Arrhenius parameters, kinetic

It is noteworthy that the value of this substrate is smaller by one order compared to non-cyclic compounds. According to the discussions proposed above, this is considered to be due to its conformation already being fixed to the one that fits to the binding site of the enzyme. This estimation was demonstrated to be true by the examination of the effect of temperature on the kinetic parameters. Arrhenius plots of the rate constants of indane dicarboxylic acid and phenyl-malonic acid showed that the activation entropies of these substrates are —27.6 and —38.5 calmol K , respectively. The smaller activation entropy for the cyclic compound demonstrates that the 5yn-periplanar conformation of the substrate resembles the one of the transition state. 

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. 

The reactions were shown, in a representative number of cases, to follow second-order kinetics and to obey the Arrhenius law. The kinetic parameters are, of course, for the entire two-stage process. 

The above form of the Arrhenius equation takes into account the high degree of correlation that exists between the kinetic parameters. This pivoting method solves a convergence problem that can occur during parameter fitting if all six parameters (Fm, Em, Fdl, Edl, Fd2, and Ed2) are allowed to vary. 

The kinetic parameters are listed in Table 1. The linearity of lnAr l/r plot is revealed by the correlation coefficient. For all reactions but the deactivation, the rate constants follow the Arrhenius law satisfactorily, implying catalyst deactivation may involve more than one elementary steps. 

Figure 7.14. The temperature-programmed reaction and corresponding Arrhenius plot based on rate expression (21) enables the calculation of kinetic parameters for the elementary surface reaction between CO and O atoms on a Rh(lOO) surface.

The Arrhenius plots for both sets of kinetic parameters together with experimental points are shown in Fig. 5.4 -32. Experimental points scatter uniformly on both sides of the straight lines indicating that the power-law model with the evaluated rate constant can be satisfactorily used to describe the kinetic experiments under consideration. 

In all the above three-component models as well as in the four-component models presented next, an Arrhenius-type temperature dependence is assumed for all the kinetic parameters. Namely each parameter k, is of the form A,erJc>(-El/RT). 

Equations of an Arrhenius type are commonly used for the temperature-dependent rate constants ki = kifiexp(—E i/RT). The kinetics of all participating reactions are still under investigation and are not unambiguously determined [6-8], The published data depend on the specific experimental conditions and the resulting kinetic parameters vary considerably with the assumed kinetic model and the applied data-fitting procedure. Fradet and Marechal [9] pointed out that some data in the literature are erroneous due to the incorrect evaluation of experiments with changing volume. 

The evolution of emulsions through coalescence can be characterized by a kinetic parameter, >, describing the number of coalescence events per unit time and per unit surface area of the drops. Following the mean field description of Arrhenius,... 

The kinetic parameters of Zn(II)/Zn(Hg) electrode reaction in aqueous solution containing perchlorate, nitrate, chloride, and bromide ions were measured at different temperatures (5-50°C) [35]. The Arrhenius activation energy and thermodynamic parameters for the Zn(II)/Zn(Hg) system... 

The induction time t is of particular interest, since it can be compared to the induction time computed for an adiabatic thermal explosion (See Ref 6, pp 173—74 or Eq 6 of Article on Hot Spots, p H172-R) to provide a check on the correctness of the supposition that the input shock"generates a thermal explosion (at the shock entry face). Unfortunately, an exact quantitative treatment of the induction times of shock-generated thermal explosions suffers from a) uncertainty of the shockgenerated temperature in the LE and b) uncertainty in the Arrhenius kinetic parameters (activation energy and pre-exponential factor) (See Kinetics in this Vol)... 

Decarboxylase reaction Kinetic constants The optimum pH of the decarboxylase reaction was determined with the natural substrates of both enzymes, pyruvate (PDC) and benzoylformate (BFD). Both enzymes show a pH optimum at pH 6.0-6.5 for the decarboxylation reaction [4, 5] and investigation of the kinetic parameters gave hyperbolic v/[S] plots. The kinetic constants are given in Table 2.2.3.1. The catalytic activity of both enzymes increases with the temperature up to about 60 °C. From these data activation energies of 34 kj moT (PDC) and 38 kJ mol (BFD) were calculated using the Arrhenius equation [4, 6-8]. 

Compensation behavior occurs in the decomposition of hydrogen peroxide on Ag-Au alloys (25) and, unlike most other alloy systems, there is a systematic change in the Arrhenius parameters with proportions of metals present. This behavior is ascribed to the progressive transformation, with alloy composition, of the reaction mechanism from that characteristic of one metal to that which occurs on the other. In contrast, decomposition of hydrogen peroxide on Pd-Au alloys (27) does not correlate with ratios of metals present in the catalyst, and kinetic parameters are sensitive to surface pretreatment. 

Common features in the various theoretical explanations of compensation behavior referred to in Section II, A, 1-7 are the occurrence of parallel reactions that are characterized by different values of the kinetic parameters (A, E) and/or a systematic change in the effective concentrations of reactants across the temperature interval used in the measurements of the Arrhenius parameters. Both influences are based on reaction models for which the kinetic behavior cannot be represented as a single desorption step and, indeed, the overall surface interactions could be much more complicated. 

Temperature is recognised as having an effect on the growth yield, the endogenous respiration rate and the Monod kinetic parameters Ks and pm. Within the temperature range of 25 to 40°C these have been shown to have dependencies which could be accounted for by Arrhenius-type exponential equations (Topiwala and Sin-CLAIR<52)). If the temperature-dependent nature of the constants has to be taken into account, equation 5.70 must be written as ... 

To avoid difficulties related to the growth of pressure in a sealed vessels as well as temperature measurement, the esterification reaction of acetic acid with propanol was carried out in an open vessel under reflux conditions. It was found that ester concentrations during the course of the reaction were comparable under both conventional and microwave conditions [20]. In a similar reaction (i.e., the esterification of trimethylben-zoic acid with propanol), the kinetic parameters of the reaction under the Arrhenius law were estimated for conventional conditions. Then ester concentrations were calculated theoretically and compared with the results obtained for the reaction under microwave conditions. It was found that the theoretical values correlated well with the experimental results so microwave irradiation did not influence the rate of the reaction [21]. 

Mass transfer can alter the observed kinetic parameter of enzyme reactions. Hints of this are provided by non-linear Lineweaver-Burk plots (or other linearization methods), non-linear Arrhenius plots, or differing Ku values for native and immobilized enzymes. Different expressions have been developed for the description of apparent Michaelis constants under the influence of external mass transfer limitations by Homby (1968) [Eq. (5.69)], Kobayashi (1971), [Eq. (5.70)], and Schuler (1972) [Eq. (5.71)]. 

The second reason is closely related to the time scale of the experiment. This merits some kinetic considerations. Arrhenius activation energy of the homolytic decomposition of AIBN in toluene is l43kJmol 1 and log A is 17.33 (32). The Arrhenius parameters are not very sensitive to the solvent (33). Not all radicals produced by AIBN decomposition yield ROO radicals, because of reaction (17)... 

On the other hand, the effective collision concept can explain the Arrhenius term on the basis of the fraction of molecules having sufficient kinetic energy to destroy one or more chemical bonds of the reactant. More accurately, the formation of an activated complex (i.e., of an unstable reaction intermediate that rapidly degrades to products) can be assumed. Theoretical expressions are available to compute the rate of reaction from thermodynamic properties of the activated complex nevertheless, these expression are of no practical use because the detailed structure of the activated complexes is unknown in most cases. Thus, in general the kinetic parameters (rate constants, activation energies, orders of reaction) must be considered as unknown parameters, whose values must be adjusted on the basis of the experimental data. 

In order to estimate the kinetic parameters for the addition and condensation reactions, the procedure proposed in [11, 14] has been used, where the rate constant kc of each reaction at a fixed temperature of 80°C is computed by referring it to the rate constant k° at 80°C of a reference reaction, experimentally obtained. The ratio kc/k°, assumed to be temperature independent, can be computed by applying suitable correction coefficients, which take into account the different reactivity of the -ortho and -para positions of the phenol ring, the different reactivity due to the presence or absence of methylol groups and a frequency factor. In detail, the values in [11] for the resin RT84, obtained in the presence of an alkaline catalyst and with an initial molar ratio phenol/formaldehyde of 1 1.8, have been adopted. Once the rate constants at 80°C and the activation energies are known, it is possible to compute the preexponential factors ko of each reaction using the Arrhenius law (2.2). 

It should be noted that for elementary reactions (1) and (2) the kinetic parameters determined to some extent conform to the theory [32] and the results recently obtained in the work [33] on Arrhenius parameters of HO radical addition to ethylene (400-500 °C). For the reaction ... 

Varna and Saraf have derived correlations of the Arrhenius type for the kinetic constants k t 14 23 24 54 respectively. The authors were not able to obtain a correlation for the kinetic parameter k due to the fact that only relatively little decomposition of MA was observed under their experimental conditions. 

TABLE 24. Kinetic and Arrhenius parameters of haloketone pyrolyses at 360 °C... 

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