Apparent kinetics

Just as the surface and apparent kinetics are related through the adsorption isotherm, the surface or true activation energy and the apparent activation energy are related through the heat of adsorption. The apparent rate constant k in these equations contains two temperature-dependent quantities, the true rate constant k and the parameter b. Thus... 

Table 5.1 presents the intrinsic kinetic parameters (Km and Vln lx) for the free lipase system and apparent kinetic parameters (K and V ) for the immobilised lipase in the EMR using fixed 2g-l 1 lipase concentration. The immobilised lipase showed higher maximum apparent reaction rate and greater enzyme-substrate (ES) affinity compared with free lipase. 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

If the same quantity of active ingredient is concentrated in an outside shell of thickness 0.015 cm, one obtains y> = 2.27. This would yield an effectiveness factor of 0.431 in a slab geometry, and the apparent kinetic constant has risen to 99.2 sec-1. If the active ingredient is further concentrated in a shell of 0.0025 cm, one obtains y> = 0.38, an effectiveness factor of 0.957, and an apparent kinetic constant of 220 sec-1. These calculations are comparable to the data given in Fig. 15. This analysis applies just as well to the monolith, where the highly porous alumina washcoat should not be thicker than 0.001 in. 

Mass loss determinations refer to the total change resulting from reactant decomposition and usually include contributions from a mixture of product compounds, some of which would normally be condensed under conditions used for accumulatory pressure measurements. Such information concerned with the overall process is, however, often usefully supplemented by evolved gas analyses (EGA) using appropriate analytical methods. Sestak [130] has made a detailed investigation of the effects of size and shape of reactant container on decomposition kinetics and has recommended that the sample be spread as a thin layer on the surfaces of a multiple plate holder. The catalytic activity of platinum as a reactant support may modify [131] the apparent kinetic behaviour. 

The decomposition of dolomite shows many points of similarity with the reactions of calcite and of other single carbonates of Group IIA metals (Sects. 3.1.1 and 3.1.2) the reaction is reversible, occurs at an interface, and both apparent kinetic parameters and reactivity are influenced by the prevailing C02 pressure. 

Although hydrogenation of 4-CBA over Pd/C is very fast, there is strong diffusion resistance. Furthermore, apparent kinetic equations on different catalyst particle sizes have been obtained from experimental data. 

Kinetic behavior of the two-enzyme system (lipase-lipoxygenase) in biphasic media (curve c in Fig. 5) is compared with kinetics of lipoxygenase in the same biphasic medium (b) and in an aqueous medium (a). These curves demonstrated that the configuration of the media influences the production rate of HP. As previously stated, lipoxygenase in biphasic media has an apparent kinetic behavior different from that in aqueous media (see difference between curves a and b in Fig. 5). 

It should be re-emphasized that although our block copolymers do not display spherulitic morphology when they are compression molded, they are nevertheless crystalline. Hence, this indicates that under this mode of film preparation, aggregation into well developed superstructure is apparently kinetically limited. 

The kinetics of hydrocracking reactions has been studied with real feedstocks and apparent kinetic equations have been proposed. First-order kinetics with activation energy close to 50 kcal/gmol was derived for VGO. The reactions declines as metal removal > olefin saturation > sulfur removal > nitrogen removal > saturation of rings > cracking of naphthenes > cracking of paraffins [102],... 

The model balance equations are developed by considering both the individual tank stages and the absorber. Component balances are required for all components in each section of the reactor column and in the absorber, where the feed and effluent streams are located. Although the reaction actually proceeds in the biofilm phase, a homogeneous model apparent kinetics model is employed, which is justified by its simplicity. 

The key factor in understanding in vitro D DI data is to determine how the apparent kinetic measurements match the unbound concentration of an inhibitor in the... 

The apparent kinetic constants were obtained from Lineweaver-Burk plots of AHH activities recorded in the presence of increasing concentrations of benzo(a)pyrene (0.001-1.0 mM). The plots were linear for both untreated and DBA-induced animals. The apparent V was 20- to 30-fold higher in hepatic microsomes from the induced skates whereas the apparent K values were of the same magnitude in control and treated fish. 

Dominant Ri R2 steric control elements are predicted to disfavor transition state T and promote enolization to give the (Z)-geometry, whereas dominant R2 L nonbonded interactions should disfavor transition state C and promote enolization to afford the ( )-enolate geometry. As summarized below in Table 10, under conditions of apparent kinetic control, esters and thioesters afford largely ( > enolates (transition state T ), and the dialkylamides exhibit predominant to exclusive (Z)-enolization (transition state C ). 

The apparent kinetics of proton-coupled ReV/in electron transfer also are dependent on 0X0 group geometry here (ks,h)cis/(ks,h)trans 100 [36]. It is proposed that the apparent kinetics is controlled by the thermodynamic accessibility of the intermediate Re (IV) state, whose effective potential is modulated by protonation, 0X0 group geometry, and pyridyl ligand substituents. 

Mirvish. later investigated the nitrosation of aminopyrine in considerable detail (12), proposing the alternative pathway shown in Fig. 5b, but presenting evidence that the mechanism is actually a great deal more complex than that. Firstly, they identified both a "fast" initial reaction, which was essentially complete within 2-5 min., and a "slow" reaction, which proceeded at a nearly constant rate for 15 min. Secondly, they found that the pH rate profile had maxima at both pH 2.0 and pH 3.1. Thirdly, they reported an apparent kinetic order for nitrite which varied considerably under some conditions from the value of 2 required by the mechanism of Fig. 5b, ranging from cleanly first order for the "slow" reaction at pH 2 to as high as 3-4 for the initial reaction at low nitrite concentration (l-6mM). 

Based on the Langmuir-Hinshelwood expression derived for a unimolecular reaction system (6) Rate =k Ks (substrate) /[I + Ks (substrate)], Table 3 shows boththe apparent kinetic rate and the substrate concentration were used to fit against the model. Results show that the initial rate is zero-order in substrate and first order in hydrogen concentration. In the case of the Schiff s base hydrogenation, limited aldehyde adsorption on the surface was assumed in this analysis. Table 3 shows a comparison of the adsorption equilibrium and the rate constant used for evaluating the catalytic surface. 

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