Catalytic rates, activated energies

Diffusional mass transfer processes can be essential in complex catalytic reactions. The role of diffusion inside a porous catalyst pellet, its effect on the observed reaction rate, activation energy, etc. (see, for example, ref. 123 and the fundamental work of Aris [124]) have been studied in detail, but so far several studies report only on models accounting for the diffusion of material on the catalyst surface and the surface-to-bulk material exchange. We will describe only some macroscopic models accounting for diffusion (without claiming a thorough analysis of every such model described in the available literature). 

Figure 1 show hydrogen conversions for dehydrocondensation at different temperatures of catalysts. It has been found that catalytic dehydrocondensation reaction displays the second order. Dehyd-rocondensation reaction rate constants are determined, and catalytic dehydrocondensation activation energies are calculated /, act = 28.1 -28.5 kJ/Mole. As a consequence, for anhydrous caustic potash and platinum hydrochloric acid application as the catalyst activation energies are almost the same. 

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... 

Enzymes increase the rate of chemical reactions by decreasing the activation energy of the reactions. This is achieved primarily by the enzyme preferentially binding to the transition state of the substrate. Catalytic groups of the enzyme are required to achieve a specific reaction path for the conversion of substrate to product. 

The IIEC model was also used to study the importance of various design parameters. Variations in gas flow rates and channeling in the bed are not the important variables in a set of first-order kinetics. The location of the catalytic bed from the exhaust manifold is a very important variable when the bed is moved from the exhaust manifold location to a position below the passenger compartment, the CO emission averaged over the cycle rose from 0.14% to 0.29% while the maximum temperature encountered dropped from 1350 to 808°F. The other important variables discovered are the activation energy of the reactions, the density and heat... 

Dependence of Catalytic Rates and Activation Energies on Catalyst Potential UWRand Work Function [Pg.152]

Figure 4.28. Electrophobic behaviour Effect of catalyst work function on the activation energy E and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt p02 4.8 kPa, Pc2H4 0.4 kPa (a) and CH4 oxidation on Pt p02 =2.0 kPa, Pch4 =2.0 kPa (b)."4 Reprinted with permission from Elsevier Science.

It has been known since the early days of electrochemical promotion that upon varying Uwr and thus , not only the catalytic rates, r, are changing in a frequently dramatic manner, but also the activation energy of the catalytic reaction is also significantly affected. An example was already presented in Fig. 4.28 which shows that both C2H4 and CH4 oxidation on Pt/YSZ conform to equation (4.50) with an values of -1 and -3, respectively. 

Figure 4.35. Effect of catalyst work function on the activation energy EA, preexponential factor k° and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt/YSZ 4 p02=4.8 kPa, Pc2H4=0-4 kPa,4,54 kg is the open-circuit preexponential factor, T is the mean temperature of the kinetic investigation, 375°C.4 T0 is the (experimentally inaccessible) isokinetic temperature, 886°C.4 25,50...

Figure 8.75 shows the dependence of the apparent activation energy Ea and of the apparent preexponential factor r°, here expressed as TOF°, on Uwr. Interestingly, increasing Uwr increases not only the catalytic rate, but also the apparent activation energy Ea from 0.3 eV (UWr=-2 V) to 0.9 eV (UWr-+2V). The linear variation in Ea and log (TOF°) with UWr leads to the appearance of the compensation effect where, in the present case, the isokinetic point (T =300°C) lies outside the temperature range of the investigation. 

For catalytic reactions and systems that are related through Sabatier-type relations based on kinetic relationships as expressed by Eqs. (1.5) and (1.6), one can also deduce that a so-called compensation effect exists. According to the compensation effect there is a linear relation between the change in the apparent activation energy of a reaction and the logarithm of its corresponding pre-exponent in the Arrhenius reaction rate expression. 

The activation energy of the catalytic reaction is significantly smaller than that of the uncatalyzed reaction hence, the rate of the catalytic reaction is much larger ( ve explain this in greater detail in Chapter 2). 

In principle this is derived from an Arrhenius plot of In r+ versus 1/T but such a plot may deviate from a straight line. Hence, the apparent activation energy may only be valid for a limited temperature range. As for the orders of reaction, one should be very careful when interpreting the activation energy since it depends on the experimental conditions. Below is an example where the forward rate depends both on an activated process and equilibrium steps, representing a situation that occurs frequently in catalytic reactions. 

Figure 2.12 shows the rate, the coverages, the reaction orders, and the normalized apparent activation energy, all as a function of temperature. Note the strong variations of all these parameters with temperature, in particular that of the rate, which initially increases, then maximizes and decreases again at high temperatures. This characteristic behavior is expected for all catalytic reactions, but is in practice difficult to observe with supported catalysts because diffusion phenomena come into play. 

Apparent activation energies for the catalytic reactions were as expected about 80 kJ/mol for the formation of formaldehyde and 60 kJ/mol for the formation of acetaldehyde from the respective alcohols (Figure 3). The turnover rates of the samples were calculated either on the basis of the number of vanadiums (all of which could be assumed to be accessible) or by assuming that oxygen uptake counted the catalytic sites ... 

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