Arrhenius activation parameters calculation

From the temperatures for the one- and ten-hour half lives, calculated using equation 6, Arrhenius activation parameters can be calculated for each initiator and compared to the experimental values. This comparison is made for some of the entries of reactions 1-4 in Table V. At least five entries were chosen for each reaction, spanning a wide range of reactivity, using common entries as much as possible for the four reactions. 

Decomposition rate constants are measured over as wide a temperature range as possible. Only the first one third to one half of the decomposition can be analyzed before it becomes severely autocatalytic. With the rate constants, an Arrhenius plot can be constructed and activation parameters calculated. Activation energies and pre-exponential factors correlate the decomposition rates with temperature. In addition, the magnitude of the activation energy may shed light on the key step in the decomposition process, and Arrhenius parameters are necessary in many explosive code calculations. Our procedure is to input the activation parameters into the Frank-Kamentskii equation [145] and use it to predict critical temperature of a reasonable size (e.g. 1 kilogram) of the energetic material ... 

All calculated data are summarized in Tables 1 and 2. Comparison of the Arrhenius activation parameters evaluated according to the method proposed in this work with those obtained by "conventional" procedure (see Table 1), shows their good coincidence. This suggests that the proposed method allows performing analysis of the temperature responses of linear voltammograms for irreversible electrode processes it seems to be less tedious in comparison with the "conventional" procedure. 

Only true rate constants (i.e., those with no unresolved concentration dependences) can properly be treated by the Arrhenius or transition state models. Meaningful values are not obtained if pseudo-order rate constants or the rates themselves are correlated by Eq. (7-1) or Eq. (7-2). This error is found not uncommonly in the literature. The activation parameters from such calculations, A and AS in particular, are meaningless. 

The TGA system was a Perkin-Elmer TGS-2 thermobalance with System 4 controller. Sample mass was 2 to 4 mgs with a N2 flow of 30 cc/min. Samples were initially held at 110°C for 10 minutes to remove moisture and residual air, then heated at a rate of 150°C/min to the desired temperature set by the controller. TGA data from the initial four minutes once the target pyrolysis temperature was reached was not used to calculate rate constants in order to avoid temperature lag complications. Reaction temperature remained steady and was within 2°C of the desired temperature. The actual observed pyrolysis temperature was used to calculate activation parameters. The dimensionless "weight/mass" Me was calculated using Equation 1. Instead of calculating Mr by extrapolation of the isothermal plot to infinity, Mr was determined by heating each sample/additive to 550°C under N2. This method was used because cellulose TGA rates have been shown to follow Arrhenius plots (4,8,10-12,15,16,19,23,26,31). Thus, Mr at infinity should be the same regardless of the isothermal pyrolysis temperature. A few duplicate runs were made to insure that the results were reproducible and not affected by sample size and/or mass. The Me values were calculated at 4-minute intervals to give 14 data points per run. These values were then used to... 

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. 

When the commodity chemical propylene oxide is heated to high temperature in the gas phase in a shock tube, unimolecular rearrangement reactions occur that generate the CsHgO isomers allyl alcohol, methyl vinyl edier, propanal, and acetone (Figure 15.9). Dubnikova and Lifshitz carried out a series of calculations to determine the mechanistic pathway(s) for each isomerization, with comparison of activation parameters to those determined from Arrhenius fits to experimental rate data to validate the theoretical protocol. 

Both ki and the ratio k2lk3 gave linear Arrhenius plots. Activation parameters were calculated from these data as follows (at 25°C) ... 

The kinetics of the addition of aniline (PI1NH2) to ethyl propiolate (HC CCChEt) in DMSO as solvent has been studied by spectrophotometry at 399 nm using the variable time method. The initial rate method was employed to determine the order of the reaction with respect to the reactants, and a pseudo-first-order method was used to calculate the rate constant. The Arrhenius equation log k = 6.07 - (12.96/2.303RT) was obtained the activation parameters, Ea, AH, AG, and Aat 300 K were found to be 12.96, 13.55, 23.31 kcalmol-1 and -32.76 cal mol-1 K-1, respectively. The results revealed a first-order reaction with respect to both aniline and ethyl propiolate. In addition, combination of the experimental results and calculations using density functional theory (DFT) at the B3LYP/6-31G level, a mechanism for this reaction was proposed.181... 

The activation parameters for the acid-catalyzed hydrolysis of long chain alkyl sulfates compared to those for non-micellar ethyl sulfate calculated from potentiometric data indicate that the rate acceleration accompanying micellization is primarily a consequence of a decrease in the enthalpy of activation rather than an increase in the entropy (Kurz, 1962). However, the activation energies for the acid-catalyzed hydrolysis of sodium dodecyl sulfate calculated from spectrophotometric data have been reported to be identical (Table 8) for micellar and non-micellar solutions, but the entropy of activation for the hydrolysis of the micellar sulfate was found to be 6 9 e.u. greater than that for the non-micellar system (Motsavage and Kostenbauder, 1963). This apparent discrepancy may be due to the choice of the non-micellar state as the basis of comparison, i.e. ethyl sulfate and non-micellar dodecyl sulfate, to temperature dependent errors in the values of the acid catalyzed rate constant determined potentiometrically, or to deviations in the rate constants from the Arrhenius equation. 

Measurements of rate constants at more than one temperature enable calculations to be made of the Arrhenius activation energy, and of the enthalpy AH and entropy of activation. In most cases, the accuracy of the nmr data is not sufficient for meaningful values of these three parameters to be obtained and in most of the experimental work to be presented in this chapter, only AG will be given. However, strain energy calculations, with few exceptions, refer to AH at absolute zero, and not to AG. Since AG=AH—TAS, and entropy effects appear to be only a minor perturbation in most cases, a comparison of AG with AH )qos. can be justified, at least as a first approximation. 

With the assumptions that (2) represents the slow step and that kj = Ogg calculated Arrhenius parameters for the concurrent bimolecular (1) and unimolec-ular (2) processes. The Arrhenius activation energy for step (2) was calculated to be 43 kcal.mole for each of the alkyl iodides, and, assuming Ogg s mechanism, this value should equal the carbon-iodine bond dissociation energy in each of these molecules. Modern studies show that the D(R—I) values are in the range 50-55 kcal.mole" and for this and other reasons Ogg s mechanism is now considered unsatisfactory. 

The main chemisorption activation parameters, that are the pre-exponential factor (A ) which does not depend on 0 and activation energy on the "free" surface (Ef ) have been calculated, proceeding from the temperature dependence of ko on T, by the Arrhenius equation. 

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)... 

In this Section, the process of deformation, relaxation, and fracture are examined only within a restricted temperature range between the main 0 and a) relaxational transitions, Tp < T < T. The kinetics of creep, relaxation of stress and Young s modulus, and fracture are investigated experimentally as a function of the external stress applied to a sample and/or the increase in temperature. It is shown that the kinetics of the processes considered are described by Arrhenius-type equations. Then, the activation parameters (the energy and the volume) of the kinetic equations are calculated and compared with each other. This procedure demonstrates the identical physical nature of these processes. 

Finally, from Arrhenius Equation and Eyring Equation plots (Fig. 3), activation parameters, e.g. energy ( .4), enthalpy (AH ) and entropy (zl5 ) of activatiOTi, were calculated. Values of these parameters are gathered in Table 2 ... 

A third indentation test parameter of fundamental importance is temperature. In several studies of the temperature dependence of hardness, an activated process becomes apparent from Arrhenius-type behavior. Calculation of the activation energies associated with thermal softening is characteristic of the activated processes governing plastic flow in crystals. " Thus, the role played by the crystal structure in determining micro- and low-load hardness values must be a major one since, apart from its effect on lattice energy, the actual arrangement of the ions in a ceramic crystal is important in determining the ease of plastic flow. This aspect of ceramic hardness and its potential applications is discussed in Chapter 3. 

Unfortunately, the values of the rate constants of the elementary reactions k) could not be evaluated because of the non-availability of the formation constants K2) at different temperatures. Therefore, the apparent rate constants k andk") are considered to be composite quantities of the rate constants, the protonation constants and the formation constants, respectively. The activation parameters of the second-order rate constants were calculated from the temperature dependence of the rate constants using Arrhenius and Eyring equations by the method of least-squares and are summarized in Table 12.4. Again, the thermodynamic parameters of the protonation constants were evaluated from the well-known thermodynamic methods and are listed in Table 12.5. 

Using the Arrhenius parameters calculate the activation parameters for the racemization of [6]helicenes 1, 3 and 4 at 200°C. Explain the behavior towards racemization of unbridged[6]-helicene 1 and its bridged congeners 3 and 4. 

Usually, only the Arrhenius energy of activation, E, is given in these papers it differs from the heat of activation,JH, by RT (about 0.6 kcal at ordinary temperatures). Only a few entropies of activa-tion, JS, were calculated the frequency factor, whose logarithm is tabulated, is proportional to this reaction parameter. It is clear that the rate, E, and JS determined for an 8jfAr2 reaction are for the overall, two-stage process. Both stages will contribute to the overall results when their free energies of activation are similar. 

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