Arrhenius plots, kinetic parameters

A ten to hundredfold decrease in the velocity of the reaction, seen as a break down of the Arrhenius plot, is observed at a temperature which, for any given pressure, is always higher than that thermodynamically foreseen for the beginning of the a-/3 transition (this discrepancy is smallest at 265 mm Hg pressure). The marked decrease of the rate of reaction is characteristic of the appearance of the /3-hydride phase. The kinetics of reaction on the hydride follows the Arrhenius law but with different values of its parameters than in the case of the a-phase. 

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.

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. 

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. 

Using the same experimental approach, a family of enantiomerically pure oxonium ions, i.e., O-protonated 1-aryl-l-methoxyethanes (aryl = 4-methylphenyl ((5 )-49) 4-chlorophenyl ((5)-50) 3-(a,a,a-trifluoromethyl)phenyl ((5)-51) 4-(a,a,a-trifluoromethyl)phenyl ((S)-52) 1,2,3,4,5- pentafluorophenyl ((/f)-53)) and 1-phenyl-l-methoxy-2,2,2-trifluoroethane ((l )-54), has been generated in the gas phase by (CH3)2Cl -methylation of the corresponding l-arylethanols. ° Some information on their reaction dynamics was obtained from a detailed kinetic study of their inversion of configuration and dissociation. Figs. 23 and 24 report respectively the Arrhenius plots of and fc iss for all the selected alcohols, together with (/f)-40) of Scheme 23. The relevant linear curves obey the equations reported in Tables 23 and 24, respectively. The corresponding activation parameters were calculated from the transition-state theory. 

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]. 

Kinetic measurements in various solvents show that addition of the monomer to the free anion depends only on the temperature and not (or practically not) on the solvent see Figure 8. The Arrhenius plot gives a straight line with the following (average) values of the parameters ... 

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)]. 

Quantitative investigations of the photoinduced electron transfer from excited Ru(II) (bpy)3 to MV2 + were made in Ref. [54], in which the effect of temperature has been studied by steady state and pulse photolysis techniques. The parameters ve and ae were found in Ref. [54] by fitting the experimental data on kinetics of the excited Ru(II) (bpy)3 decay with the kinetic equation of the Eq. (8) type. It was found that ae did not depend on temperature and was equal to 4.2 + 0.2 A. The frequency factor vc decreased about four orders of magnitude with decreasing the temperature down to 77 K, but the Arrhenius plot for W was not linear, as is shown in Fig. 9. 

The absolute rate constants for ene-addition of acetone to the substituted 1,1-diphenyl-silenes 19a-e at 23 °C (affording the silyl enol ethers 53 equation 46) correlate with Hammett substituent parameters, leading to p-values of +1.5 and +1.1 in hexane and acetonitrile solution, respectively41. Table 8 lists the absolute rate constants reported for the reactions in isooctane solution, along with k /k -, values calculated as the ratio of the rate constants for reaction of acetone and acctonc-rff,. In acetonitrile the kinetic isotope effects range in magnitude from k /k y = 3.1 (i.e. 1.21 per deuterium) for the least reactive member of the series (19b) to A hA D = 1.3 (i.e. 1.04 per deuterium) for the most reactive (19e)41. Arrhenius plots for the reactions of 19a and 19e with acetone in the two solvents are shown in Figure 9, and were analysed in terms of the mechanism of equation 46. 

The variation of the cathodic peak potential with the scan rate (0.3-0.4 mV precision on each determination, 1 mV reproducibility over the whole set of experiments) allows the determination of the rate constant with a relative error of 3-11%. The results are consistent with those derived from anodic-to-cathodic peak current ratios. Simulation of the whole voltammogram confirms the absence of significant systematic errors that could arise from the assumptions underlying the analysis of kinetic data. Activation parameters derived from weighted regression Arrhenius plots of the data points taken at 5 or 6 tern-... 

Figure 6.18 Arrhenius plots of the kinetic parameters. (Reproduced by permission of the American Chemical Society)...

Finally, the kinetic parameters for homogeneous tar conversion are determined by least squares fitting of the determined values of k, Fig. 7 shows the resulting Arrhenius plot. 

Fig. 8 Arrhenius plot of CO emission during pyrolysis of cubic dried birchwood particles of approximately 100 mg. The line corresponds to a least square fit. Kinetic parameters are given in the figure.

The isomerization of 8 -HOABA and 37 was observed as a first-order reaction in which the rate was proportional only to the concentration of the 8 -hydroxyl compound. As the pH and temperature increased the reaction proceeded more rapidly. At 25°C, the half-life of 8 -HOABA was 30 hr at pH 3, 4 hr at pH 7, and shorter than 1 min at pH 10, that is, 8 -HOABA was isomerized to PA more rapidly at pH 10 than at pH 3 by a fa.ctor of 2,000. The temperature dependence of the rate was greater under alkaline conditions than under acidic conditions. The Arrhenius plots of the rate constants gave the activation energies of Arrhenius and frequency factors, which were converted to the kinetic parameters, i.e. the activation enthalpy activation entropy (4S ) and activation free... 

Figure 6.48 Arrhenius plot of the triplet state tautomerism of2-( 2 -hydroxy-4 -methylphenyl) benzoxazole (Me-BO, upper curve) and its deuterated analog (lower curve) dissolved in alkanes. The kinetic data were taken from Al-Soufi et al, [83]. The solid lines were calculated using the parameters listed in Table 6.4.

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