Apparent activation energy, definition

As explained before, a chemical reaction can seldom be described by a single elementary step, and hence we need to adapt our definition of activation for an overall reaction. Since we are not particularly interested in the effects of thermodynamics we define the apparent activation energy as... 

We should mention, furthermore, that the polymerization rates increased by the application of a field also for systems having positive apparent activation energy, and in such a case, the rate enhancement observed was definitely larger than that which could be expected by... 

By definition, the apparent activation energy of a process is determined by the equation... 

In this case, the apparent activation energy is not equal to the activation energy of the rate-determining step. By definition, the activation energy for elementary step 2 equals... 

From the definition of Ao.s, it follows that to.s is inversely proportional to the rate constant of the chemical reaction. The influence of substrate concentration, proton concentration pH), and temperature on the reaction rate can therefore be deduced simply from the variation in For example, the reaction order of the substrate can be determined as - logros/ logCo- Likewise, apparent activation energies, Fa, may be obtained from plots of to,5 against the inverse temperature (T ), since the slope is equal to —E /R [8], Kinetic isotope effects can also easily be... 

Table 2 summarizes the apparent activation energies for some of the compounds studied to date by this method. The values are usually small and definitely below the values for the activation of chemical, thermally-... 

The respective values of Ep and Ep p calculated from Fig.5 are about 4.8 Kcal/mole and 2.3 l cal/mole respectively the low activation energy of the isothermal process being indicative of a viscous flow mechanism while.the relatively higher value of Ep j is comparable with those generally found in diffusive processes (17-19). The concept of apparent activation energies for transport in a temperature gradient arises from the different dissolution enthalpies of the permeant on opposite partition sides. From the definition of enthalpy it follows that... 

When the isoconversional method is applied to the set of dynamic runs, an activation energy lying in the 69-73 kJ mol-1 range is obtained, without any definite trend with conversion. The value is very close to the one reported by Montserrat and Malek (1993) using this method again, this is an apparent value without any physical meaning. 

As much as the definition of the LBHB proposal is concerned, it is important to address the repeated attempts to use experimental observations as operational definitions of this proposal (e.g., Refs. 109,117). Apparently, such a definition confuses the interpretation of experiments with experimental facts. As has been shown in the Ref. 114, most experimental-based definitions of the LBHB proposal are equally consistent with the existence of an ionic HB. Several experiments (e.g., studies of the N H distance) are much more consistent with the ionic HB than the LBHB picture. However, the most crucial issue is the relative energy of the VB states or the ApA a (or AGp-r) in the protein active site at the TS. Now, since the corresponding ApA"as cannot be determined experimentally (even in cases of TS analogues we do not have... 

Another common theme in FP studies is the richness of possible surface phases -in some cases, dozens of structural isomers are computed to be thermodynamically accessible at room temperature. This has led to speculation that many oxide surfaces are more dynamic than previously thought, but definitive conclusions will only be possible once the processes of surface diffusion are identified and their activation energies are computed. This is perhaps the next frontier in FP oxide simulation. Meanwhile, the flexible surface model for active sites on metals [5] is finding some application in explaining the apparently facile diffusion of interstitial ions in non-stoichiometric oxides, despite the rigidity of the oxide lattice [26]. 

An impression of the reliability of such correlations is given in Figure 2.19, which presents the data used for the correlation of Semenov. There is quite a bit of scatter apparent, such that the rather generous limits indicated in the figure should be kept in mind. Benson reports also that neither of the two Hirschfelder rules is better than about 5 kcal/mol, which is enormous when one is concerned with activation energies, and that occasionally much larger discrepancies are encountered. Hence we take these as qualitative norms to provide guidance rather than quantitative numbers to provide definition, [see also Z.G. Szabo, Chem. Soc. (London) Spec. Publ., 16, 113 (1962)]. 

The examples chosen to illustrate changes in activity all pertain to catalysis with metallic films evaporated in vacuo so that at least the chemical composition of the catalyst is definitely known. For both activity and selectivity, cases of type A are not unexpected and have their counterpart in homogeneous kinetics where, for instance in the Bronsted relation, changes in rate are attributed t changes in activation cnei alone (see p. 172). Cases of the B type are more surprising and they are apparently found only in heterogeneous catalysis. They do not conform to the intuitive idea that a catalyst will be more active or selective if the activation energy is reduced in appropriate fashion. 

Dunham et have recently summarized their spectroscopic and magnetic susceptibility results on spinach and other two-iron ferredoxins they show how the results allow a precise definition of the active centre and provide a stringent set of criteria against which any further structural information may be tested. The c.d. and absorption spectra of spinach ferredoxin and another two-iron iron-sulphur protein, adrenodoxin, suggest that the reduced forms contain a high-spin ferrous ion in a distorted tetrahedral environment. The reaction between adrenodoxin and excess 1,10-phenanthroline apparently follows zero-order kinetics under aerobic conditions but first-order kinetics under anaerobic conditions the activation energies are 3.3 and 12.6 kcal mol, respectively. A reaction sequence is proposed. ... 

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