Chemical reaction collision theory

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A]"[B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus... 

As in all mathematical descriptions of transport phenomena, the theory of polydisperse multiphase flows introduces a set of dimensionless numbers that are pertinent in describing the behavior of the flow. Depending on the complexity of the flow (e.g. variations in physical properties due to chemical reactions, collisions, etc.), the set of dimensionless numbers can be quite large. (Details on the physical models for momentum exchange are given in Chapter 5.) As will be described in detail in Chapter 4, a kinetic equation can be derived for the number-density function (NDF) of the velocity of the disperse phase n t, X, v). Also in this example, for clarity, we will assume that the problem has only one particle velocity component v and is one-dimensional in physical space with coordinate x at time t. Furthermore, we will assume that the NDF has been normalized (by multiplying it by the volume of a particle) such that the first three velocity moments are... 

D. G. Truhlar and D. A. Dixon, Direct-mode chemical reactions Classical theories, Atom-Molecule Collision Theory (R. B. Bernstein, ed.), Plenum, New York, 1979, p. 595. 

There are two major theories of chemical kinetics, collision theory (CT) and transition-state theory (TST). Both theories lead to rate equations that obey Generalization I, i.e., the effects of temperature and concentration are separable. Unfortunately, both CT and TST apply to a very limited category of reactions known as elementary reactions. An elementary reaction is one that occurs in a single step on the molecular level exactly as written in the balanced stoichiometric equation. The reactions that chemists and chemical engineers deal with on a practical level almost never are elementary. However, elementary reactions provide the link between molecular-level chemistry and reaction kinetics on a macroscopic level. Elementary reactions will be discussed in some depth in Chapter 5. For now, we must look at Eqn. (2-1) as an empirical attempt to extrapolate a key result of CT and TST to complex reactions that are outside the scope of the two theories. 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

Baer M (ed) 1985 Theory of Chemical Reaction Dynamics (Boca Raton, FL CRC Press) vols 1-4 Bernstein R B (ed) 1979 Atom-Molecule Collision Theory A Guide for the Experimentalist (New York Plenum)... 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

These observations remind us of Chapter 8, in which we considered the factors that determine the rate of a chemical reaction. Of course, the same ideas apply here. We can draw qualitative information about the mechanism of the reaction by applying the collision theory. With quantitative study of the effects of temperature and concentration on the rate, we should be able to construct potential energy diagrams like those shown in Figure 8-6 (p. 134). 

North, A. M. (1964) The Collision Theory of Chemical Reactions in Liquids. Methuen, London [3.3]. 

FIGURE 13.25 (a) In the collision theory of chemical reactions, reaction may take place only when two molecules collide with a kinetic energy at least equal to a minimum value, /rmn (which later we identify with the activation energy), (b) Otherwise, they simply bounce apart. 

A gas composed of molecules of diameter 0.5 nm takes part in a chemical reaction at 300. K and 1.0 atm with another gas (present in large excess) consisting of molecules of about the same size and mass to form a gas-phase product at 300. K. The activation energy for the reaction is 25 kj-mol. Use collision theory to calculate the ratio of the reaction rate at 320. K relative to that at 300. K. 

Kinetics on the level of individual molecules is often referred to as reaction dynamics. Subtle details are taken into account, such as the effect of the orientation of molecules in a collision that may result in a reaction, and the distribution of energy over a molecule s various degrees of freedom. This is the fundamental level of study needed if we want to link reactivity to quantum mechanics, which is really what rules the game at this fundamental level. This is the domain of molecular beam experiments, laser spectroscopy, ah initio theoretical chemistry and transition state theory. It is at this level that we can learn what determines whether a chemical reaction is feasible. 

Collisions play a tremendously important role in stimulating reacting systems to cross the activation barrier. The theory of Lindemann emphasizes this and provides us with a method to describe the influence of the surrounding medium upon a chemical reaction. It gives important insight into the conditions under which the reaction rate theories discussed here are valid. 

The rate is thus the number of collisions between A and B - a very large number - multiplied by the reaction probability, which may be a very small number. For example, if the energy barrier corresponds to 100 kj mol , the reaction probability is only 3.5 x lO l at 500 K. Hence, only a very small fraction of all collisions leads to product formation. In a way, a reaction is a rare event For examples of the application of collision theory see K.J. Laidler, Chemical Kinetics 3 Ed. (1987), Harper Row, New York. 

The science of reaction kinetics between molecular species in a homogeneous gas phase was one of the earliest fields to be developed, and a quantitative calculation of the rates of chemical reactions was considerably advanced by the development of the collision theory of gases. According to this approach the rate at which the classic reaction... 

Reaction Rates, Chemical, Collision Theory of (Widom). Reaction Rates, Chemical, Large Tunnelling Corrections 5 353... 

According to collision theory, the collision between the reactant molecules is the first step in the chemical reaction. The rate of reaction will be proportional to the number of collisions per unit time between the reactant, but it has been observed that not every collision between the reactant molecules results in a reaction. When we compare the calculated number of collisions per second with the observed reaction rate, we find that only a small fraction of the total number of collisions is effective. There can be following reasons why a collision may not be effective. 

Letter from G. N. Lewis to Paul Ehrenfest, undated but probably 1925, G. N. Lewis Correspondence, BL.UCB. G. N. Lewis and D. F. Smith promised in their paper, "The Theory of Reaction Rate," JACS 47 (1925) 15081520, to publish a demonstration that a range of frequencies of radiation affecting degrees of freedom in a molecule is responsible for chemical reaction. This paper was the subject of the letter, with anonymous referee s report, from Arthur B. Lamb to G. N. Lewis, 28 February 1925, G. N. Lewis Papers, BL.UCB. The referee said "No real unimolecular reaction has actually been observed they have been shown to be merely catalytic the idea that a unimolecular reaction is due to collision between a quantum and a molecule is not original with Lewis."... 

The collision theory describes how the change in concentration of one reactant affects the rate of chemical reactions. In this laboratory experiment, you will observe how concentration affects the reaction rate. 

In most chemical reactions the rates are dominated by collisions of two species that may have the capability to react. Thus, most simple reactions are second-order. Other reactions are dominated by a loose bond-breaking step and thus are first-order. Most of these latter type reactions fall in the class of decomposition processes. Isomerization reactions are also found to be first-order. According to Lindemann s theory [1, 4] of first-order processes, first-order reactions occur as a result of a two-step process. This point will be discussed in a subsequent section. 

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