Reaction rates collision theory

The ratio kq/kf can now be identified as ki9/k9a. We can calculate an upper limit for kl9 from ion-molecule reaction rate theory by assuming that this reaction occurs with a collision efficiency. This leads to k9il < 1 X 109 sec. -1 (7). 

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. 

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. 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

Much more can be said about the magnitude of pre-exponcntial factors and activation energies of elementary processes based on statistical thermodynamics applied to collision and reaction-rate theory [2, 61], but in view of the remark above one should be cautious in their application and limit it to well-defined model reactions and catalyst surfaces. 

In ordinary unimolecular reaction rate theory, the usual assumptions of strong collisions and random distribution of the internal energy simply serve to wash out precisely those features of the molecular dynamics that become of primary importance in the cases of photochemical, chemical, and electron impact excitation. Whereas evaluation of all the consequences is incomplete at present, it is already clear that the representation of an excited molecule in terms of the properties of resonant scattering states holds promise for the elucidation of those aspects of the internal dynamics that are important in photochemistry. 

In summary, collision theory provides a good physical picture of bimolecular reactions, even though the structure of the molecules is not taken into account. Also, it is assumed that reaction takes place instantaneously in practice, the reaction itself requires a certain amount of time. The structure of the reaction complex must evolve, and this must be accounted for in a reaction rate theory. For some reactions, the rate coefficient actually decreases with increasing temperature, a phenomenon that collision theory does not describe. Finally, real molecules interact with each other over distances greater than the sum of their hard-sphere radii, and in many cases these interactions can be very important. For example, ions can react via long-range Coulomb forces at a rate that exceeds the collision limit. The next level of complexity is transition state theory. 

For bimolecular reactions, we can easily compare collision theory with absolute reaction rate theory, using the results of the preceding section. Consider the bimolecular reaction between two polyatomic molecules A and B to yield a complex... 

Unimolecular reactions with thermal, optical, or chemical activation are governed by a competition between intramolecular isomerization, dissociation, or the reverse association (or recombination) processes, and intermolecular energy transfer in collisions. In addition to these traditional unimolecular reactions, many other reaction systems may be considered from a unimolecular point of view when a particular intramolecular event can be separated from preceding or other subsequent processes. Following this more general use of the term, unimolecular reaction rate theory has found a quite general application, and has been harmonized with other theories of reaction dynamics. 

The relations of Eyring s equations to other formulations of the statistical reaction rate theory will be discussed in the next section in the framework of the adiabatic approximation to the exact collision theory. 

The relation (184 111) could be considered a definition of a characteristic temperature Tj corresponding to Eyring s formulation of activated complex theory /20b/. However, when the non-adiabatic condition (72.Ill) is really fulfilled, equation (184.III) actually represents only a relation of equivalency of the collision and statistical formulations of reaction rate theory in the high temperature region T >T /2 to which both the formulas (177.Ill) and (183.Ill) refer. This means that if T < T, the formula (183.III) cannot be used in the temperature range TjJ/2 < T < Tj /2 for physical reasons. 

Our treatment, based on both the collision and the statistical formulations of reaction rate theory, shows that there exist two possibilities for an interpretation of the experimental facts concerning the Arrhenius parameter K for unimolecular reactions. These possibilities correspond to either an adiabatic or a non-adiabatic separation of the overall rotation from the internal molecular motions. The adiabatic separability is accepted in the usual treatment of unimolecular reactions /136/ which rests on transition state theory. To all appearances this assumption is, however, not adequate to the real situation in most unimolecular reactions.The nonadiabatic separation of the reaction coordinate from the overall rotation presents a new, perhaps more reasonable approach to this problem which avoids all unnecessary assumptions concerning the definition of the activated complex and its properties. Thus, for instance, it yields in a simple way the rate equations (7.IV), corresponding to the "normal Arrhenius parameters (6.IV), which are both direct consequences of the general rate equation (2.IV). It also predicts deviations from the normal values of the apparent frequency factor K without any additional assumptions, such that the transition state (AB)" (if there is one) differs more or less from the initial state of the activated molecule (AB). ... 

All above conclusions are involved as special cases in the general consequences of the collision theory rate equation (51j III) derived in Sec.7.III. The corresponding consequences from the statistical formulation (67.Ill) of the reaction rate theory were also discussed there. The current interpretations of kinetic isotope effects are based on transition state theory. The correction for proton tunneling is first taken into consideration by BELL et al./155/. More extensive work in this direction has been carried out by CALDIN et al. /I53/. In this treatment estimations of the tunneling correction are made using one-dimensional (parabolic) barrier by neglecting the coupling of the proton motion with other motions of reactants or solvent. 

Absolute reaction rate theory is discussed briefly in this section. Collision theory will not be developed explicitly since it is less applicable to... 

There are two important theories of reaction kinetics - the collision theory, and absolute reaction rate theory. With the aid of these theories, the rate of a reaction can be calculated. 

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