maximum life-time for C2H6 of approximately 10 sec and of about 10" sec, respectively, were estimated . The latter value appears short for a complex with so many degrees of freedom . 

The primary step is similar to that of azomethane. One interesting distinction from axomethane is the shift of the fall-off region to lower pressures and the increase in the effective number of oscillators (from 12 to 23). This is due to the higher efficiency of the C-F as compared to the C-H vibrations to exchange energy with the critical C-N stretching motion. 

Figure 2.13 is a sketch of the pressure dependence of a unimolecular reaction showing the two limiting conditions. The region joining the two extremes is known as the fall off region. Theories of unimolecular reactions have advanced considerably since Lindemann s initial proposal but they are still based on the same physical ideas so clearly highlighted in the Lindemann mechanism. 

There are also some other methods that provide a more accurate description of the fall-off region than does the simple Lindemann form. The details can be found in corresponding publications (see, for example, Allison, 2005 Gilbert et al., 1983 Stewart et al., 1989 Wagner and Wardlaw, 1988). Some kinetic simulation packages (e.g., CHEMKIN) optionally realize these approaches for representation of three-body reaction rates (Kee et al., 1996). 

May be In the fall-off region between secu>nd order and third order kinetics (see text and ref. 187). Calculated from the Arrhenius expression of ref. 167 at 305 K. 

---