Activating collision

Although much of the preceding discussion involved the synthesis of new molecules by organic and inorganic chemists, there is another area of chemistry in which such creation is important—the synthesis of new atoms. The periodic table lists elements that have been discovered and isolated from nature, but a few have been created by human activity. Collision of atomic particles with the nuclei of existing atoms is the normal source of radioactive isotopes and of some of the very heavy elements at the bottom of the periodic table. Indeed nuclear chemists and physicists have created some of the most important elements that are used for nuclear energy and nuclear weapons, plutonium in particular. 

But the fact that P is of the order of magnitude unity, combined with the parallelism between E and the temperature required to give an assigned rate of reaction, indicates that activation is the fundamental process in bimolecular reactions. The general coherence of the results would seem to justify the statement that an activating collision is not merely a necessary but a sufficient condition for chemical transformation. 

It has also been suggested that the molecular diameter of nitrogen pentoxide is effectively much greater for activating collisions, as well as for deactivating collisions, than that calculated in the ordinary way from the kinetic theory. The difficulty about this suggestion is that the... 

This problem was resolved in 1922 when Lindemann and Christiansen proposed their hypothesis of time lags, and this mechanistic framework has been used in all the more sophisticated unimolecular theories. It is also common to the theoretical framework of bimolecular and termolecular reactions. The crucial argument is that molecules which are activated and have acquired the necessary critical minimum energy do not have to react immediately they receive this energy by collision. There is sufficient time after the final activating collision for the molecule to lose its critical energy by being deactivated in another collision, or to react in a unimolecular step. 

In the condensed phase the AC permanently interacts with its neighbors, therefore a change in the local phase composition (as were demonstrated on Figs. 8.1 and 8.2) affects the activation barrier level (Fig. 8.6). Historically the first model used for surface processes is the analogy of the collision model (CM) [23,48,57]. This model uses the molecular-kinetic gas theory [54]. It will be necessary to count the number of the active collisions between the reagents on the assumption that the molecules represent solid spheres with no interaction potential between them. Then the rate constant can be written down as follows (instead of Eq. (6)) ... 

This represents a second-order reaction whose rate constant is the frequency of occurrence of activating collision between B molecules. 

The overall rate of ethane consumption then is of order one-and-a-half in ethane if the rate of C2H5 — C2H4 + H is controlled by activating collision, and of order one half if controlled by decay of the activated radical. According to Quinn, first-order behavior was observed because the reaction was studied in the "fall-off" range of pressure, that is, where rate control of C2H5 decay shifts from one step to the other. Indeed, at very low pressures the initial rate varies with (pCc) 5 [31]. 

Quinn studied initial rates—i.e., in the absence of reaction products—in a limited pressure range of 60 to 230 Torr. His hypothesis can explain the dependence on initial pressure he observed, but not what is normally defined as first-order behavior, namely, a rate proportional to the reactant concentration or partial pressure in the course of the reaction in the presence of products formed. This is because ethene (and, for that matter, almost any other molecule with the possible exception of H2) can also serve as activating collision partner. Indeed, addition of inerts has been found to boost the rate [35]. Since one mole of ethane produces approximately one mole of ethene, the concentration of potential collision partners is pc=c + pcc = pc°c and remains essentially unchanged, so that there is no effect on the form of the rate equation and the reaction order (for simplicity, this assumes ethene to be as effective a collision partner as is ethane, and H2 to be ineffective.) Nevertheless, textbooks to this day accept Quinn s explanation, if not Rice and Herzfeld s. 

The measurement of radiations emitted during the activating collision is a method that has been applied in a number of cases where the sensitivity of neutron activation analysis is otherwise poor. 

The extension of the techniques of measuring the radiation emitted during the activating collision to pile irradiation requires a method of detection sensitive to the nuclear event but relatively insensitive to the pile neutron and gamma flux. Stewart and Bentley 97) estimated uranium... 

The sticking factor gives the ratio of the number of activated collisions divided by the total number of collisions, whereas in Eq. (9.65) gives the rate of adsorption (in mol cm s" ), with an activation energy Ea for adsorption at the external surface, the other parameters having their usual meaning. 

Thus, in the scheme (L1)-(L4) one rate constant (ArLi) can be equated to the high-pressure constant k. Constant kiA can also be easily estimated with high probability its activation energy can be equated to the enthalpy of step (LI), or to the energy of A B bond dissociation. As to the pre-exponential factor, it can be derived from the active collision theory. 

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... 

The apparent first-order rate constant decreases at low pressures. Physically the decrease in value of the rate constant at lower pressures is a result of the decrease in number of activating collisions. If the pressure is increased by addition of an inert gas, the rate constant increases again in value, showing that the molecules can be activated by collision with a molecule of an inert gas as well as by collision with one of their own kind. Several first-order reactions have been investigated over a sufficiently wide range of pressure to confirm the general form of Eq. (32.61). The Lindemann mechanism is accepted as the mechanism of activation of the molecule. 

The purpose of this chapter is to review the kinetics and mechanisms of photochemical reactions in amorphous polymer solids. The classical view for describing the kinetics of reactions of small molecules in the gas phase or in solution, which involves thermally activated collisions between molecules of approximately equivalent size, can no longer be applied when one or more of the molecules involved is a polymer, which may be thousands of times more massive. Furthermore, the completely random motion of the spherical molecules illustrated in Fig. la, which is characteristic of chemically reactive species in both gas and liquid phase, must be replaced by more coordinated motion when a macromolecule is dissolved or swollen in solvent (Fig. b). Furthermore, a much greater reduction in independent motions must occur when one considers a solid polymer matrix illustrated in Fig. Ic. According to the classical theory of thermal reactions the collisional energy available in the encounter must be suificient to transfer at least one of the reacting species to some excited-state complex from which the reaction products are derived. The random thermal motion thus acts as an energy source to drive chemical reactions. 

In the simplest theories, the reaction probability is taken as a step function, zero for energy below a certain threshold Eo, and constant, say P, for energy equal to, or above, E. If we integrate from Eactivated collisions, Z. This has simply to be multiplied by P to obtain the rate constant. Thus... 

If the energy resides in the two square terms of the relative velocity along the line of centers, the number of activated collisions is... 

Equations 56 and 57 apply to monomolecular reactions in the gas phase at the low pressure limit where the rate determining step is the activating collision. On the other hand, at the high pressure limit the theory of RRK predicts (see, e.g.. Ref. 986) = Eo (see footnote, p. 245). This explains the experimentally observed decrease of Ea with decreasing pressure. The decrease of Ea with temperature at the low pressure limit, predicted by Eq. 57, is less pronounced, and is more difficult to observe (see Addendum). 

The earliest example of such a procedure seems to be due to Kassel (83, 84). For a reaction between two diatomic molecules he assumes six square terms, two each for vibration and for relative motion along the line of centers, whence the number of activated collisions with energy between E and E + dE is... 

---