Collisions collision theory

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

Simple collision theories neglect the internal quantum state dependence of a. The rate constant as a function of temperature T results as a thennal average over the Maxwell-Boltzmaim velocity distribution p Ef. 

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. 

Adhi Karl S K and Kowolski K L 1991 Dynamical Collision Theory and its Applications (New York Academic)... 

Bernstein R B (ed) 1979 Atom-Molecule Collision Theory. A Guide for the Experimentalist New York Plenum)... 

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... 

Goldberger M L and Watson K M 1964 Collision Theory (New York Wiley)... 

Joachain C J 1975 Quantum Collision Theory (Amsterdam North-Holland) p 383... 

Bransden B H 1983 Atomio Collision Theory 2nd edn (Menlo Park, CA Benjamin-Cummings)... 

Baer M (ed) 1985 Theory of Chemical Reaction Dynamics (Boca Raton, FL CRC Press) vols 1-4 Bernstein R B (ed) 1979 Atom-Molecule Collision Theory A Guide for the Experimentalist (New York Plenum)... 

In chemical kinetics, it is often important to know the proportion of particles with a velocity that exceeds a selected velocity v. According to collision theories of chemical kinetics, particles with a speed in excess of v are energetic enough to react and those with a speed less than v are not. The probability of finding a particle with a speed from 0 to v is the integral of the distribution function over that interval... 

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... 

Child, M.S., 1974, Molecular Collision Theory (Academic Press, London). 

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. 

We are concerned with bimolecular reactions between reactants A and B. It is evident that the two reactants must approach each other rather closely on a molecular scale before significant interaction between them can take place. The simplest situation is that of two spherical reactants having radii Ta and tb, reaction being possible only if these two particles collide, which we take to mean that the distance between their centers is equal to the sum of their radii. This is the basis of the hard-sphere collision theory of kinetics. We therefore wish to find the frequency of such bimolecular collisions. For this purpose we consider the relatively simple case of dilute gases. 

Note that A is predicted by collision theory to be proportional to For bimolecular reactions A has the units M s (liter per mole per second). 

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... 

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. 

If the transition state theory is applied to the reaction of two hard spheres, the result is identical with that of simple collision theory. - pp Because transition state theory is an equilibrium theory, it can be inferred that collision theory is also an equilibrium theory. 

Collision theory leads to this equation for the rate constant k = A exp (-EIRT) = A T exp (,—EIRT). Show how the energy E is related to the Arrhenius activation energy E (presuming the Arrhenius preexponential factor is temperature independent). 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

Table 11.3 compares observed rate constants for several reactions with those predicted by collision theory, arbitrarily taking p = 1. As you might expect, the calculated k s are too high, suggesting that the steric factor is indeed less than 1. 

---