Elementary reactions reaction rate theory

Bunker, D. L., Theory of Elementary Gas Reaction. Rates, pp. 48-74, Pergamon Press, Oxford, 1960. 

According to Eyring s reaction-rate theory,90 the elementary bimolecular chemical reaction between reactant species A and B proceeds through a transition-state... 

Noyes25 has proposed that application of absolute-reaction-rate theory to the elementary reactions (5) and (5a) yields the paradox that Sullivan s most recent observations23 could have been predicted regardless of the relative importance of... 

Using a simple electrostatic interaction-based model factored into reaction rate theory, the energy barrier for ion hopping was related to the cation hydration radius. The conductance versus water content behavior was suggested to involve (1) a change in the rate constant for the elementary ion transfer event and (2) a change in the membrane microstructure that affects conduction pathways. 

Bimolecular processes are very common in biological systems. The binding of a hormone to a receptor is a bimolecular reaction, as is substrate and inhibitor binding to an enzyme. The term bimolecular mechanism applies to those reactions having a rate-limiting step that is bimolecular. See Chemical Kinetics Molecularity Reaction Order Elementary Reaction Transition-State Theory... 

Under these assumptions transition state theory states that the rate constant of an elementary reaction (the rate assuming that one has the reactant in the initial state) is given by ... 

Much more can be said about the magnitude of pre-exponcntial factors and activation energies of elementary processes based on statistical thermodynamics applied to collision and reaction-rate theory [2, 61], but in view of the remark above one should be cautious in their application and limit it to well-defined model reactions and catalyst surfaces. 

The most widely used theoretical framework for elementary solution and interfacial reactions is activated complex theory (ACT), also referred to as absolute reaction rate theory, or transition-state theory (TST). The term activated complex refers to a high-energy ground-state species formed from reactants, for example. 

Wc do not attempt here to explain or justify most of the reaction rate theory which must underlie any discussion of kinetics and mechanisms. The few brief definitions have been given only as reminders, or where the concepts are particularly important in following discussion. Readers lacking the necessary elementary understanding of chemical kinetics are referred to standard physical chemistry tests. 

Various models or theories have been postulated to describe the rate of an. elementary reaction. Transition state theory (TST) is reyiewed... 

Bunker, D.L. (1966). Theory of Elementary Gas Reaction Rates. Pergamon Press, New York. Bunker, D.L. (1970). In Schlier, C., Ed., Proceedings of the International School of Physics Enrico Fermi Course XLIV Molecular Beam and Reaction Kinetics, pp. 315-319. Academic Press, New York. 

Non-RRKM behavior is discussed by W. L. Hase, in Modern Theoretical Chemistry, W. H. Miller, ed. (New York Plenum Press, 1976), Vol. 2, Part B, Chapter 3 and D. L. Bunker, Theory of Elementary Gas Reaction Rates (Oxford Pergamon Press, 1966), Chapter 3. 

D. L. Bunker, "Theory of Elementary Gas Reaction Rates" Pergamon Press, New York (1966). 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

It is worthwhile to first review several elementary concepts of reaction rates and transition state theory, since deviations from such classical behavior often signal tunneling in reactions. For a simple unimolecular reaction. A—>B, the rate of decrease of reactant concentration (equal to rate of product formation) can be described by the first-order rate equation (Eq. 10.1). 

Presently, the quantitative theory of irreversible polymeranalogous reactions proceeding in a kinetically-controlled regime is well along in development [ 16,17]. Particularly simple results are achieved in the framework of the ideal model, the only kinetic parameter of which is constant k of the rate of elementary reaction A + Z -> B. In this model the sequence distribution in macromolecules will be just the same as that in a random copolymer with parameters P(Mi ) = X =p and P(M2) = X2 = 1 - p where p is the conversion of functional group A that exponentially depends on time t and initial concen-... 

In accord with general Eyring TS theory, we may consider every elementary chemical reaction to be associated with a unique A- B supramolecular complex that dictates the reaction rate. In the present section we examine representative TS complexes from two well-known classes of chemical reactions Sn2 nucleophilic displacement reactions... 

The simple theories of reaction rates involve applying basic physical chemistry knowledge to calculate or estimate the rates of successful molecular encounters. In Section 6.3 we present important results from physical chemistry for this purpose in subsequent sections, we show how they are used to build rate theories, construct rate laws, and estimate the values of rate constants for elementary reactions. 

The two simple theories SCT and TST have been developed in the context of neutral gas-phase reactions. In this section, we consider other types of elementary reactions listed in Section 6.2.1, and include reactions in condensed phases. The rates of this diverse set of reactions, including photochemistry, can be understood with the concepts developed for gas-phase reactions. 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

Elementary reactions on solid surfaces are central to heterogeneous catalysis (Chapter 8) and gas-solid reactions (Chapter 9). This class of elementary reactions is the most complex and least understood of all those considered here. The simple quantitative theories of reaction rates on surfaces, which begin with the work of Langmuir in the 1920s, use the concept of sites, which are atomic groupings on the surface involved in bonding to other atoms or molecules. These theories treat the sites as if they are stationary gas-phase species which participate in reactive collisions in a similar manner to gas-phase reactants. 

The elementary steps in gas-phase reactions have rate laws in which reaction order for each species is the same as the corresponding molecularity. The rate constants for these elementary reactions can be understood quantitatively on the basis of simple theories. For our purpose, reactions involving photons and charged particles can be understood in the same way. 

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