Bimolecular Chemical Activation Reactions

Total pressure also affects the rate constant for a class of bimolecular reactions called chemical activation reactions. A generic example is the reaction of molecules A and B to form products D and E, but where an alternate reaction is recombination of the reactants to form the stable molecule C. An example of this type of chemical activation reaction reaction is 

The theoretical analysis of chemical activation reactions is similar to the Lindemann theory of unimolecular and association reactions. There are a number of competing reaction pathways. Depending on total pressure, concentrations of the participating species, and temperature, the outcome of the competition can change. 

Consider the sequence of elementary steps for the A + B reaction system  

In reaction 9.132, molecules A and B form the excited (energized) reactive intermediate species C. Translational energy of the reactant molecules from their relative motion before collision is converted to internal (vibrational, rotational) energy of C. Reaction 9.132 provides a chemical activation (excitation) of the unstable C, with rate constant ka. Note that 9.132 does not involve a third body M for creation of the excited intermediate species, which differs from the unimolecular initiation event in Eq. 9.100. 

The subsequent fate of C is a competition among the other reactions listed in the scheme. The reverse of reaction 9.132 occurs when the highly energetic C decomposes unimolecularly back to the reactant molecules, with rate constant kd, the internal energy in its vibrations is converted to relative translational motion of A and B when C falls apart. 

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The treatment given in this section is analogous to the Lindemann theory of unimolecu-lar reactions. It provides a general explanation of pressure effects in bimolecular chemical activation reactions. A more sound theoretical treatment of chemical activation kinetics is given in Section 10.5. 

Transition-state theory is based on the assumption of chemical equilibrium between the reactants and an activated complex, which will only be true in the limit of high pressure. At high pressure there are many collisions available to equilibrate the populations of reactants and the reactive intermediate species, namely, the activated complex. When this assumption is true, CTST uses rigorous statistical thermodynamic expressions derived in Chapter 8 to calculate the rate expression. This theory thus has the correct limiting high-pressure behavior. However, it cannot account for the complex pressure dependence of unimolecular and bimolecular (chemical activation) reactions discussed in Sections 10.4 and 10.5. 

Fig. 10.8 Reaction pathways in the QRRK analysis of bimolecular chemical activation reactions.

The QRRK treatment of bimolecular chemical activation reactions considers in more detail the energy-dependence of the rate coefficients. Begin by modifying the chemical activation reaction scheme of Eqs. 9.132 to 9.134 to account for the specific energy levels of the rate constants and activated species. 

Using the results obtained on the phenyl system for the dibenzofuran + O2 system, kinetics of each path, as a function of temperature and pressure are determined using bimolecular chemical activation analysis. The high-pressure-limit kinetic parameters from the calculation results are again obtained with cannonical Transition State Theory. QRRK analysis is utilized to obtain k(E) and master analysis is used to evaluate the fall-off behaviour of this complex bimolecular chemical activation reaction [34]. 

Unimolecular dissociation and isomerization reactions of chemically activated and stabilized adduct resulting from addition or combination reactions are analyzed by constructing potential energy diagrams. Some high-pressure rate constants for each channel are obtained from literature or referenced estimation techniques. Kinetics parameters for uni-molecular and bimolecular (chemical activation) reactions are then calculated using multifrequency QRRK analysis iork(E) [199, 200, 63]. 

High pressure limit kinetic parameters are obtained from the calculation resulting from the Canonical Transition State Theory. Quantum RRK analysis is utilized to obtain k(E) and master equation analysis is used to evaluate fall-off in this bimolecular, chemically activated reaction system. The Phenyl + O2 association results in a chemically activated phenyl-peroxy... 

These are easily the largest values ever observed for bimolecular, chemically controlled reactions and imply an enormously loose transition state complex. Since collision frequencies are of the order of 1011 3 liter/mole-sec. we see that we need to account for a positive entropy of activation of the order of 4 Gibbs/mole. 

Fig. 9.2 Bimolecular rate constant for the chemical activation reaction 9.151 as a function of pressure for three different temperatures.

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

Pressure effects are also seen in a class of bimolecular reactions known as chemical activation reactions, which were introduced in Section 9.5. The treatment in that chapter was analogous to the Lindemann treatment of unimolecular reactions. The formulas derived in Section 9.5 provide a qualitative explanation of chemical activation reactions, and give the proper high- and low-pressure limits. However, that simple treatment neglected many quantum mechanical effects, namely the energy dependence of various excitation/de-excitation steps. 

This section treats the theory of chemical activation reactions more rigorously, at the same level of approximation as in the discussion of unimolecular reactions in Section 10.4.4. That is, the QRRK theory of chemical activation reactions is developed here. This theory for bimolecular reactions was set out by Dean and coworkers [93,428],... 

The reaction of H with O2 is an example of a bimolecular chemical activation system. These species can form the stabilized product HO2 via the reaction... 

Multifrequency Quantum Rice-Ramsperger-Kassel (QRRK) is a method used to predict temperature and pressure-dependent rate coefficients for complex bimolecular chemical activation and unimolecular dissociation reactions. Both the forward and reverse paths are included for adducts, but product formation is not reversible in the analysis. A three-frequency version of QRRK theory is developed coupled with a Master Equation model to account for collisional deactivation (fall-off). The QRRK/Master Equation analysis is described thoroughly by Chang et al. [62, 63]. 

The present study calculates thermochemical properties of intermediates, transition states and products important to the degradation of the aromatic ring in the phenyl radical + O2 reaction system. Kinetic parameters are developed for the important elementary reaction paths through each channel as a function of temperature and pressure. The calculation is done via a bimolecular chemical activation and master equation analysis for fall-ofif. 

In an interesting analysis of the effects of reduction of dimensionality on rates of adsorption/desorption reactions (26), the bimolecular rate of 10 M- s- has been reported as the lower limit of diffusion control. Based on this value, the rates given in Table III indicate the desorption step is chemical-reaction-controlled, likely controlled by the chemical activation energy of breaking the surface complex bond. On the other hand, the coupled adsorption step is probably diffusion controlled. 

The QRRK approach illustrated above also constitutes the basis to analyze the behavior of the reverse, i.e., association, reactions that proceed through chemically activated transition states. Recently Dean (1985) reformulated the unimolecular quantum-RRK method of Kassel and devised a practical method for the proper description of the fall-off behavior of bimolecular reactions, including reactions when multiple product channels are present. The method developed was shown to describe the behavior of a large variety of bimolecular reactions with considerable success (Dean and Westmoreland, 1987 Westmoreland et ai, 1986). 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

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... 

Transition-state theory allows details of molecular structure to be incorporated approximately into rate constant estimation. The critical assumption of transition-state theory is that quasi-equilibrium is established between the reactants and an activated complex, which is a reactive chemical species that is in transition between reactants and products. The application of transition-state theory to the estimation of rate constants can be illustrated by the bimolecular gas-phase reaction... 

Heterogeneous or surface effects have been found to complicate the interpretation of kinetic experiments, which lead to erroneous Arrhenius parameters. However, with special precautions involving the use of seasoned vessels and the presence of a free-radical suppressor, the errors are minimized. Consequently, the present chapter will cover mostly homogeneous gas-phase processes. Studies on chemical activation, the use of catalysts, the bimolecular gas phase and heterogeneous reactions are not included. As an attempt to describe important pyrolyses data from 1972 to 1992, this review does not pretend to offer a complete coverage of the literature. 

Coming back to the a(C-C)/(3(C-H) primary split ratio (Table 3), it would be valuable to compare these values with that obtained either in the thermal pyrolysis of propene or in chemical activated systems. For example, in shock tube experiments (1650-2300 K), the dominant bimolecular initiation reaction leads to the C-C bond rupture, although a possible contribution of the 3(C-H) bond rupture cannot be excluded (50). This is also observed in the decomposition of hot propene formed from ethylcarbene f(E)(C3H ) s 414 kJ/mol] a(C-C)/ P(C-H) = 22 (51). Conversely, hot propene formed by the addition of singlet methylene to ethylene [(EXCsH ) s 464—492 kJ/mol) gives rise to C-H bond... 

Because of the active phenyl radical contained in the dibenzofliranyl structure, we consider that the dibenzofuranyl + O2 reaction system behaves the same way as the phenyl + O2 system. On this basis we have constructed a potential energy surface for the reaction of dibenzofuranyl radical + O2 as illustrated in Figure 7.8. The major features of this surface are very similar to those calculated for the phenyl + O2 system. As for the phenyl system, there are five reactions of high importance in the chemical activation (bimolecular reaction) of dibenzofuranyl + O2 ... 

The dissociation of molecules is one of the basic processes in chemistry the study of the kinetics of these reactions is therefore of considerable theoretical and practical interest, A simple method of obtaining information about dissociation reactions is to heat the gas to a sufficiently high temperature and then look for thermal decomposition. However for rich mixtures bimolecular reactions may well contribute to the reaction their influence must be separated out so that the unimolecular dissociation can be isolated. The rate of the primary dissociation is determined by elementary physical processes including both energy transfer between particles and internal energy flow. Dissociation reactions, isomerisation processes, photolytic reactions, dissociation of ions (e.g. in a mass spectrometer) and chemical activation experiments are closely related processes. 

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