Collision model steric factor

Now that we have a model, we must check its consistency with various experiments. Sometimes such inconsistencies result in the complete rejection of a model. More often, they indicate that we need to refine the model. In the present case, the results of careful experiments show that the collision model of reactions is not complete, because the experimental rate constant is normally smaller than predicted by collision theory. We can improve the model by realizing that the relative direction in which the molecules are moving when they collide also might matter. That is, they need to be oriented a certain way relative to each other. For example, the results of experiments of the kind described in Box 13.2 have shown that, in the gas-phase reaction of chlorine atoms with HI molecules, HI + Cl — HC1 I, the Cl atom reacts with the HI molecule only if it approaches from a favorable direction (Fig. 13.28). A dependence on direction is called the steric requirement of the reaction. It is normally taken into account by introducing an empirical factor, P, called the steric factor, and changing Eq. 17 to... 

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. ... 

A simple relation between the steric factor of the collision model and the partition functions used in the transition-state theory may be made by employing the relation derived in Eq. (XII.3.14) between frequency... 

The steric factor, p, of equation (2-20) can be estimated directly from TST using either exact or approximate methods. This is satisfying, since in the manner in which it was introduced p seemed to be yet another adjustable parameter. In general the steric factor is given by the ratio of the pre-exponential factor of the reaction in question to that for the binary collision model ... 

A listing of typical estimates of this sort is given in Table 2.4. It can be seen that as the reaction becomes more complex in relation to the hard-sphere collision model, the steric factor decreases. In practice, then, one might be able to use the magnitude of experimentally determined steric factors as the basis for more detailed hypotheses concerning the nature of a given reaction. 

A collision theory of even gas phase reactions is not totally satisfactory, and the problems with the steric factor that we described earfier make this approach more empirical and qualitative than we would like. Transition state theory, developed largely by Henry Eyring, takes a somewhat different approach. We have already considered the potential energy surfaces that provide a graphical energy model for chemical reactions. Transition state theory (or activated complex theory) refers to the details of how reactions become products. For a reaction fike... 

Collision theory is a simple description of reacting molecules that treats them as hard spheres. Some of the basic concepts of collision theory were considered at the end of section 20.6. Although this model does predict some numerical reaction parameters having about the right order of magnitude, its description of molecules as hard spheres and use of steric factors as fudge factors ignores the complex nature of even simple molecular reactions. A more realistic approach is necessary. 

We should bear in mind that Arrhenius pre-exponential factors (A = FZ, where P is the steric factor and Z is collision number) are almost equal for all isotopically labeled compounds. Namely, the change of the number of neutrons in nuclei does not significantly influence the value of PZ, because the charge of the species does not change. Investigating different reaction models it was found that A /Aj) was always between 0.7 and 1.2 (for the temperature range 20-2000 K) the absolute minimum was O.S. Thus, we can write ... 

Thus, we find that in this simple model the preexponential factor A in Eq. (1.1) can in principle be calculated if the reactive collision cross section nd were known. It has become common practice to define a steric factor p... 

The use of this relation assumes that there are no steric restrictions on the approach of the donor and acceptor species in polymer molecules, which are different in comparison to small molecule models. This assumption can usually be tested by selecting a range of small-molecule analogs for comparison. Even when quenching does not occur at every collision, it is still possible to apply eqs. (33) and (34), provided that an efficiency factor a is included. If this factor does not depend on the attachment of a chromophore to a polymer chain, then the procedure may still be valid. 

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