Steps series-parallel

The term competing steps is used if one and the same component participates as reactant in more than one step of the pathway or network. [The idea is that such steps "compete" with one another for the reactant they have in common an alternative term is series-parallel steps.] The simplest such case is [21]... 

Although many similarities exist between gas-solid catalytic and gas-solid noncatalytic reactions, the noncatalytic systems, particularly when a porous reactant is converted to a porous product, are more complex. Both occur as the result of a number of series-parallel steps. Mass transfer of reacting gas from the bulk gas to the exterior of the solid and that of gas product from the solid to the bulk gas are involved in each. Diffusion of the reacting gas from the exterior surface into a porous catalyst or porous solid reactant and that of gas product from the pores to the exterior surface are also common to the two types of reactions. Adsorption of reacting gas, surface reaction, and... 

To arrive at an expression for AS, we follow a series of steps which parallel-for a different model-the development of the Flory-Huggins model for AS,... 

Reaction measurement studies also show that the chemistry is often not a simple one-step reaction process (37). There are usually several key intermediates, and the reaction is better thought of as a network of series and parallel steps. Kinetic parameters for each of the steps can be derived from the data. The appearance of these intermediates can add to the time required to achieve a desired level of total breakdown to the simple, thermodynamically stable products, eg, CO2, H2O, or N2. 

The order increases with increasing concentration when the reaction proceeds by parallel pathways but decreases when a series of steps occurs. 

Consider the following mechanism for step-change polymerization of monomer M (Px) to P2, P3,..., Pr,. The mechanism corresponds to a complex series-parallel scheme series with respect to the growing polymer, and parallel with respect to M. Each step is a second-order elementary reaction, and the rate constant k (defined for each step)1 is the same for all steps. 

An illustration of a series-parallel network is provided by the step-change polymerization kinetics model of Section 7.3.2. The following example continues the application of this model to steady-state operation of a CSTR. 

This network is a series-parallel network series with respect to HCHO in steps (1) and (2), parallel with respect to CH4 in steps (1) and (3), and parallel with respect to 02 and H20 in all steps. The rate constants kl, k2, and are step rate constants (like k in equation... 

For the general series-parallel reaction we introduce two additional considerations. First of all for parallel steps if one requirement is for a high temperature and another is for a low temperature, then a particular intermediate temperature is best in that it gives the most favorable product distribution. As an example, consider the reactions... 

A series or bunch of m initially straight and parallel steps, between heights 0 and m, may be expected to relax with the same asymptotics as a pair of steps. Modifications may occur, already for a pair of steps, when step-step interactions are present in addition to the entropic step repulsion. Here, we merely refer to recent reviews on experiments and theoretical analyses " on the much studied phenomenon of step bunching for vicinal surfaces, which is accompanied by interesting phase transistions. 

In complex reaction systems the conversion of reactants to products typically takes place through a number of parallel and serial reactions. The reaction path from a reactant through a number of intermediates to the final product naturally occurs in a series of steps. The overall conversion rate and the peak concentrations of the intermediates will depend on the relative rates of the serial reactions. 

This structure differs from those of a-(BEDT-TTF)2MHg(SCN)4 salts with respect to both the donor and acceptor sublattices [7]. The donor layers in the present salt have a P -type arrangement (Fig. 1) and are built from three different BEDO-TTF donors (A, B and C). There are three different types of intermolecular interactions with the slab of organic molecules, the relative orientation of which allows us to describe this layer as being composed of a series of parallel stacks of slipped donors along the (2a-b)-direction, as a series of step-chains along the a+2b) -direction, or as a series of parallel... 

C6H4a2+Cl2 k3 >C6H3C13 + HC1 Analysis in terms of series and parallel steps is ... 

Regarding fhe kinefic modeling, few contributions propose kinetic models for fhe PC oxidation of phenol and other aromatics (Chen and Ray, 1998, 1999 Li et al., 1999b Wei and Wan 1992 ), with kinetic models being based mainly on the initial rates of reacfion only. Such models fail to account for fhe formafion of fhe differenf reaction intermediates, which may play an important role in the overall mineralization rate. More recently, Salaices et al. (2004) developed a series-parallel kinetic model based on observable aromatic intermediates. This model was applied to a wide range of pH, phenol concenfrafion, and cafalysf t)q)e. In this model, however, some steps... 

Thus, considering the Fe-assisted PC conversion of phenol, the observable effect is that phenol produces many intermediate species from the start of the reaction regardless of the pathways involved in the production of such intermediates. It can thus be concluded that the Fe-assisted PC oxidation of phenol can be equally represented with a series-parallel reaction scheme, as it was for the unpromoted PC reaction. All the steps described above are summarized in Figure 10, a reaction scheme based on observable species. It must be emphasized that although the reaction network describes both unpromoted PC and Fe-assisted PC reactions, the values of the kinetic constants will be different for both systems. 

Figure 11 Detailed series-parallel reaction scheme for the unpromoted PC and Fe-assisted PC oxidation of phenol. Broken arrow applies only to PC reaction. Double broken arrow is established as a possible kinetic step not observed at experimental conditions for the reaction (Ortiz-Gomez et al., 2008).

Figure 16.2 visualizes the same series/parallel sequence of steps, but by following the fate of a single polymer pellet just after its injection into the hot fluidized-bed pyrolyser. The pellet is fast heated up by a high-rate heat transfer mechanism that leads external surface up to the softening temperature (step 1 in Figure 16.2). Several sand particles...

When a reaction rate is measured in a chemical reactor, the reaction is generally a composite reaction comprised of a sequence of elementary reactions. An elementary reaction is a reaction that occurs at the molecular level exactly as written (Laidler, 1987). The mechanism of the reaction is the sequence of elementary reactions that comprise the overall or composite reaction. For example, mineral dissolution reactions generally include transport of reactant to the surface, adsorption of reactant, surface dilfusion of the adsorbate, reaction of the surface complex and release into solution, and transport of product species away from the surface. These reactions occur as sequential steps. Reaction of surface complexes and release to solution may happen simultaneously at many sites on a surface, and each site can react at a different rate depending upon its free energy (e.g., Schott et al., 1989). Simultaneous reactions occurring at different rates are known as parallel reactions. In a series of sequential reactions, the ratedetermining step is the step which occurs most slowly at the onset of the reaction, whereas for parallel steps, the rate-determining step is the fastest reaction. 

Series-parallel mechanisms often include off-pathway steps from the intermediates that sometimes deposit to form aggregates. In some proteins such aggregates are pathological. The biophysical properties and amyloidogenicity of the variable domain of a recombinant amyloidogenic light chain (spinal muscular atrophy, SMA) were analyzed. The mechanistic schemes were proposed in Scheme 1 and Scheme 2. 

Closure. After completing this chapter the reader should be able to describe the different types of multiple reactions (series, parallel, complex. and independent) and to select a reaction system that maximizes the selectivity. The reader should be able to write down and use the algorithm for solving CRE problems with multiple reactions. The reader should also be able to point out the major differences in the CRE algorithm for the multiple reactions from that for the single reactions, and then discuss why care must be taken when writing the rate law and stoichiometric Steps to account for the rate laws for each reaction, the relative rates, and the net rates of reaction. 

These experimental observations call for a different mechanism than that proposed by Okamoto et al. (1985a). This parallel-in-series mechanism considers both in-series reaction steps where OH groups are progressively incorporated in the phenol molecule and in the phenolic derived species, and parallel steps where the phenol molecule is being photo converted in oxidation steps of different strength. This parallel-series mechanism can be justified given the possible existence of a distribution of oxidation strengths of the photocatalytic sites. 

This much said, let us now examine the behavior of a PFR in this predicament. The classical example was provided by Froment and Bischolf [G.F. Froment and K.B. Bischoff, Chem. Eng. Set, 10, 189 17, 105 (1962)] for isothermal conditions, with catalyst deactivation by either parallel or series reaction steps (see Chapter 3), and our favorite imaginary reaction A B. Thus we deal with overall sequences such as (XXVI) or (XXVII) of Chapter 3. 

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