Steady state reaction conditions

Because there are two positive terms in the denominator of equation 4.2.85 (either of which may be associated with the dominant termination process), this equation leads to two explosion limits. At very low pressures the mean free path of the molecules in the reactor is quite long, and the radical termination processes occur primarily on the surfaces of the reaction vessel. Under these conditions gas phase collisions leading to chain breaking are relatively infrequent events, and fst fgt. Steady-state reaction conditions can prevail under these conditions if fst > fb(a — 1). 

As the pressure in the reaction vessel increases, the mean free path of the gaseous molecules will decrease and the ease with which radicals can reach the surfaces of the vessel will diminish. Surface termination processes will thus occur less frequently fst will decline and may do so to the extent that fst + fgt becomes equal to fb oc — 1). At this point an explosion will occur. This point corresponds to the first explosion limit shown in Figure 4.1. If we now jump to some higher pressure at which steady-state reaction conditions can again prevail, similar... 

The summations extend from n = 2 to n. = oo.) Keii [Kinetics of Ziegler-Natta Polymerization, Kodansha, Tokyo, 1972] has noted that under steady-state reaction conditions, the number of polymer molecules with degree of polymerization n desorbing per unit catalyst surface area in unit time may be written as... 

Figure 13(a) and (b) shows the spectrum of the supposed intermediate in the region of its strongest bands under steady state reaction conditions... 

Table 10.6 shows the catalytic performances of the selective benzene oxidation on the zeolite-supported Re catalysts under steady-state reaction conditions [107]. Catalyhc activity and selectivity largely depended on the types of zeolites and the preparation methods. The Re catalysts prepared by CVD of MTO exhibited higher catalyhc achvity and phenol selechvity than those prepared by the convenhonal impregnation method as supports (Table 10.6). Physical mixing of MTO with the supports provided poor phenol synthesis.

EXAFS analysis for the sample after the fifth pulse reaction of benzene and O2 revealed the formation of Re monomers with Re=0 bonds (CN = 3.7 0.2) at 0.173 O.OOlnm and Re-O bond (CN = 1.3 0.6) at 0.211 0.002nm (Table 10.7). The monomeric structure (vi) in Table 10.7 was similar to that after the steady state reaction (i). The Re monomers (vi) were transformed into the Rejo clusters again by NH3 treatment for 2h. NH3 has two roles, N supplier and reduc-tant, in producing the catalytically active N-interstitial Re cluster, which converts benzene and O2 into phenol with a selectivity of 93.9%, accompanied with oxidation of the cluster to the inactive Re monomer (Scheme 10.4). Thus, the formation of the N-interstitial Rejo clusters and the decomposition of the Rejo clusters to the Re monomers are balanced under the steady-state reaction conditions [73]. 

The reaction between propene and the catalyst is, in general, rate-determining, as catalyst reoxidation is a relatively fast reaction. This implies that the degree of catalyst reduction under steady state reaction conditions is fairly low (i.e. less than 10% with respect to the total amount of oxygen that can be removed with propene). Thus the observed kinetics... 

Experiments using a flow reactor under steady state reaction conditions were reported by Keulks and Krenzke [175]. A retarded breakthrough of lsO in the products was observed, after switching from 1602 to 1802 in the feed which consisted of propene (9%), oxygen (10%) and helium (81%) at 1 atm. The 180/]60 similarly increased in both acrolein and C02, contrary to the results of Gel bshtein et al. mentioned above (see also Sect. 3.2.2). 

An iron-promoted cobalt molybdate catalyst (Fe0 03Co0.9 7MoO4) was studied by Maksimov et al. [195,196] with respect to the role of iron in the transfer of charge. Iron strongly enhances the catalytic activity and at the same time increases the conductivity by a factor of 100. Mossbauer spectroscopy reveals that 4% of the iron ions are present as Fe2+ impurity . This fraction is doubled at steady state reaction conditions, and indicates participation of iron in the charge transfer process. 

Haddix et al. developed an in-situ flow probe which sacrifices the ability to rotate the sample in return for conditions that very closely mimic a bench-top flow reactor (87). A typical experiment with this probe might involve in-situ activation of the catalyst in a flowing gas stream, followed by the establishment of steady-state reaction conditions at elevated temperature through the introduction of one or two reactants into the flow stream (84). 

Under steady state reaction conditions, the effects of CO2 on the methane coupling reaction over Li/MgO catalyst were quantitatively determined. Poisoning effects of CO2 on carbon oxide formation rate, C2 formation rate, and methane conversion were observed for all methane to oxygen ratios and all temperatures. However, C2 selectivity is relatively unaffected by CO2 partial pressure. The mechanism described here accounts for important elementary steps, especially the effects of carbon dioxide. Under the low conversion conditions used in this study, further oxidation of C2 products to CO and CO2 is assumed negligible. These reactions will become more important at high conversions. Rate expressions derived from the mechanism match well the experimental conversions and selectivities. 

Catalytic experiments were done with 75 ml of a catalyst and FAV=10 000 m /h/kgcat-Combustion of toluene was chosen as a model volatile organic compound and non-steady-state reaction condition (linear increase 3.5 °C/min in reaction temperature) was applied in the catalyst activity evaluation. Concentration of toluene in air was 1 g /m. Temperatures of gaseous reaction mixture entering and leaving the catalyst layer were measured by thermocouples. Catalytic activities expressed as the inlet temperatures Tso or T90, at which 50 or 90 % conversions of toluene were achieved, were taken as a measure of the catalytic activity. 

As stated earlier, the product distribution during butadiene epoxidation over an unpromoted catalyst indicated that epoxybutene was strongly bound to the Ag surface and that the CsCI promoter lowered the desorption energy of epoxybutene. These observations should be reflected in the steady-state kinetics of the reaction. The data summarized in Table 5 list the steady-state reaction conditions used to determine the reaction orders for the reactants C4H6 and O2 as well the reaction products epoxybutene, CO2, and H2O. In all these experiments differential conversions of C4H6 and O2 were maintained and the data fitted to the typical power rate law expression for epoxybutene formation... 

Because the expressions for DPn do not depend on either steady-state reaction conditions or a knowledge of it is more convenient to... 

The all reactions to investigate proceed in autocatalytic mode due to the transition Fe(III) to Fe(II) [11,22], The products were formed with auto acceleration period longer than in the case of the H20 additives - free process (Figure 1, a-c). The reaction rates (as well as in the absence of the H2() additives [22]) rapidly becomes equal to w = wbm = wmax (w°). Under these steady — state reaction conditions the changes in oxidation rates in the both... 

Since Eq. (8.139) does not depend on either steady-state reaction conditions or a knowledge of [M" "], it is more conyenientto calculate the ratios of various rate constants from DPn data than from Rp data. However, the use of DPn data, like the use of Rp data, does require (if the Mayo equation is used) that one employs data at low conversions so that the monomer concentration does not change appreciably. 

At steady-state reaction conditions, an abrupt switch in the isotopic composition of one of the reactants does not disturb the reaction, provided there is not an isotope effect such as in the case of H2-D2. Many studies... 

If one now jumps to some higher pressure at which steady-state reaction conditions can again prevail, similar semi-quantitative arguments can be used to explain the phenomenon known as the second explosion limit. At these somewhat higher pressures the large majority of the events by which chains are terminated will occnr in the gas phase. The higher pressure hinders the diffusion of radicals to the vessel surfaces and provides a number density of gas-phase radicals that is sufficient for radical disproportionation and recombination reactions to become mnch more significant than surface termination processes. 

Following on with the water effects in FT, transient carbon isotope experiments carried out over supported and unsupported Co catalysts indicate that water vapour increases the amount of monomeric and active surface carbon species under steady state reaction conditions. This effect of water is attributed to an acceleration of the rate of CO dissociation, and as a main consequence, it induces a shift in the FT selectivity, lower methane selectivity and formation of higher molecular weight products. The impact of the water produced at high conversion level in the case of alkali promoted iron catalysts is also attributed to the water-gas shift reaction. It appears that the relative rates of the FT and WGS reactions are responsible for the drop in CO conversion to hydrocarbons. At high... 

It is evident that the six individual rate constants cannot be obtained under steady-state reaction conditions. To estimate their values, independent measures of the adsorption and reaction behavior under transient (non-steady-state) conditions are necessary. 

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