Elementary reactions, pressure effects

In this chapter, we will study the elementary reaction steps of these mechanisms focusing primarily on the anthraphos systems. This chapter begins with a description of the impact of different methods (coupled cluster, configuration interaction and various DFT functionals), different basis sets, and phosphine substituents on the oxidative addition of methane to a related Ir system, [CpIr(III)(PH3)Me]+. Then, it compares the elementary reaction steps, including the effect of reaction conditions such as temperature, hydrogen pressure, alkane and alkene concentration, phosphine substituents and alternative metals (Rh). Finally, it considers how these elementary steps constitute the reaction mechanisms. Additional computational details are provided at the end of the chapter. 

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. 

However, when the adsorption/desorption of C is fast in comparison with the elementary reaction steps, the third term in the right side of eq. 7.180 can be neglected. In that instance, the selectivity does not depend on the pressure of B and the selectivity pattern is the same for gas and liquid phase reactions, even if the adsorption properties (and therefore effective charges) differ substantially. 

In large part, the chemistry we meet in practice takes place in a solution of some kind, but a quantitative description of the chemical kinetics involved is much more complex than for gaseous reactions. The key difference lies in the interparticle distances. In a gas at atmospheric pressure, the particles occupy less then 1 % of the total volume and, effectively, move independently of each other. In a solution the solute and solvent molecules, with the latter being in the majority, take up more than 50% of the available space, the distances between the various species are relatively small, and each particle is in continuous contact with its neighbours. It is these interactions which greatly complicate the formulation of a satisfactory theory of chemical kinetics in solution. Indeed, the rate of an elementary reaction and for that matter a composite reaction, can be significantly influenced by the choice of solvent. 

Quantum chemistry has estabhshed itself as a valuable tool in the studies of polymerization processes [25,26]. However, direct quantum chemical studies on the relationship between the catalyst structure and the topology of the resulting polymer, as well as on the influence of the reaction conditions, are not practical without the aid of statistical methods. We have to this end proposed a combined approach in which quantum chemical methods are used to provide information on the microscopic energetics of elementary reactions in the catalytic cycle, that is required for a mesoscopic stochastic simulations of polymer growth [25]. A stochastic approach makes it possible to discuss the effects of temperature and olefin pressure. 

Chapter 6 presents estimations of thermochemical properties of intermediates, transition states and products important to destruction of the aromatic ring in the phenyl radical + O2 reaction system. We have employed both DFT and high-level ab initio methods to analyze the substituent effects on a number of chemical reactions and processes involving alkyl and peroxyl radicals. Partially based on the results obtained in the vinyl system, high-pressure-limit kinetic parameters are obtained using canonical Transition State Theory. An elementary reaction mechanism is constructed to model experimental data obtained in a combustor at 1 atm, and in high-pressure turbine systems (5-20 atm), as well as in supercritical water [31]. 

Studies show that the measured composition of the product mixture at constant temperature depended on the water density (Fig. 7.7). This was taken as an indication that these products could be formed by competing ionic and free-radical reaction pathways. Usually in gas-phase kinetics the product composition changes with temperature because of the different activation energies and, to a minor extent with pressure, mainly because of the concentration effect on bimolecular elementary reaction steps. In water, the drastic dependence on pressure is likely a consequence of the competition between reactions with different polarity. Free radical reaction rates (involving large free radicals beyond the RRKM high-pressure limit, see, for example, [25]) should decrease with pressure as a result... 

The effect of pressure P, on the rate of an elementary reaction at constant temperature is given by the Equation (2.23). 

The basis of the models consisting of elementary reactions are well investigated gas phase models [e.g. 27,28,29]. The gas phase models are transformed to higho pressure conditions by increasing the reaction rate of the elementary reactions as a consequence of the increased energy transfer at higho pressure. No specific solvent effect of water is considered. 

The model description of the measured differences in high pressure oxidation is not satisfactory concerning the influence of small wato amounts. Eiiher the model is not complete or th e is a specific solvent effect in addition to the pressure effect on the chemical kinetics. Until now the reaction rate of elementary reactions at high pressure has been measured only in helium [e.g. 32] Calculation of the fugacity coefficients of the HO2 free radical in supCTcritical water also shows specific solvent interactions as a consequence of partial charges [33]. It can be assumed that these inta actions are much lower in supCTcritical carbon dioxide which may lead to somewhat different reaction rates of elementary reactions in the reaction network. 

One of the objectives of this book is to demonstrate how the overall reaction rate of a catalytic reaction can be predicted once the rate constants and equilibrium constants of the elementary reaction steps are known. Such data can be obtained from model experiments, often in surface science, or from theoretical calculations. The ammonia synthesis was among the first catalytic reactions for which the rate was predicted under high pressure conditions. This was a remarkable success, as the calculation involved an extrapolation of data obtained under vacuum over a pressure interval of ten orders of magnitude. Here the effective rate constant of a less complex reaction is derived, the oxidation of carbon monoxide on platinum. We will use the reaction mechanism of Scheme (6.1) and label rate and equilibrium constants according to the number of the elementary steps in (6.1). 

The effect of pressure on the gas-phase process can manifest itself, in particular, through the pressure dependence of the rate constants of the elementary reactions comprising the mechanism of the process. However, at pressures above 10 atm, most of the elementary reactions of the mechanism of methane partial oxidation occur almost in the high-pressure-limit mode i.e., only slightly depend on the pressure. 

In these equations, A is the change in the reaction volmne, given by the difference between the partial molar volmnes of the product(s) and the reactant(s) and R is the imiversal gas constant. The equation for the pressure effect on concentration-based equilibrium constant (Eq. (3)) has an additional term that accoimts for the volmne effects, that is, the isothermal compressibility Kj of the reaction mixture and the stoichiometric coefficients v j. According to transition-state theory [4], for elementary reactions, the variation of the magnitude and direction of the mole fraction based rate constant with... 

---