Collision theory of reactions

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

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. 

The collision theory of reaction rates in its simplest form (the simple collision theory or SCT) is one of two theories discussed in this chapter. Collision theories are based on the notion that only when reactants encounter each other, or collide, do they have the chance to react. The reaction rate is therefore based on the following expressions ... 

While the collision theory of reactions is intuitive, and the calculation of encounter rates is relatively straightforward, the calculation of the cross-sections, especially the steric requirements, from such a dynamic model is difficult. A very different and less detailed approach was begun in the 1930s that sidesteps some of the difficulties. Variously known as absolute rate theory, activated complex theory, and transition state theory (TST), this class of model ignores the rates at which molecules encounter each other, and instead lets thermodynamic/statistical considerations predict how many combinations of reactants are in the transition-state configuration under reaction conditions. 

Although the collision theory of reaction rates is evidently satisfactory when applied to a number of reactions, it fails conspicuously in many cases such as rapid chain reactions, reactions involving complex molecules etc. The collision theory has been oversimplified and suffers from following weaknesses ... 

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,... 

First, we recognize that reaction is likely to occur only when reactants meet. An encounter between two molecules in a gas is a collision, so the model we are about to build is called the collision theory of reactions. In this model, we suppose that molecules behave like defective billiard balls they bounce apart if they collide at low speed, but they might smash into pieces when the impact is really energetic. If two molecules collide with less than a certain kinetic energy, they simply bounce apart. If they meet with more than that energy, bonds can break and new bonds can form (Fig. 13.16). Let s denote the minimum kinetic energy needed for reaction by Emin. 

Application of the collision theory of reaction rates to surface processes is not straightforward. The meaningful definition of a surface collision is difficult and the necessary assumptions, inherent in any quantitative treatment based on this approach, make the results of dubious validity and restricted usefulness. The movement of surface entities within the temperature range of interest could necessitate activation, but (in different systems) may alternatively be a rapid and facile process, and the expression defining the... 

Absolute Rote 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 Theory of Reaction)... 

Collision Theory of Reaction. A theory to account for observed kinetics of reaction in terms of the molecular behavior of the reacting systems. For interaction, this theory requires that the molecules must collide and, in addition, have sufficient energy to be activated (See also Absolute Rate Theory in Vol 1 of Encyclopedia, pA4-R)... 

The collision theory of reaction rates dealt with earlier gives a useful, even if a crude, picture of reaction rates and permits us to calculate the rates of reactions between simple molecules when the activation energies are known. However, this theory leaves much to be desired. It does not furnish a method of calculating activation energies theoretically. It provides no information on the details of reactive collisions. It also does not account for the role that the internal energy might play in the reaction. 

The idea that reaction rates are tied to the rate of collision is aptly called the collision theory of reaction rates. But nature s mysteries are not so easily solved. During a chemical reaction, the electron orbitals (that is, the electron clouds) on individual reactants overlap and coalesce, the way two bubbles come together and merge into one. Once the conditions are right, it takes about a quadrillionth of a second for the electrons in the individual orbitals to readjust themselves into the orbitals around the products. But if all reactions took place as fast as collisions, then food would cook before... 

Originally E was regarded as a constant quantity which represented the difference between the energies of normal and activated molecules (Arrhenius, 1889), a conclusion which also arises from the collision theory of reaction rates. The linear relation between In and 1/T then required by equation (1) has been found to be valid within the limits of the experimental error on innumerable occasions. However, Hinshel-wood (1926) pointed outiihat E would vary with the temperature if the additional energy of the activated molecules was distributed among more than two square terms, and even before the development of... 

OUTLINE 16-1 The Rate of a Reaction 16-5 Collision Theory of Reaction... 

The fundamental notion of the collision theory of reaction rates is that for a reaction to occur, molecules, atoms, or ions must first collide. Increased concentrations of reacting species result in greater numbers of collisions per unit time. However, not all collisions result in reaction that is, not all collisions are effective collisions. For a collision to be effective, the reacting species must (1) possess at least a certain minimum energy necessary to rearrange outer electrons in breaking bonds and forming new ones and (2) have the proper orientations toward one another at the time of collision. 

One of the most useful theories of activation is the collision theory of reactions. This theory assumes that the activated molecules are formed from collisions with other normal reactant species. Such thermally activated molecules decompose to or react with other molecules. The number and frequencies of collisions indicate that not all collisions are effective in producing an activated molecule. As it was shown before [13], the key point is the effective collision factor in the theory. In the case of a heterogeneous reaction, if the surface catalyst concentration is relatively small compared with the bulk concentration of the reactants, the number of active sites for the catalytic reaction will suffice for the reaction to occur. Therefore, the catalytic reaction has one more advantage only a small quantity of the additive is enough for the reaction. 

Theoretical chemistry is the discipline that uses quantum mechanics, classical mechanics, and statistical mechanics to explain the structures and dynamics of chemical systems and to correlate, understand, and predict their thermodynamic and kinetic properties. Modern theoretical chemistry may be roughly divided into the study of chemical structure and the study of chemical dynamics. The former includes studies of (1) electronic structure, potential energy surfaces, and force fields (2) vibrational-rotational motion and (3) equilibrium properties of condensed-phase systems and macromolecules. Chemical dynamics includes (1) bimolecular kinetics and the collision theory of reactions and energy transfer (2) unimolecular rate theory and metastable states and (3) condensed-phase and macromolecular aspects of dynamics. 

With the distribution laws established, we can now attack the problem that is central to a collision theory of reaction the number of collisions experienced per molecule per second in the Maxwellian gas. Clearly the magnitude of this collision number is a function of temperature (through the constant a), and if we define a total collision number, collisions of all molecules per second per volume, it will also depend on molecular density (i.e., concentration). Thus, the two independent variables of concentration and temperature used in power-law rate equations will appear in the total collision number. 

This probably represents the first stop on the way to a collision theory of reaction rates. If, indeed, we have the passage of a single molecule through a dilute, fixed matrix of other molecules (sometimes called a dusty gas ) with a known speed ca, and with every collision resulting in reaction, then the reaction rate would in fact be given by equation (2-9). Yet, we know that we do not have a single molecule, we do not have a fixed speed, and we do not have a dusty gas, so this simple theory needs some cosmetics at this point. 

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