Description of Elementary Chemical Reactions

It is the combination of individual elementary reaction steps, each with its own rate law, that determines the overall kinetics of a reaction. Elementary reactions have simple rate laws of the form 

This chapter presents the underlying fundamentals of the rates of elementary chemical reaction steps. In doing so, we outline the essential concepts and results from physical chemistry necessary to provide a basic understanding of how reactions occur. These concepts are then used to generate expressions for the rates of elementary reaction steps. The following chapters use these building blocks to develop intrinsic rate laws for a variety of chemical systems. Rather complicated, nonseparable rate laws for the overall reaction can result, or simple ones as in equation 6.1-1 or -2. 

An elementary step must necessarily be simple. The reactants are together with sufficient energy for a very short time, and only simple rearrangements can be accomplished. In addition, complex rearrangements tend to require more energy. Thus, almost all elementary steps break and/or make one or two bonds. In the combustion of methane, the following steps (among many others) occur as elementary reactions  

These two steps are simple rearrangements. The overall reaction 

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V. Aquilanti, S. Cavalli, G. Grossi, and A. Lagana, Nonadiabatic effects in the hyperspherical description of elementary chemical reactions. J. Mol. Struct., 107 95-99, 1984. 

The last few years have seen dramatic advances in the rigorous theoretical description of elementary chemical reactions, i.e. in exact quantum mechanical reactive scattering calculations [1 6]. These theoretical developments are especially timely because of parallel advances in experimental studies of elementary reactions [7-12]. Several groups have reported new studies of the H+H2, D+H2, and H-1-D2 reactions, and this makes possible comparisons of unprecedented detail between theory and experiment. Most intriguing are the integral cross section results of Nieh and Valentini [10, 11] for the reaction... 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

Mechanism I illustrates an important requirement for reaction mechanisms. Because a mechanism is a summary of events at the molecular level, a mechanism must lead to the correct stoichiometry to be an accurate description of the chemical reaction. The sum of the steps of a mechanism must give the balanced stoichiometric equation for the overall chemical reaction. If it does not, the proposed mechanism must be discarded. In Mechanism I, the net result of two sequential elementary reactions is the observed reaction stoichiometry. 

The chemical kineticists of the previous century developed a phenomenological understanding of chemical change that provided an accurate description of many chemical reactions in vitro. This description is known as the Law of Mass Action and is now rationalized in terms of certain probability considerations, which in turn can be represented by empirically determined rate constants and the concentrations of reactants. Let us begin with two elementary cases. 

The differential diffusion coefficients are characteristic of any mechanically normal and chemically stable equilibrium mixture they represent properties of state. This reminds us of the necessity in (non-dilute) chemical kinetics of assuming a small change, so that the medium effects will not turn the rate constants into variables of time. This fact regarding the elementary description of a chemical reaction rate is not always explicitly stated in the texts. The reasons may be that a chemical change has often been conveniently measured only in a rather limited concentration range of the reactants and that most experiments have been confined to dilute solutions. If this simplification were not introduced, the kinematics in question would, for instance, contain partial volumes. 

The above described statements are confirmed by theory. The authors of works [207,208] established the concept of constant velocity spectrum of elementary chemical reactions, which is due to the different levels of reciprocal arrangement of reactive molecules. This concept is used for the description of chemical processes in liquid condensed systems within the polychronic kinetics model [209,210]. The level of structural organization is characterized by the orientation order parameter a, similar in its physical sense to orientation interaction coefficient 8, which was used by the authors of works referred to in Part 2.6.4. Parameter a can vary from 0 (isotropic system) to 1 (maximum anisotropy, the molecules are parallel). 

A reaction mechanism is a step-by-step detailed description of a chemical reaction. Each step in a mechanism is called an elementary process, which describes any molecular event that significantly alters a molecule s energy or geometry or produces a new molecule. Two requirements of a plausible reaction mechanism are that it must... 

Reaction Mechanisms—A reaction mechanism is a step-by-step description of a chemical reaction consisting of a series of elementary processes. Rate laws are written for the elementary processes and combined into a rate law for the overall reaction. To be plausible, the reaction mechanism must be consistent with the stoichiometry of the overall reaction and its experimentally determined rate law. 

Mechanisms. Mechanism is a technical term, referring to a detailed, microscopic description of a chemical transformation. Although it falls far short of a complete dynamical description of a reaction at the atomic level, a mechanism has been the most information available. In particular, a mechanism for a reaction is sufficient to predict the macroscopic rate law of the reaction. This deductive process is vaUd only in one direction, ie, an unlimited number of mechanisms are consistent with any measured rate law. A successful kinetic study, therefore, postulates a mechanism, derives the rate law, and demonstrates that the rate law is sufficient to explain experimental data over some range of conditions. New data may be discovered later that prove inconsistent with the assumed rate law and require that a new mechanism be postulated. Mechanisms state, in particular, what molecules actually react in an elementary step and what products these produce. An overall chemical equation may involve a variety of intermediates, and the mechanism specifies those intermediates. For the overall equation... 

Development of the quantum mechanical theory of charge transfer processes in polar media began more than 20 years ago. The theory led to a rather profound understanding of the physical mechanisms of elementary chemical processes in solutions. At present, it is a good tool for semiquantitative and, in some cases, quantitative description of chemical reactions in solids and solutions. Interest in these problems remains strong, and many new results have been obtained in recent years which have led to the development of new areas in the theory. The aim of this paper is to describe the most important results of the fundamental character of the results obtained during approximately the past nine years. For earlier work, we refer the reader to several review articles.1 4... 

The brief review of the newest results in the theory of elementary chemical processes in the condensed phase given in this chapter shows that great progress has been achieved in this field during recent years, concerning the description of both the interaction of electrons with the polar medium and with the intramolecular vibrations and the interaction of the intramolecular vibrations and other reactive modes with each other and with the dissipative subsystem (thermal bath). The rapid development of the theory of the adiabatic reactions of the transfer of heavy particles with due account of the fluctuational character of the motion of the medium in the framework of both dynamic and stochastic approaches should be mentioned. The stochastic approach is described only briefly in this chapter. The number of papers in this field is so great that their detailed review would require a separate article. 

For elementary chemical reactions, it is sometimes possible to assume that all chemical species reach their chemical-equilibrium values much faster than the characteristic time scales of the flow. Thus, in this section, we discuss how the description of a turbulent reacting flow can be greatly simplified in the equilibrium-chemistry limit by reformulating the problem in terms of the mixture-fraction vector. 

An elementary description of the course of any chemical reaction by the amount of substance used up or generated in that reaction. Consider the general reaction ... 

I learned about chemical reactors at the knees of Rutherford Aris and Neal Amundson, when, as a surface chemist, I taught recitation sections and then lectures in the Reaction Engineering undergraduate course at Minnesota. The text was Aris Elementary Chemical Reaction Analysis, a book that was obviously elegant but at first did not seem at all elementary. It described porous pellet diffusion effects in chemical reactors and the intricacies of nonisothermal reactors in a very logical way, but to many students it seemed to be an exercise in applied mathematics with dimensionless variables rather than a description of chemical reactors. 

The set of elementary reactions that allows a qualitative and quantitative description of major characteristics of the process studied to be made, will be termed the mechanism of the chemical reaction. A mechanism consisting only of linear steps will be described as a linear mechanism. In our further exposition we shall study only linear mechanisms although a large number of reactions proceed via a nonlinear mechanism, e.g. they include elementary reactions having rates that depend nonlinearly on the concentration of the ISCs. These classes of mechanisms can be formally described within the framework of a linear model if the assumption is made that the nonlinear steps are equilibria which proceed at a high rate so that it is possible to combine them with slow linear steps. 

The description of complex photochemical reactions is facilitated by subdividing the total reaction into a series of elemental steps, of which the primary (or initiation) process follows the absorption of a photon, and the subsequent processes are thermal (or dark) reactions. The interaction of solar radiation with the atmosphere and its constituents, and the ensuing primary photochemical processes are examined in this chapter. Dark reactions will be discussed whenever appropriate. The identification of the individual reaction steps and their characterization by rate laws are the subject of chemical kinetics. Some familiarity with reaction kinetics and the behavior of elementary reactions is essential to the discussion of atmo-... 

For the rest of Part 1 of this book, we turn our attention to the discussion of just how chemical reactions occur and, as a consequence, we adopt a more theoretical viewpoint. To begin such a discussion we extend the description of elementary reactions that we started in Section 2.1. You should recall from that section that an elementary reaction is one which takes place in a single step, does not involve the formation of any intermediate species, and which passes through a single transition state. 

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. 

The mechanism of a chemical reaction is a microscopic description of the reaction in terms of its constituent elementary reactions. The fnndamental principle from which one starts is that the rate of an elementary reaction is proportional to the freqnency of collisions indicated by the sto-ichiometric/mechanistic eqnation for the reaction (i.e., to the prodnct of the concentrations indicated by the molecu-larity of the elementary reaction). In addition, one usually bases the analysis on one or more of the following simplifications to make the mathematics amenable to closed-form solntion. 

Most of the classical, semiclassical and quantal calculations of transition probabilities (or cross sections) refer to colinear atom-diatom gas phase reactions. However, a consideration of the nonlinear collisions seems to be very important for an adequate description of the chemical elementary processes in physical space. Quite recently, encouraging progress in this direction has been made / /. 

The theory of kinetics as a theory of an intermediate substance serves first of all to solve two main problems. The first problem is the quantum-chemical description of elementary acts, the total of which makes up a chemical process. This problem includes questions about the determination of the nature of intermediate substances and their thermodynamic characteristics, composition and structure of activated complexes of an elementary reaction for the calculation of the activation energy and entropy. Thus, we talk about a full or partial description of a topographic map of the potential energy of a system, which provides the information about potential holes, corresponding to the states of an intermediate substance, and an activated barrier separating one hole from another. The presence of. such a topographic map of the potential energy of a s)fstem exactly determines the so-called chemical mechanism of a reaction. 

The vast majority of stoichiometric reactions do not occur by transformation of the reactants to the products in a single step rearrangement of the constituent atoms. They occur via a series of reactive interactions at the atomic and molecular levels, and they involve reactive chemical species that are formed and then entirely consumed, so they do not appear in the stoichiometric equation. These molecular level interactions are called elementary chemical reactions. The reactants and products in an elementary reaction may be atoms, molecules, free radicals, ions, excited states, etc. An elementary chemical reaction is an isolated interaction between such species in which the transformation from reactants to products occurs by rearrangement of the constituent atoms. Elementary reactions are fundamental descriptions of how chemical transformations occur. The list of elementary reactions that take place during the course of a stoichiometric reaction is called the mechanism of the reaction. The mechanism thus embodies the detailed atomic and molecular level chemistry that accounts for the overall chemistry that is observed in a stoichiometric reaction. 

It should be stressed that the wave-packet picture of photophysical relaxation and photochemical reaction dynamics described in this chapter is substantially different from the traditional concepts in this area. In contrast to the established picture of radiationless transitions in terms of interacting tiers of zero-order molecular eigenstates, the dynamics is rationalized in terms of local properties of PE surfaces such as slopes, barriers and surface intersections, a view which now becomes widely accepted in photochemistry. This picture is firmly based on ah initio electronic-structure theory, and the molecular relaxation d3mamics is described on the basis of quantum mechanics, replacing previously prevaUing kinetic models of electronic decay processes. Such a more detailed and rigorous description of elementary photochemical processes appears timely in view of the rich and specific information on ultrafast chemical processes which is provided by modern time-resolved spectroscopy. " ... 

A balanced chemical eqnation is a description of the overall result of a chemical reaction. However, what actually happens at the molecular level may be more involved than is represented by this single equation. The reaction may take place in several steps. In the next sections, we will examine some reactions and see how the rate law can give us information about these steps, or elementary reactions. 

Chemical kinetics describes the progress of a chemical reaction. The most common description of the progress is given by the term rate of reaction —a positive quantity that expresses how the concentration of a reactant or product changes with time. For the elementary reaction... 

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