Apparent activation energy determination

Fig. 5. Apparent activation energies of the ethane hydrogenolysis and cyclopropane hydrogenation reactions on the group VIII noble metals. The activation energies were determined at hydrogen and hydrocarbon partial pressures of 0.20 and 0.030 atm, respectively (63).

The activity is strongly influenced by the temperature. An Arrhenius plot of the activity as a function of temperature is given in Figure 5A. Using Arrhenius law, the (apparent) activation energy was determined at Eapp= 55 kJ/mol. 

The velocity constant and the apparent activation energy were determined (similar case 1) from the RT experimental data. The velocity constant can be written ... 

Table 5 shows the activation energies determined for the various etching systems. In general, the apparent activation energy, as determined from the... 

This equation is first order in [Ca ], [P04 ] and s. The average rate constant kf was determined to be 173 11 mof m sec The apparent Arrhenius activation energy was determined over a temperature range of 10 to 40°C to be 186 15 kJ mol Inskeep and Silvertooth (1988) speculated that the rate-limiting step is a surface process, specifically that it is the surface diffusion of Ca and PO4 ions and dehydration commensurate with binding at surface sites of incorporation. Using a constant-composition method and seeded solutions with Sha = 3.05-5.58 Koutsopoulos (2001) found hydroxylapatite formed without a precursor phase. The spiral growth model was found to best fit their kinetic data. 

We have tried to estabUsh whether there is any influence of the proposed repulsive interactions on the apparent activation energy for diffusion. In a theoretical study on isobutane diffusion in silicaUte-1 [82], a change in the apparent activation energy was determined. At lower temperatures, the apparent activation energy was lower than at elevated temperatures. This effect was proposed to be caused by repulsive interactions. We determined the ap-... 

These properties will be examined in the next paper. However it is useful to already single out the aciditic properties of T substituted zeolites. These incorporated trivalent elements generate acid sites different, in their strength, as the elements differ. These differences may appear via acidity measurements but they are more clearly apparent as the catalytic rate constants are measured in test reactions or as the corresponding activation energies are determined. POST and coworkers clearly showed that these parameters vary as a function of the nature of the substituting element, thus ascertaining the isomorphous substitution (45). 

The fractional fi ee volume at the glass transition, fg, was calculated from C (30). The apparent activation energy was determined from the following equations (27,31,32) ... 

The methane conversion obtained on the Pd/AbOa catalyst at the steady state within the temperature range 250-500°C, increases with temperature from 2% at 250°C to 100 % at 500°C. The reaction is selective toward carbon dioxide and water. The apparent activation energy value determined from Arrhenus plot is around 82 KJ.mof. Similar values are usually observed in the literature[l-9]. 

Table 2 summarizes the temperatures at which 50% of methane oxidation was achieved (TjQ ), the apparent activation energies and the reaction rates. The catalytic activities were compared at a GHSV of 135 (X)0 h. The overall activity of the unsupported Lao gSrQ2Mn03+,j was higher than the activity of the supported catalysts, probably due to the higher accessible active surface area of the unsupported perovskite. The apparent activation energies were determined at conversions below 10%. They were for the LaA103 supported catalysts about 10 - 30 kJ/mol lower than for the other samples. 

Polymerization efficiencies for the initiator systems hexamethylene di-isocyanate and 7V-acetyl caprolactam have been evaluated and the di-isocyanate found to be the more active. Studies on -caprolactam in closed systems have been made and the main polymerization processes for the system, caprolactam, water, and a viscosity stabilizer (acetic acid or butylamine), were evaluated. These are ring-opening polymerizations by hydrolysis, polycondensation of amine and carboxyl ends, and polyaddition of caprolactam to amino end-groups. Apparent activation energies were determined for these main reactions and it was suggested that addition occurred in preference to polycondensation. Post-polymerization of E-caprolactam under reduced pressure in the presence of water vapour and phosphoric acid has been kinetically analysed and the rate of increase of the degree of polymerization was derived theoretically as a function of reaction variables. 

Figure 4 Zero shear viscosity of 11b versus the reciprocai temperature (1/7) the apparent activation energy is determined according to the Andrade-Eyring equation (dotted iine) in which S is a constant and Eji is the activation energy for viscous flow.

In this case, an apparent activation energy is determined, and it has higher values than secondary relaxations 100-300 kJ/mol for urethane-soybean oil networks (Cristea et al. 2013), 200-300 kJ/mol for polyurethane-epoxy interpenetrating polymer networks (Cristea et al. 2009), more than 400 kJ/mol for semicrystalline poly(ethylene terephtalate) (Cristea et al. 2010), and more than 600 kJ/mol for polyimides (Cristea et al. 2008, 2011). The glass transition temperature is the most appropriate reference temperature when applying the time-temperature correspondence in a multifrequency experiment. The procedure allows estimation of the viscoelastic behavior of a polymer in time, in certain conditions, and is based on the fact that the viscoelastic properties at a certain tanperature can be shifted along the frequency scale to obtain the variation on an extended time scale (Brostow 2007 Williams et al. 1955). The shift factor is described by the Williams-Landell-Ferry (WLF) equation ... 

Electrical conductivity of reaction mixtures and polymerization kinetics have been investigated for the pyridine- and picoline-initiated polymerization of MA. In acetic anhydride, it was found that the electrical conductivities of the polymerizing mixtures increased during the course of the reaction. Rates were examined at 25°C and found to increase with both monomer and pyridine concentration. Also, both the conductivity of the reaction mixtures and polymer conversion increased appreciably with increasing temperatures. An apparent overall activation energy was determined to be about 10 kcal/mol and the equation representing the overall rate was formulated as follows ... 

Xhe Rietveld method was used to compute the phase contents as a function of temperature during vacuum-annealing of each MAX phase. Xhe decomposition rates k) at different temperatures were calculated and the corresponding apparent activation energies ( ) were determined using the Arrhenius equation,... 

Figure 6, Apparent activation energies for reductive dechlorination of CT at an iron electrode. Activation energies were determined from Arrhenius analysis of dechlorination rates at temperatures of2, 12, 22, 32 and 42...

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

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