Deactivation kinetics rate constant

The kinetic parameters are listed in Table 1. The linearity of lnAr l/r plot is revealed by the correlation coefficient. For all reactions but the deactivation, the rate constants follow the Arrhenius law satisfactorily, implying catalyst deactivation may involve more than one elementary steps. 

FIGURE 10.3 Metal (often copper) hgand (M/L) structure to support ATRP reactions. Here, and Pm+c are polymers with length m and m+c, respectively, X is typically a hahde atom, such as Cl or Br, and the A s are kinetic rate constants for activation (ka), deactivation (kja), and termination (A ,)-Reprinted from [16] with permission from Elsevier. 

Bertole et al.u reported experiments on an unsupported Re-promoted cobalt catalyst. The experiments were done in a SSITKA setup, at 210 °C and pressures in the range 3-16.5 bar, using a 4 mm i.d. fixed bed reactor. The partial pressures of H2, CO and H20 in the feed were varied, and the deactivation, effect on activity, selectivity and intrinsic activity (SSITKA) were studied. The direct observation of the kinetic effect of the water on the activity was difficult due to deactivation. However, the authors discuss kinetic effects of water after correcting for deactivation. The results are summarized in Table 1, the table showing the ratio between the results obtained with added water in the feed divided by the same result in a dry experiment. The column headings refer to the actual experiments compared. It is evident that adding water leads to an increase in the overall rate constant kco. The authors also report the intrinsic pseudo first order rate-coefficient kc, where the overall rate of CO conversion rco = kc 6C and 0C is the coverage of active... 

As mentioned earlier, practically all reactions are initiated by bimolecular collisions however, certain bimolecular reactions exhibit first-order kinetics. Whether a reaction is first- or second-order is particularly important in combustion because of the presence of large radicals that decompose into a stable species and a smaller radical (primarily the hydrogen atom). A prominent combustion example is the decay of a paraffinic radical to an olefin and an H atom. The order of such reactions, and hence the appropriate rate constant expression, can change with the pressure. Thus, the rate expression developed from one pressure and temperature range may not be applicable to another range. This question of order was first addressed by Lindemann [4], who proposed that first-order processes occur as a result of a two-step reaction sequence in which the reacting molecule is activated by collisional processes, after which the activated species decomposes to products. Similarly, the activated molecule could be deactivated by another collision before it decomposes. If A is considered the reactant molecule and M its nonreacting collision partner, the Lindemann scheme can be represented as follows ... 

If the rate constants for parallel reactions are to be resolved, then analysis of the products is essential (Sec. 1.4.2). This is vital for understanding, for example, the various modes of deactivation of the excited state (Sec. 1.4.2), Only careful analysis of the products of the reactions of Co(NH3)jH20 + with SCN, at various times after initiation, has allowed the full characterization of the reaction (1.95) and the detection of linkage isomers. Kinetic analysis by a number of groups failed to show other than a single second-order reaction.As a third instance, the oxidation of 8-Fe ferredoxin with Fe(CN)g produces a 3Fe-cluster, thus casting some doubt on the reaction being a simple electron transfer. 

The elements of range in value from 0 to 1 and are the ratio of the reformer kinetic constants at time on stream t to the values at start of cycle. At any time on stream t, the deactivation rate constant matrix K(a) is determined by modifying the start-of-cycle K with a. From the catalytic chemistry, it is known that each reaction class—dehydrogenation, isomerization, ring closure, and cracking—takes place on a different combination of metal and acid sites (see Section II). As the catalyst ages, the catalytic sites deactivate at... 

The start-of-cycle rate constant for ring isomerization X° is modified to include deactivation by multiplying its kinetic equations by a, ... 

The deactivation kinetics were determined through a series of seven separate parameter estimation problems. As with the start-of-cycle case, separate estimating problems resulted from uncoupling the reactions of each carbon number by properly selecting the charge stock. This allowed the independent determination of submatrices in the rate constant matrix Dp [Eq. (37)]. 

Consider the simple unimolecular reaction of Eq. (15.3), where the objective is to compute the forward rate constant. Transition-state theory supposes that the nature of the activated complex. A, is such that it represents a population of molecules in equilibrium with one another, and also in equilibrium with the reactant, A. That population partitions between an irreversible forward reaction to produce B, with an associated rate constant k, and deactivation back to A, with a (reverse) rate constant of kdeact- The rate at which molecules of A are activated to A is kact- This situation is illustrated schematically in Figure 15.1. Using the usual first-order kinetic equations for the rate at which B is produced, we see that... 

Rate constants of unimolecular processes can be obtained from spectral data and are useful parameters in photochemical kinetics. Even the nature of photoproducts may be different if these parameters change due to some perturbations. In the absence of bimolecular quenching and photochemical reactions, the following reaction steps are important in deactivating the excited molecule back to the ground state. 

The other interpretation is based on the idea of electron tunneling from excited molecules. In this instance there occurs an overlap of the exponential decay at a rate constant k0 which refers to spontaneous deactivation of the Nh molecules from the excited to the ground state and of the logarithmic kinetics characteristic of electron tunneling reactions (cf. Chap. 4, Sect. 2)... 

Figure 32. Rate constants for collisional deactivation of electronically excited ions on collision with 02 as function of kinetic energy in center-of-mass system.46 ...

The conversion in a catalytic reaction performed under constant conditions of reaction often decreases with time of run or time on stream. This phenomenon is called catalyst deactivation or catalyst decay. If it is possible to determine the kinetic form of the reaction and, thus, to measure the rate constant for the catalytic reaction k, it is sometimes possible to express the rate of deactivation by an empirical equation such as... 

The monomers 82-86 all give living polymers when initiated by 7 and related complexes. The ROMP of 85 shows well behaved second-order kinetics in C De at 25 °C. The rate constant is about 10 times lower than for the reaction of 5,6-dicarbomethoxynorbomadiene, no doubt due to the greater deactivating effect of the COOR groups in 85. Polymers of 84 and 85 have 45-93% cis content depending on the initiator337. 

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

Paramagnetic NO and 02 molecules and reactive CO molecules efficiently quench the PL in the order NO > 02 > CO, whereas N20 only weakly affects the PL intensity. This work allowed confirmation of some important steps of the mechanism proposed earlier for the photocatalytic reduction of NO by carbon monoxide on Mo/Si02 (Subbotina et al., 1999). In particular, the NO photoreduction kinetics was consistently described by Subbotina et al. (1999) assuming first that the deactivation rate constant is much smaller than the quenching rate constant and second that the NO molecules efficiently quench the (Mo5+=0-) excited triplet state without chemical interaction (i.e., "physical quenching"), in contrast to the "chemical quenching" by CO molecules to yield C02 molecules. The PL data demonstrate the correctness of those assumptions. 

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