Collision theory steric factor

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. 

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... 

For complex organic molecules, geometric considerations alone lead one to the conclusion that only a small fraction of bimolecular collisions can lead to reaction. One can represent the fraction of the collisions that have the proper geometric orientation for reaction by a steric factor (Ps). Except for the very simplest reactions, this factor will be considerably less than unity. On the basis of simple collision theory, it is not possible to make numerical estimates of Ps, although it may occasionally be possible to make use of one s experience with similar reactions to determine whether Ps for a given... 

A comparison of equations (4.54) and (4.55) shows that the rate constant for a complex reaction differs from that obtained in simple atomic reaction by a factor of (qjqr)5. Since qv is nearly unity, while qr varies from 10 to 100 for a complex molecule, the ratio qv/qr, therefore, varies from 10 I to 10 2 and (qv/qT)5 varies from 10 5 to 10 10. This factor may link to steric factor p. On comparing equation (4.55) with collision theory and Arrhenius equation, we get... 

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. ... 

Transition state theory is more commonly applied today than collision theory. It is especially useful in examining reactions in solution and avoids the problem of introducing arbitrary factors such as the steric factor to take into account steric requirements. 

The preexponential factor involves the entropy change in going from reactants to the transition state the more highly ordered and tightly bound is the transition state, the more negative A S° will be and the lower the preexponential factor will be. Transition state theory thus automatically takes into account the effect of steric factors on rate constants, in contrast to collision theory. 

Compare the collision theory rate with the database value and calculate the steric factor, that is, the ratio between the measured rate constant and the rate constant estimated from collision theory. 

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,... 

The chemical reaction is characterized on the one hand by the kinetic mechanism, that is to say the dependence on the concentrations of the participants in the reaction, on the other hand by the reaction (velocity) constant. This latter in the simplest form is k — Ae EIRT in which E is the energy of activation and A the frequency factor. The latter is in the classical collision theory equal to where Z the collision number ( io11) and P the probability factor or steric factor. The latter can be much larger than unity if the activation energy is divided over several internal degrees of freedom (mono-molecular reactions) but it can also be as low as io 8, e.g., in cases where steric hindrance plays a role. 

Here, / is in amu A2, M is in amu, d is in A, a is in A-1, and v is in cm-1. The second exponential term results from a correction for the change in velocity due to the increase in rotational energy. The steric factor, Z0, is introduced as in V-T theory to account for noncolinear collision orientations. Moore tested this equation, along with two other more approximate forms, on a series of molecules having one or more H (or D) atoms. He also examined V-R transfer for collisions of dissimilar molecules, such as C02-CH4, C12-HC1, and CH4-Ar. Twenty-five different molecules having small moments of inertia were fitted with a single curve represented by equation (71) using a = 2.94 A-1 and Z0 = 5.0, with at least qualitative success. 

This simple collision theory thus predicts preexponential factors of about 10 cc/mole-sec, since we expect P < 1. Values of P < 1 are interpreted kinetically as due to improperly oriented collisions ( steric hindrance) or thermodynamically as a negative entropy of activation, i.e., a loss of freedom of A and B in forming the collision complex. As we shall see, these results are in good qualitative agreement with observations and Zab does indeed seem to be an upper limit for bimolecular frequency factors. ... 

In comparing both these theories with the simple collision theory we see that what has happened is that the rather vague steric factor P of the latter has been replaced by the—in principle more meaningful—ratios of partition functions of the species A, B, and AB". In the case that A and B are atoms then P = 1, and all theories have the same factors. The same is true if we assume that the groups A and B interact so weakly in forming the transition state that their rotational and vibrational modes are unaltered. 

Since hvfkT will generally be greater than unity, we see that the steric factors computed by the detailed theory will generally be about an order of magnitude greater than those computed from the transition-state theory and may in fact be somewhat greater than unity. Unfortunately, collision diameters are not well enough known to check such calculations with any reliability. 

In this last expression, the preexponential factors are all similar in containing a product of two collision frequencies, a steric factor, and a mean lifetime. The latter may be approximated in a number of ways, each of which yields about 10 sec. Since bimolecular collision frequencies are about 10 liters/mole-sec, this would make Z V about 10 liters /mole -sec. The collision theory thus leads to a frequency of termolecular collisions of about 10 liters /mole -sec, which as we shall see from Table XII.9, is about the order of magnitude observed for the fastest reactions. 

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 frequency factor calculated from collision theory is usually the upper boimd and is usually multiplied by a steric factor. Because this number is an upper boimd on the actual rate of reaction, a multiplication steric factor is used to adjust AB empirically. 

This resembles the result of simple collision theory, the AH corresponding closely to ii, and the entropy factor replacing the fsteric factor P. Usually, in gases, ZlS° is negative (often large) because formation of the complex involves an association of molecules and a consequent reduction in the number of ways in which translational and rotational energy can be shared out, and hence a reduction in S (p. 168). In this way, the old steric factor, which commonly had empirical values as low as 10, receives a much more plausible interpretation. 

We can extend the collision theory to calculate the rate constant for bimolecular reactions of two species, A and B. Comparing observed and predicted rate constants gives the values of P shown in Table 18.1. As the colliding molecules become larger and more complex, P becomes smaller because a smaller fraction of collisions is effective in causing reaction. The steric factor is an empirical correction that has to be identified by comparing results of the simple theory with experimental data. It can be predicted in more advanced theories but only for especially simple reactions. 

S. W. Benson, The Foundations of Chemical Kinetics, McGraw-Hill Book Company, New York, 1960. The stationary-state hypothesis mentioned in Secs. 2-6 and 2-11 is defined and illustrated on pp. 50-53. In chap. XII the collision theory is considered in detail, complications related to the energy distribution of molecules and the steric factor are discussed, and the results are compared in depth with those from the transition-state theory. 

This is integrated over the Q,Q2Q,-space. If the collision pair wave functions never overlap the vibration wave function Xiku(Qi>Q2>Q3 2Zu) of the QTS, there will be zero contribution to the cross section. In this case, the QTS defines the reaction domain. This is quantized by the corresponding vibration-rotation wave function. Therefore, from all possible collisions among the reactants, only those having a non-zero FC factor will contribute to the reaction rate. This is related to the steric factor, P, in elementary chemical kinetics theory. Selection rules for VR-transitions apply. The probability to find the system in one of the product channel states when starting from a QTS is controlled by the FC integral formed by the products of the type... 

Examples are known in which equation (62) agrees closely with experiment (for example, the reaction 2HI H2 -I- 12)- However, experimentally determined frequency factors often differ considerably from the values given by equation (62) (a difference of a factor of 10 is not uncommon). Since the experimental rates usually are lower than the rates predicted by collision theory, equation (62) is conventionally corrected by introducing a steric factor P, which originally was interpreted as accounting for the fact that activated collisions lead to reaction only if the incident molecules have the correct relative geometrical orientation (or, alternatively, only if the activation energy is in the proper modes). Thus, in place of equation (62), use is made of the expression... 

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