Deactivation rate constants

Figure B2.5.19. The collisional deactivation rate constant /c, (O3) (equation B2.5.42 ) as a fimction of the vibrational level v". Adapted from [ ]. Experimental data are represented by full circles with error bars. The broken curve is to serve as a guide to the eye.

Do not infer from the above discussion that all the catalyst in a fixed bed ages at the same rate. This is not usually true. Instead, the time-dependent effectiveness factor will vary from point to point in the reactor. The deactivation rate constant kj) will be a function of temperature. It is usually fit to an Arrhenius temperature dependence. For chemical deactivation by chemisorption or coking, deactivation will normally be much higher at the inlet to the bed. In extreme cases, a sharp deactivation front will travel down the bed. Behind the front, the catalyst is deactivated so that there is little or no conversion. At the front, the conversion rises sharply and becomes nearly complete over a short distance. The catalyst ahead of the front does nothing, but remains active, until the front advances to it. When the front reaches the end of the bed, the entire catalyst charge is regenerated or replaced. 

Transition metal-catalyzed atom transfer radical addition Atom transfer radical polymerization Equilibrium constant for atom transfer Activation rate constant for atom transfer Deactivation rate constant for atom transfer 2,2 -Bipyridine... 

Additionally, deactivation rate constants (kd) for the more active catalysts such as Cu X/Me4CYCLAM have been estimated from the initial degree of polymerization without reactivation, end functionality, and molecular weight distributions [138,141,142], With recent advances in determination of the equilibrium constant for atom transfer (KATRP=kJkd), deactivation rate constants (k =k KX[M,) can now be easily obtained from readily accessible activation rate constants (k) [115],... 

Fig. 11 Correlation of activation rate constants (kac[) and deactivation rate constants with...

Deactivation Energy, Kcal/mole Fraction of ZSM-5 in inventory Catalyst Inventory, tons Deactivation Rate Constant Pre-Exponential Term of Kp Water Partial Pressure Effect Makeup Rate of Base Catalyst, tons/min Makeup Rate of ZSM-5 Catalyst, tons/min Motor Clear Octane Number Base Motor Octane Number Deactivation Order... 

The peroxyoxalate system is the only intermolecular chemiluminescent reaction presumably involving the (71EEL sequence (Scheme 44), which shows high singlet excitation yields (4>s), as confirmed independently by several authors Moreover, Stevani and coworkers reported a correlation between the singlet quantum yields, extrapolated to infinite activator concentrations (4> ), and the free energy involved in back electron-transfer (AG bet), as well as between the catalytic electron-transfer/deactivation rate constants ratio, ln( cAx( i3), and E j2° (see Section V). A linear correlation of ln( cAx( i3) and E /2° was obtained for the peroxyoxalate reaction with TCPO and H2O2 catalyzed by imidazole and for the imidazole-catalyzed reaction of 57, both in the presence of five activators commonly used in CIEEL studies (anthracene, DPA, PPO, perylene and rubrene). A further confirmation of the validity of the CIEEL mechanism in the excitation step of... 

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... 

Each component in the deactivation rate constant matrix > ) is normalized to reference conditions ... 

D Deactivation rate constant matrix P tc C6. hydrocarbon partial pressure,... 

Deactivation rate constant kd at 643 K as a function of catalyst and carrier gas natures PodCg = 8.42 kPa. 

Every (bio)catalyst can be characterized by the three basic dimensions of merit -activity, selectivity and stability - as characterized by turnover frequency (tof) (= l/kcat), enantiomeric ratio (E value) or purity (e.e.), and melting point (Tm) or deactivation rate constant (kd). The dimensions of merit important for determining, evaluating, or optimizing a process are (i) product yield, (ii) (bio)catalyst productivity, (iii) (bio)catalyst stability, and (iv) reactor productivity. The pertinent quantities are turnover number (TON) (= [S]/[E]) for (ii), total turnover number (TTN) (= mole product/mole catalyst) for (iii) and space-time yield [kg (L d) 11 for iv). Threshold values for good biocatalyst performance are kcat > 1 s 1, E > 100 or e.e. > 99%, TTN > 104-105, and s.t.y. > 0.1 kg (L d). ... 

The validity of a first-order decay law over time for the activity of enzymes according to Eq. (2.19), with [E]t and [E]0 as the active enzyme concentration at time t or 0, respectively, and kd as the deactivation rate constant, is based on the suitability of thinking of the deactivation process of enzymes in terms of Boltzmann statistics. These statistics cause a certain number of active protein molecules to deactivate momentarily with a rate constant proportional to the amount of active protein [ for evidence for such a catastrophic decomposition, see Craig (1996)]. 

Ratio between Catalytic Constant Deactivation Rate Constant lrd... 

Relationship between Deactivation Rate Constant lrd and Total Turnover Number TTN... 

In the following paragraphs, we will investigate the relationship between the observed deactivation rate constant kd obs and the intrinsic deactivation rate constant kd. 

In addition to mastering the various processes leading to electronic excitation of the lanthanide ions, one has to prevent excited states to de-excite via nonradiative processes. The overall deactivation rate constant, which is inversely proportional to the observed lifetime r0bs, is given by ... 

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