Overall activation energy determination

Minimize the effects of transport phenomena If we are interested in the intrinsic kinetic performance of the catalyst it is important to eliminate transport limitations, as these will lead to erroneous data. We will discuss later in this chapter how diffusion limitations in the pores of the catalyst influence the overall activation energy. Determining the turnover frequency for different gas flow velocities and several catalyst particle sizes is a way to establish whether transport limitations are present. A good starting point for testing catalysts is therefore ... 

The typical systems are BPO-DHET(N,N-di(2-hy-droxyethyl)-p-toluidine) system, BPO-DHPT(N,N-di(2-hydroxypropyl)-p-toluidine) system, BPO-HMA(N-2-hydroxyethyl-N-methyl-aniline), and BPO-HMT(N-2-hydroxylethyl-N-methyl-p-toluidine) system [17-19]. Their polymerization rate and overall activation energies of polymerization Ea are determined and the data are compiled in Table 2. 

The number of active centers determined by the quenching technique was dependent on the polymerization temperature (98) that was the reason for the difference between the overall activation energy and the activation energy of the propagation step. 

A comparative study [10] is made for crystal-growth kinetics of Na2HP04 in SCISR and a fluidized bed crystallizer (FBC). The details of the latter cem be found in [11]. Experiments are carried out at rigorously controlled super-saturations without nucleation. The overall growth rate coefficient, K, are determined from the measured values for the initial mean diameter, t/po, masses of seed crystals before and after growth. The results show that the values for K measured in ISC are systematically greater than those in FBC by 15 to 20%, as can be seen in Table 2. On the other hand, the values for the overall active energy measured in ISC and FBC are essentially the same. 

The overall activation energy was then determined by measuring the rate as a function of temperature. How do you extract the overall activation energy ... 

CH3CHO decomposition - determination of the mechanism, 211-213 the steady state analysis, 233-238 setting up of the steady state expression for the overall activation energy in terms of the activation energies for the individual steps, 238-239 H2/Br2 reaction - a steady state analysis on the reaction with inhibition, 213-216 without inhibition 216-217 determination of the individual rate constants, 217-218 Stylised Rice-Herzfeld mechanisms, 221-224, with surface termination, 240-243 RH/Br2 reaction - a steady state analysis, 225-227... 

The times of the complete oxidation of alkanes with oxygen or air under the action of nanosecond pulsed discharges have been determined 222 The kinetics of liquid-phase oxidation of isomeric methoxy(l-methylethyl)benzenes with oxygen to the corresponding hydroperoxides has been studied. The overall activation energies of the oxidation and initiating properties of some of the hydroperoxides were determined 223... 

Reaction 3 is undoubtedly the rate-controlling step. At 77° K, the overall rate constant for the formation of the paramagnetic species is 2.0 X 10 ° seer1 the rate constant determined from intensity data is of the same order (k, = 2.0 d= 0.5 X 10 9 seer1) if a quantum yield between 0.5 molecule/ftv and 1 molecule/hv (4) is assumed. The overall activation energy, Ea = 1360 cal./mole, for the thermal reaction is small as expected for the fragmentation of the associated species. 

Effect of temperature. The results for the determination of rates of polymerisation at various temperatures are summarised in Figure 11, from which it is seen that the temperature variation of rate is of the Arrhenius type. The slope of the relationship between the logarithm of the rate of polymerisation and the reciprocal of the absolute temperature corresponds to an overall activation energy of polymerisation of 15.8 kcal mole. This value is very close to that which has been reported for the aqueous -phase polymerisation of butadiene initiated by rhodium chloride(16). However, in view of the marked dissimilarity in reaction product, and therefore presumably in reaction mechanism, it seems likely... 

Figure 11. Plot of log Rp against 1/T for the determination of the overall activation energy of polymerization, 4. Recipe differs from Figure 1 in that the aqueous solution contains 2.1 g/l. NaHCOa and pH 10.6.

Fig. 9. (a) Model interpreting a rate-determining step in a four-step series reaction. Step 3 with largest activation energy determines the overall rate, (b) Simplified scheme of photocatalytic reaction with a photocatalyst pc. It is clear that this process is not a series reaction since a deactivation step is included. 

Acrylamide polymerization initiated by the H202-hydroxylamine system also has been described 59). The polymerization rate is proporti onal to the square root of H202 and hydroxylamine concentrations, and first order with respect to the monomer concentration. If traces of Fe (a few ppm) are added, the order with respect to the hydroxylamine concentration has been found to depend on the Fe concentration. A thermokinetic method has been applied in determining the overall activation energy... 

Experimentally, E is found by plotting measured values of In k against /T and computing the slope of the best-fit straight line through the data points (slope = E/R ). After E has been obtained, A may be calculated from equation (58) and the measured values of /c. Often E can be determined within a few percent however, difficulties in measuring the absolute value of the reaction-rate constant often produce uncertainties in A that exceed a factor of 2. If the reaction were not an elementary step then E obtained in this way would be called an overall activation energy. 

Example 5.3.2 demonstrates how the heat of adsorption of reactant molecules can profoundly affect the kinetics of a surface catalyzed chemical reaction. The experimentally determined, apparent rate constant Ikj/Ki) shows typical Arrhenius-type behavior since it increases exponentially with temperature. The apparent activation energy of the reaction is simply app = E2 - AHadsco = - A//adsco (see Example 5.3.2), which is a positive number. A situation can also arise in which a negative overall activation energy is observed, that is, the observed reaction rate... 

The overall activation energy calculated in this manner agrees, within 1 kcal. mole, with that determined experimentally. 

TaUe 3. Data on the overall activation energies ( ), activation energies of the propagation reaction ( p), and the value E = E — Er) determining the change of the number of active centers with temperature Catalyst TiClj... 

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