Frequency Factor unimolecular reactions

These values indicate a collision eflSciency for the recombination of NO2 + NO3 of about 1 in 300 collisions, which is very close to the value observed for NO2 + NO2. The frequency factor of reaction 1 is very much higher than the usual factor for unimolecular fissions but lower than the estimated value for the fission of N2O4. The frequency factor for fcs is about 10 lower than collision frequencies and is in the expected range of values for atom transfers between large molecules. It is the activation energy for this reaction, Ez = 3.65 Kcal, which seems surprising. From Table XIII. 16, one finds that AH3 = 5.1 Kcal ... 

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. 

Several of the reference texts and review articles on kinetics give discussions of entropies of activation in terms of structure and mechanism, and it is sufficient here only to refer briefly to a few of them. Values of AS (or its equivalent, frequency factors) for unimolecular gas reactions have been considered in some detail (Benson, 1960b Frost and Pearson, 1961c Gowenlock, 1960). Summaries of thermodynamic data for solution reactions may be found in several sources (Frost and Pearson, 1961d Moelwyn-Hughes, 1947 Pearson, 1952). 

The pre-exponential factor of an apparent unimolecular reaction is, roughly, expected to be of the order of a vibrational frequency, i.e., fO13 to 1014 s 1. The pre-exponential factor of a bimolecular reaction is, roughly, related to the collision frequency, i.e., the number of collisions per unit time and per unit volume. 

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. 

First-order unimolecular fission reactions in which the products are stable molecules have been compiled in Table XI.4. As can be seen, the frequency factors all fall in the range between 3 X 10 to about 10 sec with most of them very close to the value of 10 sec b... 

The dissociation of N2O4 has a frequency factor in excess of 10 sec and this seems reasonable if in the transition complex the originally stiff vibrations of the two NO2 groups change over to only slightly hindered rotations. This dissociation is of further interest in that it is one of the few unimolecular reactions for which the experimental first-order rate... 

Thus before any given set of data may be reliably used in applying the details of a theory of unimolecular reactions, the chemical complexity of the reaction and the effects of the walls must first be completely established. There are at present only a few cases for which an exhaustive and convincing study has been presented they are the decompositions of N2O6, cyclopropane, and N2O4. In all of these cases the frequency factors reported have been abnormally high (10 to 10 scc ), which has had as a consequence that the characteristic pressure at which the first-order rates could be observed to fall was higher than would have been predicted for molecules of such complexity (see Table XI.2). In each case the reactions show the qualitative features which are to be expected in the intermediate... 

It has long been held that the A factor of unimolecular reactions should be of the order of magnitude of molecular vibration frequencies, 1013 sec-1. In Fig. 4 is shown a distribution curve of log A values for a... 

This mechanism has been confirmed by numerous experimental studies. Nevertheless, in the vast majority of cases unimolecular reactions are observed in their first order regime. The experimental rate constant in these cases is composed of an experimental pre-exponential (A, = A2Ai / A i) and an experimental activation energy (E = E2 + Ei - E. ). Theoretical considerations lead to the conclusion that the pre-exponential of k2 has an upper limit of about 1013 sec 1, which corresponds to the vibrational frequency of an average bond that may break in the reaction. At the same time the frequency factors for k and k i are expected to be very similar, making the expected A, A2. 

Since most elementary unimolecular reactions require that die molecule must be in an appropriate configuration while breaking a bold, the actual frequency factor is usually lower than the universal value. The factor reducing the upper limit is by agreement thought of as the stearic factor and represents an entropy requirement for achieving the transition state. When the stearic feet or is expressed, not by a simple number (P), but by an entropy of activation (AS) it can be written as ... 

Unimolecular frequency factors, unlike activation energies, cannot be estimated from other data. There is some chance that one can estimate frequency factors by comparison to the frequency factors of similar reactions. 

Our treatment, based on both the collision and the statistical formulations of reaction rate theory, shows that there exist two possibilities for an interpretation of the experimental facts concerning the Arrhenius parameter K for unimolecular reactions. These possibilities correspond to either an adiabatic or a non-adiabatic separation of the overall rotation from the internal molecular motions. The adiabatic separability is accepted in the usual treatment of unimolecular reactions /136/ which rests on transition state theory. To all appearances this assumption is, however, not adequate to the real situation in most unimolecular reactions.The nonadiabatic separation of the reaction coordinate from the overall rotation presents a new, perhaps more reasonable approach to this problem which avoids all unnecessary assumptions concerning the definition of the activated complex and its properties. Thus, for instance, it yields in a simple way the rate equations (7.IV), corresponding to the "normal Arrhenius parameters (6.IV), which are both direct consequences of the general rate equation (2.IV). It also predicts deviations from the normal values of the apparent frequency factor K without any additional assumptions, such that the transition state (AB)" (if there is one) differs more or less from the initial state of the activated molecule (AB). ... 

Hence, the pre-exponential factor of the rate constant for unimolecular reaction is equal, in order of magnitude, to the universal frequency of transition-state theory. This conclusion is supported by a vast amount of experimental data. Exceptions to this rule can be ascribed to important changes of structure taking place in the transition state. It is still usually difficult to foresee such exceptions. 

Molecules consist of finite masses that vibrate within certain limits as if cmmected by perfect springs. A reaction event such as the breaking of a bond can occur at most oily once per vibration, en the extension of the spring exceeds its breaking strength. This vibrational frequency has been measured to be about lO sec for bonds in organic molecules, a value that therefore represents the upper limit of bond breaking frequency. This value has been accepted as the universal frequency factor for unimolecular elementary reactimis and represents the upper limit of unimolecular frequency fectOTs. 

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