Sequential Parallel Reactions

The limiting cases require separate forms and we have 

The differential equation obeyed by U is, of course, that of a reaction of order (a + l)/o that governing V can be put in many forms by eliminating t between V and V. One such is  

We have only considered the simplest case of constant k(x), but there are no reasons to limit the sequential reaction to this form save the wantonness of idle proliferation and the awkwardness of the resulting integrals. Thus if the second step were at a rate independent of x we would have ( ) = k/x and with the usual distribution x, 

Besides having the capital property of being able to imitate any kinetics—see Eq. 61—Astarita s uniform kinetics are often patient of a mechanistic derivation. Thus, for what Astarita and Ocone call uniform generalized Langmuir isotherm kinetic mechanism (UGLIKM), we might take 6(x) dx to be the fraction of catalytic surface occupied by the species A(x) with index in 

This leads straight to be UGLIKM kinetics and provides an interpretation for the kernel K(x). 

---

A cascade of 3 tanks in series is used to optimise the selectivity of a complex sequential-parallel reaction. Depending on the kinetics, distributing the feed of one reactant among the tanks may lead to improved selectivity. 

SEMISEQ - Sequential-Parallel Reactions in a Semi-Continuous Reactor System... 

Temperature Control for Semi-Batch Reactor 430 Parallel Reactions in a Semi-Continuous Reactor 347 Sequential-Parallel Reactions in a Semi-Continous Reactor 350... 

Electrochemical impedance spectroscopy Reaction mechanisms, kinetic parameters of surface reactions, identification of sequential/parallel reaction steps, evaluation of post-CMP formulations Zheng and Roy (2009), Shi et al. (2012), Sulyma and Roy (2010a), Tsai et al. (2003)... 

The reaction mechanism depends on the chemistry of the active oxidant and chemical contaminants. Multiple sequential and parallel reaction steps occur frequently. Partial oxidation produces noxious byproducts. 

Over the years, TAP systems have been used in catalyst industry research ranging from determining selectivity and activity of well-defined surfaces to distinguishing between sequential or parallel reaction paths. The capabilities of the TAP system are varied and can perform applications such as TPD, TPSR, TPO and TPR. In pulse experiments, the adsorption of reactants provides detailed information on the thermal stability of adsorbed intermediates. Fig. 4 shows the general parameters of the TAP system. 

An overall reaction may be accomplished by parallel paths or sequential steps. If it is realized by sequential steps, it is called a chain reaction and the slowest step determines the reaction rate. If it is achieved hy parallel paths, it is called a parallel reaction and the fastest path (more accurately, the sum of the rates of all paths) determines the reaction rate. To distinguish parallel paths versus sequential steps, each of the parallel paths can accomplish the whole reaction alone but each of the sequential steps cannot. 

The dependence of ethene selectivity on the conversion of ethane for the better catalysts shown in Fig. 1 shows that the selectivity is high at low conversions and decreases as the conversion increases. This trend is consistent with a reaction pathway that consists of mostly sequential reactions [Eq. (3)]. Depending on the reaction temperature, the reaction network may involve two parallel reaction pathways shown below, which is modified from... 

A 48-membered library of 2-arylbenzoxazoles has been prepared by the condensation of substituted 2-aminophenols with a series of acid chlorides. The reactions proceeded in the absence of a base in sealed tubes in an automated microwave instrument, which used sequential rather than parallel reaction processing. Comparisons to the conventional thermal conditions demonstrated the importance of the high temperatures and pressures achieved under microwave heating, which ensured that the reactions proceeded efficiently (Scheme 3.16)26. An analogous synthesis ofbenzoxazolesby the cyclocondensation reaction of 2-aminophenols with S-methylisothioamide hydroiodides on silica gel, under microwave irradiation, has also been reported (Scheme 3.16)27. 

Kinetic models which consider demetallation as a complex reaction network of consecutive and parallel reactions taught by model compound studies have been recognized with real feedstocks. Tamm et al. (1981) suggest a sequential mechanism where the metal compounds are activated by H2S. Model compound reaction pathway studies in the absence of H2S, discussed in Section IV,A,1, and experiments in which H2S was present in excess (Pazos et al., 1983) indicate that sequential reactions are inherent to the chemistry of the metal compounds irrespective of the presence of H2S. However, it is possible that both mechanisms contribute to metal removal. 

In order to determine the reaction pathway for 1,2-dichlorobenzene, Schiith fitted kinetic data and found that the primary pathway was direct reaction to benzene with a parallel reaction of sequential dechlorination through chlorobenzene to benzene. (Figure 7) These pathways were further supported by independent determination and verification of the reaction rate constant for the second hydrodechlorination step. (Schiith and Reinhard 1998)... 

A one-dimensional horizontal adsorption process was considered whereby the adsorption of ions from solution by soil particles occurs in a series rather than a parallel reaction mode, with three main consecutive steps FD, PD, and CR. Since these processes are sequential steps, the slowest of the three is rate-controlling. 

The reaction in Bq. 3.1 is an overall reaction that can, therefore, be the resultant of several parallel or sequential elementary reactions. Bor example, the... 

At this point, it should be emphasized that steps 2-6 are not linked in a sequential manner. Instead, diffusion and reaction inside the pore system, steps 3-5, occur simultaneously, as observed in the macroporous pellet as well. Moreover, the opportunities for a reactant molecule either to be converted at the outer surface of the crystallite or to enter the porous structure also represent parallel reaction paths. 

It follows that the overall selectivity Cs(t)ICc(t) is not constant in time, contrary to what happens in the single-component case. Astarita and Ocone (1991) also discuss the uniform cooperative case of parallel reactions, and the analogous analysis of the sequential case does not present substantial problems. 

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. 

---