The Collision Theory

The collision model of reactions provides an enlightening method for visualizing chemical reactions. In order for a chemical reaction to occur, the reacting molecules must collide. However, for most reactions, the. rate of a given reaction is found to be much lower than the frequency of collisions. This indicates that most collisions do not result in a reaction. 

Dors Uie rate of an exothermic reaction increase with temperature Ydu bei it does. Remember, do not confuse kinetics with thermodynamics, increasing the rate is not necessarily a statement about the equilibrium. It simply means that equilibrium is achieved more quickly, 

In an elementary reaction, the coefficient tells you how many molecules participate in a reaction producing col listen. 

The product of the collision frequency 2, the fraction of collisions having the effective spatial orientations p (called the steric factor), and the fraction of collisions having sufficient relative energy (where Ea is the activation energy) gives the rate constant k of a reaction. This relationship is called tire Arrhenius equation  

An understanding of reaction rates can be explained by adopting a collision model for chemical reactions. The collision theory assumes chemical reactions are a result of molecules colliding, and the rate of the reaction is dictated by several characteristics of these collisions. An important factor that affects the reaction rate is the frequency of collisions. The reaction rate is directly dependent on the number of collisions that take place, but several other important factors also dictate the speed of a chemical reaction. 

Consider a piece of coal, which for our purposes can be considered pure carbon, sitting on the table. The coal is exposed to billions upon billions of collisions with oxygen molecules, O2 each second. Yet, the reaction C + O2 — CO2 does not occur. The coal 

The activation energy is often depicted as an energy hill or barrier that reactants must overcome for a reaction to take place. 

At the top of the energy hill a transition state exists called the activated complex. The activated complex represents the stage in the reaction where reactants may be transformed into products. The idea of an activated complex was first proposed by Svante August Arrhenius (1859-1927) around 1890. Arrhenius received the Nobel Prize in chemistry in 1903. Reactants may reach the activated complex stage and still not be converted into products, but slide down the activation energy hill back to reactants. On 

The activation energy, E, acts as an energy barrier. For a reaction to occur, the amount of kinetic energy converted to potential energy during a collision must be greater than the activation energy. 

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There is an inunediate coimection to the collision theory of bimolecular reactions. Introducing internal partition functions excluding the (separable) degrees of freedom for overall translation. 

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... 

An estimate of the enthalpy change which conesponds to the activation energy of the collision theory analysis of 167kJmoP may be made by assuming that the formation of tire dimer from two molecules of the monomer is energetically equivalent to tire dipole-dipole and dispersion interactions of two HI molecules. These exothermic sources of interaction are counterbalanced... 

The collision theory considers the rate to be governed by the number of energetic collisions between the reactants. The transition state theory considers the reaction rate to be governed by the rate of the decomposition of intermediate. Tlie formation rate of tlie intermediate is assumed to be rapid because it is present in equilibrium concentrations. 

Tests of the collision theory consist of comparisons between calculated and experimental values of the preexponential factor, the comparison often being made in terms of a ratio P defined by... 

We see that the collision theory provides a good explanation of reaction rate behavior. It is quite reasonable that the reaction rate should depend upon collisions among the reactant molecules. In fact, it is so reasonable that we are left wondering why the concentrations of some reactants in some reactions do not affect the rate. 

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 ... 

From what we know about molecular sizes, we can calculate that a particular CH4 molecule collides with an oxygen molecule about once every one-thousandth of a microsecond (1(M seconds) in a mixture of household gas (methane, formula CH4) and air under normal conditions. This means that every second this methane molecule encounters 10 oxygen molecules Yet the reaction does not proceed noticeably. We can conclude either that most of the collisions are ineffective or that the collision theory is not a good explanation. We shall see that the former is the case—we can understand why most collisions might be ineffective in terms of ideas that are consistent with the collision theory. 

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. 

According to the collision theory of gas-phase reactions, a reaction takes place only if the reactant molecules collide with a kinetic energy of at least the activation energy, and they do so in the correct orientation. 

The case of m = Q corresponds to classical Arrhenius theory m = 1/2 is derived from the collision theory of bimolecular gas-phase reactions and m = corresponds to activated complex or transition state theory. None of these theories is sufficiently well developed to predict reaction rates from first principles, and it is practically impossible to choose between them based on experimental measurements. The relatively small variation in rate constant due to the pre-exponential temperature dependence T is overwhelmed by the exponential dependence exp(—Tarf/T). For many reactions, a plot of In(fe) versus will be approximately linear, and the slope of this line can be used to calculate E. Plots of rt(k/T" ) versus 7 for the same reactions will also be approximately linear as well, which shows the futility of determining m by this approach. 

The kinetic theory—also called the collision theory—... 

Why does the collision theory of reaction rates conflict with 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 —... 

Summarize the collision theory and how surface area applies to reaction rates. 

Drawing Conclusions How does the collision theory explain the reaction times ... 

In this equation it is the reaction rate constant, k, which is independent of concentration, that is affected by the temperature the concentration-dependent terms, J[c), usually remain unchanged at different temperatures. The relationship between the rate constant of a reaction and the absolute temperature can be described essentially by three equations. These are the Arrhenius equation, the collision theory equation, and the absolute reaction rate theory equation. This presentation will concern itself only with the first. 

Comparison of this equation with the Arrhenius form of the reaction rate constant reveals a slight difference in the temperature dependences of the rate constant, and this fact must be explained if one is to have faith in the consistency of the collision theory. Taking the derivative of the natural logarithm of the rate constant in equation 4.3.7 with respect to temperature, one finds 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-... 

Termolecular Reactions. If one attempts to extend the collision theory from the treatment of bimolecular gas phase reactions to termolecular processes, the problem of how to define a termolecular collision immediately arises. If such a collision is defined as the simultaneous contact of the spherical surfaces of all three molecules, one must recognize that two hard spheres will be in contact for only a very short time and that the probability that a third molecule would strike the other two during this period is vanishingly small. 

In terms of the collision theory a bimolecular reaction rate is written as... 

The collision theory of reaction rates states that molecules, atoms or ions must collide effectively in order to react. For an effective collision to occur, the reacting species must have (1) at least a minimum amount of energy in order to break old bonds and make new ones, and (2) the proper orientation toward each other. 

Changes in the rate of a reaction can be explained by the collision theory. The three main assumptions of this are ... 

An increase in the concentration of a reactant (or reactants) in solution, or an increase in the pressure on a gas-phase reaction, increases the rate of reaction. In terms of the collision theory ... 

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... 

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