Kinetic energy collision theory

Simple collision theory does not provide a detailed interpretation of the energy barrier or a method for the calculation of activation energy. It also fails to lead to interpretations in terms of molecular structure. The notable feature of collision theoiy is that, with very simple means, it provides one basis for defining typical or normal kinetic behavior, thereby directing attention to unusual behavior. 

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 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 principles of kinetic theory may be used to arrive at an expression for the number of collisions whose relative kinetic energy along the line of centers is greater than ec. The result is the following expression for the number of such collisions per unit volume per unit time. 

The Bohr criterion k I depends on the projectile speed rather than its kinetic energy. This, together with the fact that Zi — l, implies that for electrons or positrons the validity of semiclassical collision theory becomes... 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

Arrhenius recognized that for molecules to react they must attain a certain critical energy, E. On the basis of collision theory, the rate of reaction is equal to the number of collisions per unit time (the frequency factor) multiplied by the fraction of collisions that results in a reaction. This relationship was first developed from the kinetic theory of gases . For a bimolecular reaction, the bimolecular rate constant, k, can be expressed as... 

The rate of collision of gas molecules is given by gas kinetic theory. Molecules have an average kinetic energy given by the expression... 

The kinetic molecular theory (KMT see Sidebar 2.7) of Bernoulli, Maxwell, and others provides deep insight into the molecular origin of thermodynamic gas properties. From the KMT viewpoint, pressure P arises merely from the innumerable molecular collisions with the walls of a container, whereas temperature T is proportional to the average kinetic energy of random molecular motions in the container of volume V. KMT starts from an ultrasimplified picture of each molecule as a mathematical point particle (i.e., with no volume ) with mass m and average velocity v, but no potential energy of interaction with other particles. From this purely kinetic picture of chaotic molecular motions and wall collisions, one deduces that the PVT relationships must be those of an ideal gas, (2.2). Hence, the inaccuracies of the ideal gas approximation can be attributed to the unrealistically oversimplified noninteracting point mass picture of molecules that underlies the KMT description. 

Processes in which two atoms combine to give a single molecule demand further consideration. No activation is required, but another condition has to be fulfilled, as Herzfeld j- and Polanyi J have pointed out. When two atoms collide, the nascent molecule which is formed contains all the energy of formation, and this, moreover, must be exactly quantized. Unless therefore its energy can be adjusted by a collision with a third molecule or with the wall of the vessel it will be incapable of continued existence and will fall apart again. This view about the necessity of collision with a third molecule is often referred to as the Dreierstoss theory. Reactions of the type A + BC = AC + B are not affected by these considerations, since the kinetic energy with which the two products of the reaction fly apart adjusts itself in accordance with the quantum demands of the molecule AB. 

A simple way of analyzing the rate constants of chemical reactions is the collision theory of reaction kinetics. The rate constant for a bimolecular reaction is considered to be composed of the product of three terms the frequency of collisions, Z a steric factor, p, to allow for the fraction of the molecules that are in the correct orientation and an activation energy term to allow for the fraction of the molecules that are sufficiently thermally activated to react. That is,... 

An attempt was made by Daniel Bernoulli (1738) to explain Boyle s law on tlie basis of what later became known as the kinetic theory of gases. Bernoulli introduced tlie concept that the pressure of a gas results from the collisions of gas molecules within tlie walls of the gas container. This established a connection between the numbers of gas molecules present and their kinetic energy present at any given temperature. 

The mechanism by which equilibrium is attained can only be visualized in terms of microscopic theories. In the kinetic sense, equilibrium is reached in a gas when collisions among molecules redistribute the velocilies lor kinetic energies) of each molecule until a Maxwellian distribution is reached for the whole bulk. In the case of the trend toward equilibrium for two solid bodies brought into physical contact, we visualize the transfer of energy by means of free electrons and phonons (lattice vibrations). 

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