Arrhenius parameter

Arrhenius Parameters A. Interrelation Between Arrhenius Parameters 

The elementary rate constants of the polymerization of vinyl acetate have been determined over a temperature range of 50 degrees (Berezhnykh-Foldes and TiidSs, 1964 Tiidos et al., 1967), and Arrhenius parameter determinations became possible for inhibition processes of radical polymerization of vinyl acetate according to equations (40)-(42) 

Arrhenius Parameters for Hydrogen Atom Abstraction Reactions 

Correlations of the above type are called compensation effects since the correlated variation of A and E results usually in slight changes of the rate constant, a good part of the individual influences of A and E being cancelled. 

Equation (43), if strictly valid, implies that rate constants of reactions of the given series depend only on one instead of two parameters. (The strong resemblance of this problem to that of the Hammett equation was considered by Leffler and Grunwald, 1963, and by Ritchie and Sager, 1964.) In a general case, the correlation may be given by 

The parameter A (which has the same units as k ) is called the pre-exponential factor and the parameter (which is a molar energy and normally expressed as kilojoules per mole) is called the activation energy. Collectively, A and are called the Arrhenius parameters of the reaction. 

The rate constant of the acid hydrolysis of sucrose discussed in Section 6.6b varies with temperature as follows. Find the activation energy and the preexponential factor. 

Strategy We plot In fc, against 1/T and expect a straight line. The slope is -EJR and the intercept of the extrapolation to 1/T = 0 is In A. It is best to do a least-squares fit of the data to a straight fine. Note that, as remarked in the text, A has the same units as k.  

Solution The Arrhenius plot is shown in Fig. 6.17. The least-squares best fit of the line has slope -1.10 X 10 and intercept 31.7 (which is well off the graph), therefore 

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Although the Arrhenius equation does not predict rate constants without parameters obtained from another source, it does predict the temperature dependence of reaction rates. The Arrhenius parameters are often obtained from experimental kinetics results since these are an easy way to compare reaction kinetics. The Arrhenius equation is also often used to describe chemical kinetics in computational fluid dynamics programs for the purposes of designing chemical manufacturing equipment, such as flow reactors. Many computational predictions are based on computing the Arrhenius parameters. 

There are available from experiment, for such reactions, measurements of rates and the familiar Arrhenius parameters and, much more rarely, the temperature coefficients of the latter. The theories which we use, to relate structure to the ability to take part in reactions, provide static models of reactants or transition states which quite neglect thermal energy. Enthalpies of activation at zero temperature would evidently be the quantities in terms of which to discuss these descriptions, but they are unknown and we must enquire which of the experimentally available quantities is most appropriately used for this purpose. 

TABLE 8.1 The acidity dependence and Arrhenius parameters for the nitration of some cations in... 

Further problems arise if measurements of the rate of nitration have been made at temperatures other than 25 °C under these circumstances two procedures are feasible. The first is discussed in 8.2.2 below. In the second the rate profile for the compound imder investigation is corrected to 25 °C by use of the Arrhenius parameters, and then further corrected for protonation to give the calculated value of logio/i fb. at 25 °C, and thus the calculated rate profile for the free base at 25 °C. The obvious disadvantage is the inaccuracy which arises from the Arrhenius extrapolation, and the fact that, as mentioned above, it is not always known which acidity functions are appropriate. 

Kinetic data are available for the range 7S S 98 i % sulphuric acid, and Arrhenius parameters at several acidities. The relative rate was obtained as before. 

The case of i-methyl-4-quinolone is puzzling. The large proportion of the 3-nitro isomer formed in the nitration (table 10.3 cf. 4-hydroxyquinoline) might be a result of nitration via the free base but this is not substantiated by the acidity dependence of the rate of nitration or by the Arrhenius parameters. From r-methyl-4-quinolone the total yield of nitro-compounds was not high (table ro.3). 

Arrhenius parameters, and nitration of bases, 155-9 for nitration of aza-naphthalenes, 209-11... 

Pyridine, 3-(dimethylamino)-amination, 2, 236 methylation, 2, 342 nitration, 2, 192 iV-oxide synthesis, 2, 342 Pyridine, 4-(dimethylamino)-in acylation, 2, 180 alkyl derivatives pK, 2, 171 amination, 2, 234 Arrhenius parameters, 2, 172 as base catalysts, 1, 475 hydrogen-deuterium exchange, 2, 286 ionization constants, 2, 172 methylation, 2, 342 nitration, 2, 192 iV-oxide synthesis, 2, 342... 

In a senes of papers. Tedder and co-workers reported the factors determining the reactivity of perfluormated radicals with various fluoroethylenes Relative Arrhenius parameters for tnfluoromethyl radicals [17] and pentafluoroethyl radicals [/5] were determined, with higher selectivity demonstrated for the higher homologue Selectivity of addition to unsymmetncal olefins was found also to increase with greater radical branching [19]... 

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are... 

The reaction between nitroxides and carbon-centered radicals occurs at near (but not at) diffusion controlled rates. Rate constants and Arrhenius parameters for coupling of nitroxides and various carbon-centered radicals have been determined.508 311 The rate constants (20 °C) for the reaction of TEMPO with primary, secondary and tertiary alkyl and benzyl radicals are 1.2, 1.0, 0.8 and 0.5x109 M 1 s 1 respectively. The corresponding rate constants for reaction of 115 are slightly higher. If due allowance is made for the afore-mentioned sensitivity to radical structure510 and some dependence on reaction conditions,511 the reaction can be applied as a clock reaction to estimate rate constants for reactions between carbon-centered radicals and monomers504 506"07312 or other substrates.20... 

Viswanadhan and Matticc278 carried out calculations aimed at rationalizing the relative frequency of backbiting in these and other polymerizations in terms of the ease of adopting the required conformation for intramolecular abstraction (see 2.4.4), More recent theoretical studies generally support these conclusions and provide more quantitative estimates of the Arrhenius parameters for the... 

A and E refer to the desorption, dissociation, decomposition or other surface reactions by which the reactant or reactants represented by M are converted into products. If [M] is constant within the temperature interval studied, then the values of A and E measured refer to this process. Alternatively, if the effective magnitude of [M] varies with temperature, the apparent Arrhenius parameters do not specifically refer to the product evolution step. This is demonstrated quantitatively by the following example [36]. When E = 100 kJmole-1 andA [M] = 3.2 X 1030 molecules sec-1, then rate coefficients at 400 and 500 K are 2.4 X 1017 and 1.0 X 1020 molecules sec-1, respectively. If, however, E is again 100 kJ mole-1 and A [M] varies between 3.2 X 1030 molecules sec-1 at 500 K and z X 3.2 X 1030 molecules sec-1 at 400 K, the measured values of A and E vary significantly, as shown in Fig. 7, when z ranges from 10-3 to 103. Thus, the measured value of E is not necessarily identifiable with the rate-limiting step if a concentration of a participant is temperature-dependent. This... 

Arrhenius parameters were shown to be consistent with the Polanyi—Wigner model, eqn. (19), and E = 125 kJ mole 1. 

Fig. 16. Graphical representation of Arrhenius parameters for the low temperature decomposition of ammonium perchlorate (pelleted, orthorhombic, o, and cubic, , forms). Compensation behaviour is observed. Data from Jacobs and Ng [452]. N = nucleation, B = branching, G = growth processes.

Powell and Searcy [1288], in a study of CaMg(C03)2 decomposition at 750—900 K by the torsion—effusion and torsion—Langmuir techniques, conclude that dolomite and C02 are in equilibrium with a glassy phase having a free energy of formation of (73 600 — 36.8T)J from 0.5 CaO + 0.5 MgO. The apparent Arrhenius parameters for the decomposition are calculated as E = 194 kJ mole-1 and activation entropy = 93 JK-1 (mole C02)-1. 

A detailed account of transport phenomena in crystals is outside the scope of the present review, though it is relevant to point out that factors which determine the rate at which reactants penetrate a barrier layer include the numbers, distributions and mobilities of vacancies. Oleinikov et al. [1173] conclude that Arrhenius parameters are devoid of any physical significance if due allowance is not made for imperfection concentration, which may vary with temperature (and a [77]). 

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