High-pressure rate coefficients

According to Eqs. (2.8) and (3.1), the high-pressure limiting rate coefficient fcoo.diss is given by 

In this pressure range the actual populations of excited molecular states are close to the equilibrium populations given by f. The rate coefficient /c2 is therefore the thermal equilibrium average of the specific rate coefficient k(E) of the unimolecular reaction. The rate coefficient for the reverse recombination of a simple bond fission reaction 

Equation (4.1) can be expressed in the form of transition-state theory (Chapter 3) 

We do not intend to discuss these approaches but propose instead a simpler procedure which is not much more empirical than they are. Here we have to distinguish various cases. 

Reactions with small energy barriers H + C2H2C2H3 5.5 X 10 3 exp(-1210/7) (d) 

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Fig. 6. High-pressure rate coefficients of the unimolecular decomposition of hydrazine , 1.5-5x 10 5 mole.l-1 N2H4 A,9-14xl0-5 mole.l 1 N2H , 18-28X10"5 mole.l 1 N2H4. (From Olschewski et a/.sl.)... 

From the experiments with the lowest N2H4 concentrations, an Arrhenius expression for the high-pressure rate coefficient... 

High-Pressure Rate Coefficients for Elementary Reactions"... 

At these low pressures the reaction is in the second-order region of the unimolecular falloff, and low-pressure-limit rate coefficients, k0, are obtained. A master equation calculation was used to obtain the critical energy, E0, and average energy transferred per collision, from which an expression for the high-pressure rate coefficient was obtained. 

The limiting, high pressure rate coefficient is found by setting cj = °°. 

In order to compare the experimental results at 416 K with theoretical predictions, / 4aatlhe higher temperature was calculated from the transition state theory expression. For model A and A this indicated that k should increase by a factor of 1.6 and for model B by 1.2 times. The positive temperature coefficient is associated with the low bending frequencies in the complex and decreases if these are replaced by rotations. Where the radicals are completely free to rotate in the complex then the high pressure rate coefficient becomes proportional to T. A comparison of the curves in fig. 5 and 6 indicates that the temperature dependence of the rate in the transition range is well represented only when it is assumed that k4. is approximately the same at 416 K as at 300 K. 

The pressure dependence of k of the fully NO inhibited reaction was studied by Forst and the limiting high pressure rate coefficient found by extrapolation to have the value 10 exp (—55,500/RT) sec ... 

As with the dissociation methods of Section 2.4.3. the calculated rate depends on w, P E/E ) and k E). In the results discussed shortly calculated using the ILT method the only difference being that this time it is the parameters A , n and that are to be determined. In the iso-propyl case the parameters APt and AE)a were floated but for the methyl association scheme these are known from previous experiments and ab initio calculations. The fitting of all three parameters simultaneously would yield a x hypersurface which in principle can be explored and minimized just as any other surface. For reasons related to the fitting of the isopropyl data it was found convienent to reduce the number of parameters fitted. This was achieved by prescribing that the high pressure rate coefficient at 300 K which was fixed at 6.0 x 10 cm molecule s a value that has been accurately measured by a number of groups (see Baulch et al. [28]). 

The described procedme for modeling the limiting low and high pressure rate coefficients ko and k and the falloff curves interpolating between these values, can be... 

Table 4. High-pressure rate coefficients for elimination reactions .

This is a very important reaction both for flame propagation and ignition, since it competes with the oxidation reactions of CH3. Furthermore, it is an important source of C2-hydrocarbons in methane combustion, leading eventually to the formation of soot and NO in rich flames of CH4. Values of the high-pressure rate coefficient are given in Fig. 34. The pressure dependence of this reaction is well known examples of fall-ofl curves are given in Fig. 35. No recommendation of the low-pressure rate coefficient can be derived from experimental data, but values calculated from the reverse reaction rate coefficient should be reliable at high temperature. 

Figure 34. High-pressure rate coefficient of the reaction CHj -I- CHj - CjHg. References in Table 7 and in the review of Baulch and Duxbury (1980). Fall-off curves are given in Fig. 35.

The reverse of this step has been discussed before (Section 5.2). There are sufficient rate data on the pressure dependence of this reaction to allow the determination of Arrhenius parameters for low- and high-pressure rate coefficients and (Fig. 55). Examples of fall-off curves are given in Fig. 36. 

This is an important and often rate-determining step because of the formation of H atoms (Fig. 4). The high-pressure rate coefficient is well defined by a number of measurements and by determination from the reverse reaction (Fig. 59). Fall-off curves are shown in Fig. 60. 

Figure 61. High-pressure rate coefficient Table 15. Fall-off curves are given in Fig. 60.

For this pressure-dependent reaction some rate data are available for the low-pressure rate coefficient /co high temperature, whereas there is a lack of information about the high-pressure rate coefficient (Fig. 66). Fall-off curves are presented in Fig. 67. 

This reaction has been extensively investigated only at low temperature, where the rate coefficient was found to be pressure dependent (Perry et a/., 1977 Michael et a/., 1981). At first glance, the high-temperature measurements and the high-pressure rate coefficient extrapolated from low temperature seem to match one another (Fig. 71). However, the high-temperature measurements... 

Figure 83. High-pressure rate coefficient for CsHg - CH3 -f C2H5. References in Table 25.

Figure 88. High-pressure rate coefficients for the reactions + H - and C3H6 + H - References in Table 27.

Figure 95. High-pressure rate coefficient of n-CJiiQ-ences in Table 29.

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