Activation in unimolecular reactions

In the unimolecular reactions which are also of the first order, only one molecule takes part in the reaction. The process of activation in unimolecular reactions, if caused by collisions should ordinarily lead to second order reactions. How then the observed rate of reaction could be of first order. If however, the activation is by absorption of the radiant energy, this problem can be avoided. But many unimolecular reactions take place under conditions where there is no absorption of radiant energy. For example... 

With bimolecular gas reactions, as we have seen, it is plausible to assume that the kinetic energy of the impact between the two molecules provides the energy of activation, and on this assumption we find for the number of molecules reacting number of collisions x e ElRT. This equation in six out of seven known examples is as nearly true as experiment can decide. Thus there is no absolute necessity to look any further for the interpretation of bimolecular reactions. At first it seemed natural to apply an analogous method of calculation to determine the maximum possible rate of activation in unimolecular reactions this led to the result that unimolecular reactions in general proceed at a rate many times greater than the expression Ze ElRT requires, e. g. about 105 times as many molecules of acetone decompose at 800° abs. in unit time as this method of calculation would admit to be possible, f... 

Hirschfelder, in discussing a simpler and more schematic model of stepwise activation in unimolecular reactions assumed the absorption coefficient a kplk = 1 in Hirschfelder notation) to be 0.5 and obtained the equation... 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

In unimolecular reactions, where complex molecules are involved, a fraction only of the activated molecules react, and this fraction is determined by specific factors. Thus a rigid parallelism between the heats of activation and the temperatures at which different reactions attain some assigned rate cannot be expected. Nevertheless in any expression containing an exponential term that term tends to play a predominant role, and a definite, if rough, parallelism still exists, showing that even in the case of more complex reactions the value of E is perhaps the most important factor in determining the rate of reaction. 

In unimolecular reactions one single reactant molecule passes into the activated complex and reacts. Experimental observations show that, within any given experiment, unimolecular reactions are strictly first order irrespective of the initial concentration or pressure (Figure 4.29). 

How thermal activation can take place following the Lindemann and the Lindemann-Hinshelwood mechanisms. An effective rate constant is found that shows the interplay between collision activation and unimolecular reaction. In the high-pressure limit, the effective rate constant approaches the microcanonical rate... 

In unimolecular reactions only one molecule is involved in the reaction. Since, however, the molecules prior to the reaction are stable, it is necessary to activate them in order to initiate the reaction. Based on the different methods of activation, we distinguish between the following two types of unimolecular reaction ... 

How do molecules in unimolecular reactions attain their energy of activation Lindemann (1922) suggested its answer by pointing out that the behaviour of unimolecular reactions can be explained on the basis of bimo-lecular collisions provided we postulate that a time lag exists between activation and reaction during which activated molecules may either react or be deactivated to ordinary molecules. Thus, the rate of reaction will not be proportional to all the molecules activated, but only to those which remain active. Lindemann suggested that the above reaction takes place as follows ... 

In unimolecular reactions, where the connection with collision frequency is not obvious, 5 is usually but not always found to have a value of about 1013 and this is about the frequency of vibration of atoms in a molecule as revealed by near-infra red absorption spectra. Since e EIRT is merely a number, s has the same dimensions as k namely, a number per second. If it is desired to visualize the factor s, it may be considered roughly as the vibration frequency of an atom in a molecule. After a molecule receives suffi- cient energy for activation it may disrupt at a given bond, but it can not do this in less time than the normal frequency of vibration of the atoms at this bond. A more complete but more complicated conception of s will be given later. 

E.E.Nikitin, Activation mechanisms and nonequilibrium distribution functions in unimolecular reactions, Teor.Eksp.Khim. 2, 19 (1966)... 

Our approach to the study of the departure from equilibrium in chemical reactions and of the "microscopic theory of chemical kinetics is a discrete quantum-mechanical analog of the Kramers-Brownian-motion model. It is most specifically applicable to a study of the energy-level distribution function and of the rate of activation in unimolecular (dissociation Reactions. Our model is an extension of one which we used in a discussion of the relaxation of vibrational nonequilibrium distributions.14 18 20... 

For 0=1 Hirschfelder thus finds XNJXN<0) — 0.387 while we obtain XNfXN(0) = 0.632 from Eq. VII.38. The difference in the numerical values is not important, being due to different models and different assumptions used by Hirschfelder and by us. The important point, as already expressed by Hirschfelder, is that in unimolecular reactions the concentration of molecules in the activated state is less than the value calculated for statistical equilibrium. 

Note added in proof In view of the failure of the harmonic oscillator model to account for the observed rate of activation in unimolecular dissociation reactions (the dissociation lag problem) these calculations have been repeated for a Morse anharmonic oscillator with transition between nearest and next-nearest neighbor levels [S. K. Kim, /. Chem. Phys. (to be published)]. The numerical evaluation of the analytical results obtained by Kim has not yet been carried out. From the results obtained by us and our co-workers [Barley, Montroll, Rubin, and Shuler, /. Chem. Phys. in press)] on the relaxation of vibrational nonequilibrium distributions of a system of Morse anharmonic oscillators it seems clear, however, that the anharmonic oscillator model with weak interactions (i.e., adiabatic perturbation type matrix elements) does not constitute much of an improvement on the harmonic oscillator model in giving the observed rates of activation. The answer to tliis problem would seem to lie in a recalculation of the collisional matrix elements for translational-vibrational energy exchange which takes account of the strong interactions in highly energetic collisions which can lead to direct dissociation. 

The sign and magnitude of the entropy of activation, A5, is taken as a gauge of the probability of forming the transition state. In unimolecular reactions, does not depend on concentration units and is assigned a normal value of zero, so that normal reactions have pre-exponential factors close to, or 10 s at ordinary temperatures, and reactions with improbable transition states are expected to have negative entropies of activation and - as a result -pre-exponential factors significantly lower than 10 s . ... 

One thus notes the similarity in activated diffusions and in unimolecular reactions. 

The general dominance of the lowest energy pathway in thermally activated systems is also seen in unimolecular reactions. Studies of the dissociation of N2O and of related isoelectronic molecules illustrate this, even though another factor restricts the lowest energy channel. In spite of the spin-forbidden nature of the reaction, the thermal decomposition of N2O yields products in their electronic ground states ... 

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