Collision theory and rates of reaction

The branch of chemistry concerned with reaction rates and the sequence of elementary steps by which a chemical reaction occurs is called reaction kinetics or chemical kinetics. The study of 

We cannot see the reactions taking place between atoms and molecules but we can build a theory of the interactions taking place based on our overall model of the nature of substance. 

Having developed the atomic theory of matter as our working model of how materials are made up, it is a relatively straightforward step to think through the essential steps that need to take place for a reaction to happen. The most obvious requirement is that the particles -whether they are atoms, molecules or ions - must actually meet (or collide). 

These considerations illustrate how ideas in science converge to develop an increasingly sophisticated model of the nature of the sub-microscopic world. In the development of a scientific theory the principle of Occam s razor, with its emphasis on looking for the simplest option or explanation, can be useful. It can certainly be seen to apply to the model we have developed as the basis of reaction kinetics. However, we need to be careful in applying the razor as it cannot be the only consideration. Indeed the very basis of our ideas here, Dalton s atomic theory, was initially rejected by Ernst Mach and the logical positivists on the grounds that it was too complex. It took observations such Brownian motion and the explanations of this phenomenon put forward by Einstein to generate acceptance of the theory. 

Simple collision theory states that before a chemical reaction can occur, the following requirements must be met  

---

As in collision theory, the rate of the reaction depends on the rate at which reactants can climb to the top of the barrier and form the activated complex. The resulting expression for the rate constant is very similar to the one given in Eq. 15, and so this more general theory also accounts for the form of the Arrhenius equation and the observed dependence of the reaction rate on temperature. 

Estimate based on collision theory the rate of the reaction at 1000 K, assuming that the activation energy for the reaction is zero. The molecular radii for C2H5 and H can be assumed to be 0.43 and 0.205 nm, respectively. 

There are a number of other variables in the collision theory expression for the rate constant and rate of reaction. These are considered explicitly in the following worked problems. 

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

Here, a molecule of C is formed only when a collision between molecules of A and B occurs. The rate of reaction r. (that is, rate of appearance of species C) depends on this collision frequency. Using the kinetic theory of gases, the reaction rate is proportional to the product of the concentration of the reactants and to the square root of the absolute temperature ... 

By the collision theory, we expect that increasing the partial pressure (and thus, the concentration) of either the HBr or 02 will speed up the reaction. Experiments show this is the case. Quantitative studies of the rate of reaction (8) at various pressures and with various mixtures show that oxygen and hydrogen bromide are equally effective in changing the reaction rate. However, this result raises a question. Since reaction (8) requires four molecules of HBr for every one molecule of 02, why does a change in the HBr pressure have just the same effect as an equal change in the 02 pressure ... 

Although collision theory provides a useful formalism to estimate an upper limit for the rate of reaction, it possesses the great disadvantage that it is not capable of describing the free energy changes of a reaction event, since it only deals with the individual molecules and does not take the ensemble into consideration. As such, the theory is essentially in conflict with thermodynamics. This becomes immediately apparent if we derive equilibrium constants on the basis of collision theory. Consider the equilibrium... 

The collision theory explains why reactions occur and how certain factors increase or decrease the rate of reaction. The collision theory involves all of the following EXCEPT that —... 

Consideration of a variety of other systems leads to the conclusion that very rarely does the collision theory predict rate( constants that will be comparable in magnitude to experimental values. Although it is not adequate for predictions of reaction rate constants, it nonetheless provides a convenient physical picture of the reaction act and a useful interpretation of the concept of activation energy. The major short-... 

The rate of reaction in collision theories is related to the number of successful collisions. A successful reactive encounter depends on maw things, including (1) the speed at which the molecules approach each other (relative translational energy), (2) how close they are to a head-on collision (measured by a miss distance or impact parameter, b, Figure 6.10), (3) the internal energy states of each reactant (vibrational (v), rotational (/)), (4) the timing (phase) of the vibrations and rotations as the reactants approach, and (5) orientation (or steric aspects) of the molecules (the H atom to be abstracted in reaction 634 must be pointing toward the radical center). 

In some reactions involving gases, the rate of reaction estimated by the simple collision theory in terms of the usually infened species is much lower than observed. Examples of these reactions are the oxidation of H2 and of hydrocarbons, and the formation of HC1 and of HBr. These are examples of chain reactions in which very reactive species (chain carriers) are initially produced, either thermally (i.e., by collision) or photochemically (by absorption of incident radiation), and regenerated by subsequent steps, so that reaction can occur in chain-fashion relatively rapidly. In extreme cases these become explosions, but not all chain reactions are so rapid as to be termed explosions. The chain... 

On considering the collision frequency, energy and the probability factors discussed above, the rate of reaction by collision theory is given as... 

A comparison of equations (4.54) and (4.55) shows that the rate constant for a complex reaction differs from that obtained in simple atomic reaction by a factor of (qjqr)5. Since qv is nearly unity, while qr varies from 10 to 100 for a complex molecule, the ratio qv/qr, therefore, varies from 10 I to 10 2 and (qv/qT)5 varies from 10 5 to 10 10. This factor may link to steric factor p. On comparing equation (4.55) with collision theory and Arrhenius equation, we get... 

In this section, you used collision theory and transition state theory to explain how reaction rates are affected hy various factors. You considered simple reactions, consisting of a single-step collision between reactants. Not all reactions are simple, however. In fact, most chemical reactions take place via several steps, occurring in sequence. In the next section, you will learn about the steps that make up reactions and discover how these steps relate to reaction rates. 

Use collision theory and transition state theory to explain how concentration, temperature, surface area, and the nature of reactants control the rate of a chemical reaction. 

Hence, collision theory gives the correct reaction rate law (Equation 1-94) and a reaction rate constant of the form... 

Absolute Rate Theory(also known as Transition State or Activated Complex Theory). A theory of reaction rates based on the postulate that molecules form, before undergoing reaction, an activated complex which is in equilibrium with the reactants. The rate of reaction is controlled by the concn of the complex present at any instant. In general, the complex is unstable and has a very brief existance(See also Collision Theoty of Reaction)... 

Since the complications due to solvent structure have already been discussed, the remainder of this chapter is mainly devoted to a discussion of the complications introduced into the theory of reaction rates when the collision of solvent molecules does not lead to a complete loss of memory of the molecules about their former velocity. Nevertheless, while such effects are undoubtedly important over some time scale, the differences noted by Kapral and co-workers [37, 285, 286] between the rate kernel for reaction estimated from the diffusion and reaction Green s function and their extended analysis were rather small over times of 10 ps or more (see Chap. 8, Sect. 3.3 and Fig. 40). At this stage, it is a moot point whether the correlation of solvent velocity before collision with that after collision has a significant and experimentally measurable effect on the rate of reaction. The time scale of the loss of velocity correlation is typically less than 1 ps, while even rapid recombination of radicals formed in close proximity to each other occurs over times of 10 ps or more (see Chap. 6, Sect. 3.3). 

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. 

If the values of E found by Wulf and Tolman or the other recent value, 27,800, found by Belton, Griffith, and McKeown are substituted in the equation number of molecules reacting = number entering into collision x e ElRT, it appears that the rate of activation is not great enough to account for thd rate of reaction. The reason for this departure from the simple theory is discussed on page 102. 

Perrin s argument that the very nature of a unimolecular reaction demands independence of collisions, and therefore dependence on radiation, is adequately met both by the theory of Lindemann and by that of Christiansen and Kramers. Both these theories have the essential element in common that the distribution of energy among the molecules is not appreciably disturbed by the chemical transformation of the activated molecules thus the rate of reaction is proportional simply to the number of activated molecules and therefore to the total number of molecules, sinc in statistical equilibrium the activated molecules are a constant fraction of the whole. Thus the radiation theory is not necessary to explain the existence of reactions which are unimolecular over a wide range of pressures. 

The chain theory can obviously provide a rate of activation great enough to account for any observed rate of reaction. With Lindemann s theory it is necessary that the normal rate of production of activated molecules by collision should be at least equal to and indeed considerably greater than the number of molecules undergoing chemical transformation in unit time. 

---