Kinetic parameters, from Arrhenius plots

Table 11.2 Kinetic parameters from Arrhenius plot (Reprinted with permission from B.B. Busch, M.M. Paz, K.J. Shea et al., The boron-catalyzed polymerization of dimethylsulfoxonium methylide. A living polymethylene synthesis, Journal of the American Chemical Society, 124, 14, 3636-3646, 2002. 2002 American Chemical Society.)...

Introduction Dehydrations of metal hydroxides are attractive model reactions for basic studies of the kinetics of solid-state reactions and these reactions are widely used for the commercial production of metal oxides [45]. However, as shown in the recent paper by L vov and Ugolkov [55], available data on the reaction mechanisms and kinetics are inconsistent. For example, the parameter E for the dehydration of Mg(OH)2, reported in different papers, varies from 53 to 372 kJ mol One of the factors responsible for the large scatter of the E values estimated from Arrhenius plots is the low precision and accuracy of this method, especially as applied to decomposition to gaseous and solid products. The results obtained in [55[ by the third-law method, as indicated below, are much more reliable. 

From Arrhenius plots, shown in Figure 3, the kinetic parameters for the decomposition rate constant of diallyl were obtained as below ... 

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]. 

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 6.48 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.

The rate constant and activation parameters (E, InA) were calculated from the Arrhenius equation by plotting InK, vs T and collected in Table 4. Further the kinetic parameters like DS", DH", DG are calculated through Eyring equation by plotting (Kj/T)... 

A plot of In K versus 1/T is, therefore, expected to be a straight line, providing/the order of reaction is correctly chosen. The Arrhenius kinetic parameters, E and A, can be calculated from this plot. A plot of the initial self-heat rate versus the reciprocal of the initial temperature gives... 

Quantities corresponding to the above are frequently calculated from an Arrhenius plot for the parameters of empirical rate expressions. The sizes of these are not constrained by theory. The size of all fundamental kinetic parameters, in contrast, is invariably constrained by physical realities. On the low side the limit is usually zero. The high side is constrained, if only by the simple impossibility of accepting infinite values for approachable physical quantities. The reasons for the existence of limits less extreme but no less definite than zero and infinity must be understood, so that parameters which fell beyond realistic limits can be spotted in fitted rate expressions. Parameters that are out of realistic range cast serious doubt on the validity of the mechanism behind the rate expression being fitted. 

Using the above Arrhenius plot from a TS-PFR, a linear regression was performed and yielded the following kinetic parameters ... 

In the discussion so far, orders of one or two have been considered. Surface processes with other orders (and fractional orders) have been found and changes in Arrhenius plot slopes can be caused by changes in desorption mechanism. Equation (94) shows the general form of the dependence of the kinetic parameters on the desorption order in terms of initial coverages. Another important relationship can be derived from the work of Falconer [280] who showed that... 

One more typical systematic error that arises in determination of the E parameter with the Arrhenius plot method is the fairly arbitrary choice of kinetic model used to estimate the rate constant k from primary TA measurements. This statement is confirmed by numerous studies generalized, in... 

Rate constants have been calculated, and Arrhenius plots for the rate constants at several temperatures are given in Fig. 8. The kinetic parameters for the formation of methoxymethyl ion from the formate and acetate esters are given in Table XVII, where is the rate constant at 300°K the rate constants for the two compounds differ by a factor of two, with methoxy-... 

The Arrhenius plot generated from cure kinetics parameters (Figure 3) for this system essentially is linear through the cure region. The excellent fit obtained with the linear least squares regression over the temperature range of the cure reaction confirms the validity of the nth order kinetic model used to describe the cure of the uncatalyzed gel coat resins. 

Fig. 3. Arrhenius plot for kinetics parameters determined from DSC and a linear regression line over the temperature range selected for kinetics evaluation.

The mechanism for the modification of the kinetic parameters under the influence of the dietary lipids will be easily understood by describing the studies performed with the acetylcholinesterase from rat erythrocytes. The allosteric behavior (Hill plots) and temperature-dependent activity (Arrhenius plots) of the enzyme from rats fed a fat-free diet will be discussed in detail in the first part of this presentation. 

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