Arrhenius A-factor

Arrhenius A factors 24 combination ns disproportionation 41 2 disproportionation with fiuoromcthyl radicals 41... 

O Neil, H. E., and Benson, S. W, A method for estimating Arrhenius A factors for four- and six-center unimolecular reactions, J. Phys. Chem. 71, 2903 (1967). 

The most striking aspect of these results is the low Arrhenius A factors corresponding to p factors of the order of 10-3. Callear and Wilson attribute this to a lack of equilibrium involving the transition state caused by relaxation to the lower surface. It is clearly possible in principle to extend this type of measurement to other hydrocarbons. Its extension to the reactions of Br A Py2), although thermochemically favorable (Table X), would be very difficult experimentally on account of more rapid relaxation of Br(42/>i/2) (Table IX) yielding low stationary concentrations of the excited atoms, and possibly even lower yields of the products than with l(52Py, which, in the case of propane,65-88 involved measurement of the order of 10-9 moles in a given experiment.65... 

Marcus and Rice6 made a more detailed analysis of the recombination from the point of view of the reverse reaction, the unimolecular decomposition of ethane, C2Ha - 2CH3. By the principle of microscopic reversibility the transition states must be the same for forward and reverse paths. Although they reached no definite conclusion they pointed out that a very efficient recombination of CH3 radicals would imply a very high Arrhenius A factor for the unimolecular rate constant of the C2H6 decomposition which in turn would be compatible only with a very "loose transition state. Conversely, a very low recombination efficiency would imply a very tight structure for the transition state and a low A factor for the unimolecular decomposition. 

Table V shows the efficient organization of this reaction chemistry into five reaction families. Bond fission, for example, is the elementary step that creates two free radicals from a parent molecule. In chain processes this will often be the initiation step. Thermochemical estimates often show that the logarithm of the Arrhenius A factor (logioA) is of the order 14-17, whereas the activation energy is essentially equivalent to the bond dissociation energy (19,42). This equality is the result of the essentially unactivated reverse reaction step, radical recombination.

Ethyl bromide, in a static system, was studied at 724.5-755.1 K103. The pressure dependence for the HBr elimination was observed in its fall-off region. Evaluation of the rate coefficients was performed by using the RRKM theory and the values were compared with the experimental observation. The work reported an activation energy of 216.3 kJ moT1 and an Arrhenius A factor of 1012 5. The low-frequency factor was rationalized in terms of the formation of a tight activated complex and a molecular elimination as a prevalent reaction mode. 

The Arrhenius A factors for the propagation reactions are low and of the order one would expect from any of the transition-state theories for a bimolecular reaction between two large molecules (Table XII.2). The activation energies Ep for propagation are also low and of the order observed for similar addition reactions in the gas phase of radicals to a double bond. The values of At are in the range to be expected for diffusion-controlled reactions (Sec. XV.2) except for vinyl chloride, which must certainly be in error. As pointed out earlier in discussing diffusion-controlled reactions, it is expected that the activation energies will be of the order of a... 

At 60 C the reaction of a pure gas A is found to obey a rate law —dA/dt — /bA with k = 4.2 X 10 when A is measured in mm Hg pressure. At 100°C k = 1.4 X 10 in the same units, (a) Calculate the activation energy for the reaction and the Arrhenius A factor. (6) Compute the values of k at both 60 and 100°C when A is measured in units of moles/liter, (c) Calculate the activation energy and the Arrhenius A factor for the rate constant measured in the units of moles/liter and seconds. Arc these the same values as those obtained in (a) Is there a true activation energy for the reaction Explain. 

Fig. 19 yield —E and the intercepts giveApS/ZAtV, where Ep and Ft are the activation energy for polymerization and termination reaction and Ap and A the Arrhenius A factors for the same reactions. The data are li ed in Tables 9 and 10, together with values from other work. 

Low Arrhenius A factors suggest a tight" transition State, with loss of entropy compared with reagents. High A factors suggest a loose" transition state, with a gain of entropy compared with reagents... 

The Arrhenius A factor for the first-order gas-phase pyrolysis of ethyl acetate is 1012 5. Which of the two postulated mechanisms shown below does this favour ... 

Mechanism (a) is a molecular reaction with a "tight transition slate, whereas the rate determining step in (b) is homolysis into two radicals with a "loose" transition state, which would give a larger Arrhenius A factor. The observed A factor falls within the range expected for molecular reactions shown in Table 2.1 thus (a) is favoured. 

It has been seen (p. 92) that, on energetic grounds, a radical non-chain process may be excluded except in very special cases, and so no further consideration need be given to this mechanism. This leaves the decision to be made between the radical chain and the unimolecular mechanisms. There is, at the present time, no criterion which is both necessary and sufficient to prove that a given reaction is proceeding by a unimolecular mechanism. Necessary conditions for a unimolecular mechanism are (a) first-order kinetics at high pressures, (b) Lindemann fall-off at low pressures, (c) absence of induction periods, (d) lack of effect of inhibitors, and (e) an Arrhenius A factor of the order of 1013 sec-1. An additional useful test, though neither a necessary nor a sufficient condition, is the absence of stimulation of the reaction in the presence of atoms or radicals. Finally, the effects of structural alterations on the rates of those related reactions that are claimed to be unimolecular should be capable of interpretation within the framework of current chemical theory. 

Despite the potential interest in isomerization reactions, very little quantitative data exist. Only a few scattered and probably not very reliable activation energies have been reported, while two recent studies of 1,5-H atom shifts give unbelievably low values of the Arrhenius A-factors (22, 71). 

The introduction of competitive alkali metal flame reactions has allowed the experimental determination of activation energy differences for alkali metal flame reactions. The method involves the reaction of sodium or potassium with a pair of organic halides, one of which contains chlorine-36. Analysis of the solid halides produced provides a method of obtaining relative yields of the halides and thus relative rate coefficients. The use of a large temperature range (90—120°C) allows accurate measurements of activation energy differences and ratios of Arrhenius A factors. The values in Table 1 were so obtained. 

In the Arrhenius equation the parameter is known as the Arrhenius activation energy but usually is just referred to as the activation energy. The parameter A is the Arrhenius A-factor but, again, this is usually shortened to just A-/ ctor it is worth noting that the terms pre-exponential factor ox frequency factor are sometimes used. Together, the two parameters A and E are known as the Arrhenius parameters. 

According to Equation 6.3, this factor is equivalent to the Arrhenius A-factor. In the collision model it is a measure of the standard rate at which reactant species collide that is it is a measure of the number of collisions per second when the concentrations of the reactant species are both 1 mol dm"-. It is necessary to specify standard conditions since, in general, the collision rate depends on the concentrations of the species present (cf. Section 4.1). The value of Atheory a given bimolecular reaction depends on the hard-sphere radii and masses of the reactant species. Calculations show that it does not vary significantly from reaction to reaction with values usually of the order of 10 dm mol s . Table 7.1 compares the calculated values of Atheory for gas-phase bimolecular reactions with those derived from experiment. 

Transition state theory, if valid, can also be used to determine the tightness or looseness of the transition state molecular configuration as compared to that of the reactants. When transition state theory is formulated in thermodynamic terms it is found that the high pressure Arrhenius A- factor is given by... 

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