Arrhenius activation

In the high barrier limit, E is approximately equal to the Arrhenius activation energy. The ratio of... 

This equation results from the assumption that the actual reaction step in themial reaction systems can happen only in molecules (or collision pairs) with an energy exceeding some tlireshold energy Eq which is close, in general, to the Arrhenius activation energy defined by equation (A3.13.3). Radiative energization is at the basis of classical photochemistry (see e.g. [4, 3 and 7] and chapter B2.5) and historically has had an interesting sideline in the radiation... 

Collision theory leads to this equation for the rate constant k = A exp (-EIRT) = A T exp (,—EIRT). Show how the energy E is related to the Arrhenius activation energy E (presuming the Arrhenius preexponential factor is temperature independent). 

Figure 6-3. Distriburion of Arrhenius activation energies for 147 drug decomposition reactions.

The Arrhenius activation energy,E. c Entropy of activation, 8 jjgt. 

Bimolecular rate constants determined at temperatures giving conveniently measurable rates and calculated for the temperature given in parentheses, c The Arrhenius activation energy,... 

Ea = Arrhenius activation energy Es = excess stress energy AEr = potential barrier for bond rotation Eel = molecular elastic energy F = mean force potential f = average force on the chain fb = bond breaking force H0 = Hookean spring constant kB = Boltzmann constant... 

If a data set containing k T) pairs is fitted to this equation, the values of these two parameters are obtained. They are A, the pre-exponential factor (less desirably called the frequency factor), and Ea, the Arrhenius activation energy or sometimes simply the activation energy. Both A and Ea are usually assumed to be temperature-independent in most instances, this approximation proves to be a very good one, at least over a modest temperature range. The second equation used to express the temperature dependence of a rate constant results from transition state theory (TST). Its form is... 

Thus, In k will vary linearly with 1 fT. This plot yields A from the intercept and Ea from the slope. Equation (7-1) or (7-3) provides a definition of the Arrhenius activation energy, which is expressed as... 

The Arrhenius activation energy,3 obtained from the temperature dependence of the three-halves-order rate constant, is Ea = 201 kJ mol-1. This is considerably less than the standard enthalpy change for the homolysis of acetaldehyde, determined by the usual thermodynamic methods. That is, reaction (8-5) has AH = 345 kJ mol-1. At first glance, this disparity makes it seem as if dissociation of acetaldehyde could not be a predecessor step. Actually, however, the agreement is excellent when properly interpreted. 

As the reaction proceeds higher sulfanes and finally Ss are formed. The reaction is autocatalytic which makes any kinetic analysis difficult. The authors discussed a number of reaction mechanisms which are, however, obsolete by today s standards. Also, the reported Arrhenius activation energy of 107 17 kJ mol is questionable since it was derived from the study of the decomposition of a mixture of disulfane and higher sulfanes. Nevertheless, the observed autocatalytic behavior may be explained by the easier ho-molytic SS bond dissociation of the higher sulfanes formed as intermediate products compared to the SS bond of disulfane (see above). The free radicals formed may then attack the disulfane molecule with formation of H2S on the one hand and higher and higher sulfanes on the other hand from which eventually an Ss molecule is split off. 

Arrhenius activation energy potential energy zero-point energy degrees of freedom... 

From the temperatures for the one- and ten-hour half lives, calculated using equation 6, Arrhenius activation parameters can be calculated for each initiator and compared to the experimental values. This comparison is made for some of the entries of reactions 1-4 in Table V. At least five entries were chosen for each reaction, spanning a wide range of reactivity, using common entries as much as possible for the four reactions. 

It is sometimes informative to separate AG into hypothetical enthalpic and entropic terms, and then the Arrhenius factors may be related to the transition state activation parameters by Eqs 10.4 and 10.5. Thus, the Arrhenius activation energy can be approximately related to the potential energy of a transition state, and the preexponential A value includes probability factors. 

If errors in each of the experimental quantities ku k2, T i and T2 are random, the relative error in the Arrhenius activation energy is given by... 

The activation energy Ee is related to the experimentally determined Arrhenius activation energy E by the relation ... 

Td is the decomposition temperature (K) and Ea is the Arrhenius activation energy (kcal/mol). 

Table 5 Arrhenius activation energies, entropies of activation and rate constants at 308 K for reaction of A-acetoxy-A-alkoxybenzamides 25, iV-acetoxy-iV-butoxybenzamides 26, iV-benzoyloxy-iV-benzyloxybenzamides 2842,43 and other iV-acyloxy-iV-alkoxyamides with A-methylaniline in d4-methanol...

Electronic effects. Nucleophilic attack is favoured by electron-withdrawing groups on the amide and the acyloxyl side chains. Interpolated bimolecular rate constants at 308 K for the series of para-substituted /V-acetoxy-/V-butoxybenzamides 25c, 26b-g and 26i (Table 5) gave a weak but positive Hammett correlation with a constants ip = 0.13, r = 0.86).42,43 These Sn2 reactions are analogous to those of aniline and substituted pyridines with phenacyl bromides, which have similar Arrhenius activation energies and entropies of activation in methanol (EA= 14-16 kcal mol-1, AS = — 27 to —31 calK-1 mol-1) and 4-substituted phenacyl halides afforded a similar Hammett correlation with pyridine in methanol (cr, p — 0.25).175... 

Carbon dioxide decomposes behind a shock front in accordance with the kinetics expected of a unimolecular reaction in its low-pressure region31-37. The second-order rate coefficients obtained by a number of experimentalists in the temperature range 2500-11000 °K are in reasonable agreement, but there is a considerable spread in the values derived for the Arrhenius activation energy (Table 3). Furthermore, even the highest of these values31 is much smaller than the endothermicity (D = 125.8 kcal.mole-1) of... 

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