Limiting overall transformation rate

In the case of slow reactions, the transformation rate is limited by intrinsic kinetics. A drastic increase of the temperature allows exponential acceleration of the reaction rate in agreement with the Arrhenius Law. Moreover, the pressure can be advantageous to accelerate reactions, to shift equilibrium, to increase gas solubility, to enhance conversion and selectivity, to avoid solvent evaporation, and to obtain single-phase processes [8, 13]. The overall transformation rate of such reactions could be significantly increased in these wove/ operating windows. 

In the fluid-solid systems, the reaction takes place on the catalyst surface. Prior to this, the reactant molecules have to reach the catalyst surface (Figure 2.9) and therefore the rate of mass transfer is an important operational parameter. Two types of mass transfer need to be considered external and internal mass transfer. Internal mass transfer can be avoided by limiting the thickness of the porous catalytic layer, dcat- Internal mass transfer has a negligible influence on the overall transformation rate, if the following conditions are fulfilled [25] ... 

Soil is a key component of the rock cycle because weathering and soil formation processes transform rock into more readily erodible material. Rates of soil formation may even limit the overall erosion rate of a landscape. Erosion processes are also a key linkage in the rock cycle... 

The major focus in the discussions below is on the chemical nature of the enzymatic catalysts and coenzymes used in the initial transformation step. We will also pay some attention to the details of these enzymatic mechanisms. This will provide a basis for understanding how mathematical expressions describing the associated transformation rates can be derived when enzyme-catalyzed reactions limit the overall biotransformation rate (i.e., steps 2, 3 or 4 shown in Fig. 17.1). 

In the reaction controlled regime the overall rate of layer formation is only limited by the rate of chemical transformations (chemical reaction as such). Therefore, the ApBq layer grows at the highest rate possible under given conditions ... 

In Lhe case of slow reacLions for which k,. A di(Y, the overall rate constant Arnet is equal to the rate constant for transformation of the precursor complex, k. However, for very fast reactions, k is greater than A difr, so that the overall rate constant is close to Ardiff- Therefore, it is important to understand that there is an upper limit on reaction rates that can be measured experimentally for diffusion controlled processes. In section 7.5 it is shown that A difr for molecular reactants is given by... 

In the physiological pH range, the specific first-order rates of dissociation of both NAD+ and NADH from their respective binary complexes are slow relative to the rate of the chemical transformation. Indeed, Bernhard et al. (78) have shown that for aldehyde reduction the chemical step occurs at an overall rate which is one to two orders of magnitude greater than the steady-state turnover rate. Hence, for many substrates, the velocity of substrate turnover under steady-state conditions is limited by the rate of dissociation of coenzyme product (78— 80). The steady-state kinetic studies of Wratten and Cleland (77) and the rapid (transient-state) kinetic studies of Bernhard et al. (78), McFarland and Bernhard... 

With prolonged exposure, the concentration of ion pairs in the aqueous phase gradually increases. If supersaturation is reached, the ion pairs precipitate into a solid phase. This transformation is complex and the ion pairs may pass through the colloidal state before they reach the solid state. Nucleation of precipitated species is facilitated by the heterogeneous nature of the substrate surface and the overall formation rate of the precipitate seems more often to be limited by its growth rate rather than by its nucleation rate. Evidence of this lies in the frequent observation of many small precipitated nuclei rather than a few larger ones, see Fig. 5 [11]. 

Water reacts with the barrier layer, which transforms into bayerite or boehmite depending on the temperature, and thus increases the thickness of the external oxide layer. The barrier layer will rebuild instantaneously from underlying aluminium, and therefore this reaction does not limit the overall corrosion rate. The corrosion rate in water, which follows a parabolic law, is controlled by the external film and depends on its thickness (Figure D.1.10). 

On the basis of the CO dependence of the transformation of the P-chelates into the carbonyl acyl compounds, it was proposed that the rate-limiting step in the overall conversion of the P-chelates to carbonyl acyl complexes is related to the opening of the metallacycle by CO (steps a and b in Scheme 7.13) rather than to the following migratory insertion of the alkyl carbonyl complex that is independent of the CO pressure (step c). 

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