Activation energy, calculation

Findings with Bench-Scale Unit. We performed this type of process variable scan for several sets of catalyst-liquid pairs (e.g., Figure 2). In all cases, the data supported the proposed mechanism. Examination of the effect of temperature on the kinetic rate constant produced a typical Arrhenius plot (Figure 3). The activation energy calculated for all of the systems run in the bench-scale unit was 18,000-24,000 cal/g mole. 

The reader may now wish to verify that the activation energy calculated by logarithmic differentiation contains a contribution Sk T/l in addition to A , whereas the pre-exponential needs to be multiplied by the factor e in order to properly compare Eq. (139) with the Arrhenius equation. Although the prefactor turns out to have a rather strong temperature dependence, the deviation of a In k versus 1/T Arrhenius plot from a straight line will be small if the activation energy is not too small. 

The chemical reactivity of compounds is studied by transition state location, activation energy calculations, and relative energies of the products versus reactants. 

In the second investigation [34], involving a coumarin synthesis by Knoevenagel condensation, supported by rate constant measurements and activation energy calculations, it was found that the effect of MW was more important when the reaction was conducted in xylene - it was noticeably reduced in ethanol (Eq. (5) and Tab. 3.3). 

Certain specific steric effects are operative on intramolecular nitrile oxide— olefin cycloadditions. These effects are governed by both ring size and character of substituents. Thus, cycloadditions to the exomethylene group are successful with substituted methylenecyclohexanones 334 (m = 1, 2 n = 2) and gave tricyclic 335 (m = 1, 2), but do not occur with methylenecyclopentanones 334 (m = 1, 2, 3 n = 1). Activation energies calculated by molecular mechanics are consistent with these results. Cleavage of 335 (m = 2) by Raney Ni gives cA-decalone 336 (403). 

Fig. 17 The Bergman cyclizations of parent and fluoro-substituted enediynes with the triple bond and the incipient bond lengths and the activation energies calculated at the BS-UB3LYP/6-31G level.

The new features of this Table are (i) the values calculated by me (1, 2 and 3) (ii) the recognition that the values quoted apply only over a range of m which depends on the nature of the solvent (iii) the k+p for styrene and EVE in solvents of low polarity are very similar. In my view none of these values and others in the literature are sufficiently reliable for any activation energies calculated from them to afford useful information. I have refrained from attempting a correlation of the rate constants with the dielectric constant of the diluent because in my view even the same cation in each different solvent is a different species, so that the fundamental hypothesis of theories of the Laidler type is not valid. 

The preceding data, though limited in nature, represent one of the first attempts to measure solid state diffusion rates of alkali elements into the near-surface region of feldspars and natural glasses at low temperature. As such, interesting comparisons can be made with diffusion coefficients and activation energies calculated from numerous high temperature isotope and tracer diffusion studies f 11-181. 

The activation energies calculated for Rb, Cs and Sr in the present study (Table III and Figure 8) are considerably lower than those calculated for high temperature diffusion in both crystalline and glass silicates. This discrepancy in the latter case implies that the glass matrix may be significantly different in high and low temperature diffusion studies. 

Data from tests at 250,275,300, and 325 C were used to calculate pseudo-first order rate constants for the formation of H2S. These data are expressed on a standard Arriienius plot (Fig. 2) for which the linear least squares coefficient of determination, r, is 0.98. The apparent activation energy calculated from the slope is 28.5 kcal/mol. This result is in excellent agreement with the recent work of Abotsi, who studied the performance of carbon-supported hydrodesulfurization catalysts (10). Using Ambersorb XE-348 carbon lo ed with sulfided ammonium molybdate (3% Mo loading) prepared by the same procedure reported here, Abotsi hydrotreated a coal-derived recycle solvent The apparent activation energy for... 

The activation energies calculated for the two steps of the above reaction are + 160 kJ/mol for the ki step and -l- 78 kJ/mol for the k2 step [15]. The overall enthalpy of reaction is — 78 kJ/mol. It has been found that the half-life for the ki reaction is sensitive to the counterion concentration in case of SDS micelles. The effect of added counterion may be due to the charge neutralisation of the sulphate anion heads in the SDS micellar Stern layer, to facilitate approach and penetration of the CN- ions at the micelle-water interface. Hemin encapsulated in CTAB micelles reacts much faster with cyanide compared to that in SDS presumably because of the cationic Stern layer in CTAB. The... 

Calculations confirm the Cossee mechanism for olefin insertion [7, 26-28]. For the simple Me2AlEt model, the ethene complexation energy is only a few kcal/mol. The activation energy calculated at the highest theoretical level [7] agrees well with the experimental estimate. 

It goes without saying that direct comparison of calculated (absolute) activation energies with experimental 8a parameters is likely to prove problematic in some situations. For this reason, it is perhaps better to judge the performance of individual models by comparison with activation energies calculated from a standard reference. This standard has been chosen as MP2/6-311+G, the same level used as a standard to judge transition-state geometries. 

Is it always necessary to utilize exact transition-state geometries in carrying out activation energy calculations, or will approximate geometries suffice ... 

Both 3-21G and 6-3IG Hartree-Fock models provide better and more consistent results in supplying reactant and transition-state geometries than the AMI calculations. Also the two Hartree-Fock models (unlike the AMI model) find reasonable transition states for all reactions. With only a few exceptions, activation energies calculated using approximate geometries differ from exact values by only 1-2 kcal/mol. 

A second set of comparisons assesses the consequences of use of approximate reactant and transition-state geometries for relative activation energy calculations, that is, activation energies for a series of closely related reactions relative to the activation energy of one member of the series. Two different examples have been provided, both of which involve Diels-Alder chemistry. The first involves cycloadditions of cyclopentadiene and a series of electron-deficient dienophiles. Experimental activation energies (relative to Diels-Alder... 

Localized MP2 (LMP2) models have already been shown to provide results which are nearly indistinguishable from MP2 models for both thermochemical calculations (see Chapter 12) and for calculation of conformational energy differences (see Chapter 14). Activation energy calculations provide an even more stringent test. Transition states necessarily involve delocalized bonding, which may in turn be problematic for localization procedures. 

Table I Activation energies for H and D transfer Three values are shown the activation energies calculated using a one- and two-dimensional Kramers problem and the experimental values.

Temperature Effects. Runs made at temperatures above 0°C., when plotted on Arrhenius graphs, gave fairly straight lines over the 25° to 30°C. interval (Figure 5). Table V shows activation energies calculated from the slopes, including some solutions for which only two temperatures were used. 

In addition to these few examples of kinetic studies related to acid-base equilibria in azoles, there are reports in the literature on activation energies calculated theoretically for proton transfer involving azoles (80CCC3482 80MI3 84JPC5882 86BSF429). Generally, the inclusion of solvent molecules is necessary to find a double minimum potential function. 

The diagram shown in Fig. 20, which gives the log of the polymerization rate under steady-state conditions, plotted vs. the reciprocal of the absolute temperature, was drawn from the above data. The activation energy calculated from the data reported in Fig. 20 is about 10,000 cal./mol. 

Values of activation energy calculated by the initial rise method are in the range 0.25-0.45 eV. Continuous distribution of locahzed states in this range was confirmed by an increase of activation energy in a sequence—curves 2-4 (Fig. 2.6). 

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