Apparent activation energies

Thus, the radius of the atom carrying the free valence has a substantial influence on the activation barrier to the addition reaction the greater the radius of this atom, the higher the activation energy. Apparently, this effect is due to the repulsion in the transition state, which is due to the interaction between the electron shells of the attacked double bond and the atom that attacks this bond. 

Finally, is observed that the rcw increases with the pcH4 [16-18] and with the reduction temperature, while it diminishes with the reaction temperature. The influence of the ph2 has no clear effect. The effect of the reaction temperature is due to the fact that high reaction temperatures favor gasification over the growth of coke filaments [15,19,26,27] which would explain the negative value of the activation energy apparent for the filament growth. 

E,E, Intrinsic activation energy, apparent activation energy of reaction j J mol"2... 

These approximations also provide elegant physicochemical insights into the mechanism as summarized in two recent papers by Stoltze [2] and Dumesic [3]. Thus, as shown by Stoltze [2], under the RDS approximation many characteristics of the microkinetic mechanisms, e.g., rate equations (De Donder relations), apparent activation energies, apparent reaction orders, etc., may be naturally partitioned into a sum of contributions associated with a special class of reactions involving only one surface species. Dumesic [3] extended the idea to general systems. 

Activation energy, apparent (kJ/mol) Copolymer 0-80°C Copolymer, branched, 50°C Diffilsion coelficient, average, 25°C (cm /s) Copolymer Copolymer, branched Copolymer, linear and branched Carbon dioxide Activation energy (kJ/mol)... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Just as the surface and apparent kinetics are related through the adsorption isotherm, the surface or true activation energy and the apparent activation energy are related through the heat of adsorption. The apparent rate constant k in these equations contains two temperature-dependent quantities, the true rate constant k and the parameter b. Thus... 

The apparent activation energy is then less than the actual one for the surface reaction per se by the heat of adsorption. Most of the algebraic forms cited are complicated by having a composite denominator, itself temperature dependent, which must be allowed for in obtaining k from the experimental data. However, Eq. XVIII-47 would apply directly to the low-pressure limiting form of Eq. XVIII-38. Another limiting form of interest results if one product dominates the adsorption so that the rate law becomes... 

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... 

Measuring tire pressure dependence of k at different temperatures shows that the apparent activation energy at constant viscosity decreases with increasing viscosity [46, ( figure A3,6,8). From a detailed analysis one... 

The first term, the apparent activation energy of the encounter reaction, was evaluated from the temperature coefficient of the viscosity of sulphuric acid. 

The apparent rate constant in Eq. (6.26) follows the Arrhenius equation and yields an apparent activation energy ... 

This enables us to identify the apparent activation energy in Eq. (6.30) with the difference in E values for the various steps ... 

Applying the Arrhenius equation to Eq. (6.116) shows that the apparent activation energy for the overall rate of polymerization is given by... 

Rheology. Both PB and PMP melts exhibit strong non-Newtonian behavior thek apparent melt viscosity decreases with an increase in shear stress (27,28). Melt viscosities of both resins depend on temperature (24,27). The activation energy for PB viscous flow is 46 kj /mol (11 kcal/mol) (39), and for PMP, 77 kJ/mol (18.4 kcal/mol) (28). Equipment used for PP processing is usually suitable for PB and PMP processing as well however, adjustments in the processing conditions must be made to account for the differences in melt temperatures and rheology. 

Even when there is a transport disguise, the reaction order remains one for a first-order reaction. But for reactions that are not intrinsically first order, the transport disguise changes the observed reaction order for an intrinsically zero-order reaction, the observed order becomes 1/2 and for an intrinsically second-order reaction it becomes 3/2 when 0 10. For all reaction orders the apparent activation energy is approximately half the intrinsic... 

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