Two parallel first-order reactions

For two first-order parallel reactions A — B and A — C, the rate of depletion of reactant A is given by  

According to Eq. (4.1.10) the selectivity for product B for a constant volume reaction is  

Consequently, for parallel first-order reactions, the selectivity depends solely on the ratio of the rate constants and not on the reaction progress and conversion of the reactant. This is also valid for parallel reactions of higher order, if all reactions are of the same order. 

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Suppose there are two parallel, first-order reactions in a steady-state CSTR. Show that neither the fed-batch nor fast-fill-and-hold strategies can achieve a bumpless startup if the reactions have different rate... 

Two Reactions, Parallel—In the case of two parallel first-order reactions, A —> B and A —> C, where only one of the products, B, is desired, the CSTR is... 

The marine facultative anaerobe bacterium Serratia marinoruhm and the yeast Rhodotoruhi rubra both methylate arsenate ion to methylarsonate, but only the latter produces cacodylic acid (258). Human volunteers who ingested 500 fig doses of As as sodium arsenite, sodium methylarsonate, and sodium cacodylate excreted these compounds in their urine (259). Of these three, approximately 75% of the sodium arsenite is methylated, while 13% of methylarsonate is methylated. Rat liver subcellular fractions methylated sodium arsenate in vitro, providing the first direct evidence for possible mammalian methylation independent of symbiotic bacteria (260). Shariatpanahi el al. have reported kinetics studies on arsenic biotransformation by five species of bacteria (261). They found that the As(V)-As(IIl) reduction followed a pattern of two parallel first-order reactions, while the methylation reactions all followed first-order kinetics. Of the five species tested, only the Pseudomonas produced all four metabolites (arsenite, methylarsonate, cacodylate, trimethylarsine) (261). 

As will be shown later, sorption of most radionuclides may be a function of two or more mechanisms. The combination two first-order reactions has been successfully applied to Sr migration over a twenty-year time period in a sandy-aquifer (1) The equations describing two parallel first-order reactions are... 

Luss, D., and Golikeri, S. V., Grouping of many species each consumed by two parallel first-order reactions, AIChE J. 21,865 (1975). 

This single-step process lacks the flexibihty required to describe much of the experimental data and nonisothermal effects. More sophisticated but still essentially empirical models describe devolatilization with two parallel, first-order reactions, by a first-order reaction with a statistical distribution of activation energy, and by various combina-... 

The simplest model of a bubbling fluidized bed, with uniform bubbles exchanging matter with a dense phase of catalytic particles which promote a continuum of parallel first order reactions is considered. It is shown that the system behaves like a stirred tank with two feeds the one, direct at the inlet the other, distributed from the bubble train. The basic results can be extended to cases of catalyst replacement for a single reactant and to Astarita s uniform kinetics for the continuous mixture. 

Fig. 4.3 Concentration-time profiles for two parallel first-order unidirectional reactions of a single compound A.

Several quantitative analyses of the effect of intraparticle heat and mass transport have been carried out for parallel, irreversible reactions [1]. Roberts and Lamb [2] have worked on the effect of reversibility on the selectivity of parallel reactions in a porous catalyst. The reaction selectivity of a kinetic model of two parallel, first order, irreversible reactions with a second order inhibition kinetic term in one of them has also been investigated [3]. 

The proposed NSPS can be met by hydrotreating the coal liquids obtained by filtering the product from the coal dissolution stage. The desulfurization kinetics can be presented by two parallel first-order rate expression, and hydrogen consumption kinetics can be presented by a first-order rate expression. A linear relationship exists between total sulfur content and SRC sulfur content of the hydrotreated product. For the Western Kentucky bituminous 9/14 coal studied here, the maximum selectivity and lowest SRC conversion to oil for a fixed SRC sulfur content are obtained using the highest reaction temperature (435°C) and the shortest reaction time 7 min.). ... 

In many practical cases, several reaction pathways are possible, and we may even have a complicated network of parallel and serial reactions. Here we only treat the simple cases of two parallel and two serial first-order reactions. 

The reapportionment of residence time in r u ial flow is analogous to variable volume CSTRs in series. As such, radial flow would be expected to affect product selectivity in series and parallel reactions. For two parallel first order, exothermic reactions, the particle equations [3, 4] become... 

Figure 4. Fractional yield as a function of cell number for two parallel first-order, exothermic reactions in CPRF, CFRF (p = 0.25), and axial flow yjyt = 2, = 2, y,...

From the above two expressions we see immediately that the ratio of the rate constants of parallel first-order reactions is equal to the ratio of yields of the products. 

Irreversible First-Order Parallel Reactions. Consider the irreversible decomposition of a reactant A into two sets of products by first-order reactions. 

Meehan and Bond (23) on the other hand, have taken an opposite view, namely that k3I1(C) k3I(C), while k3II(T) k3I(T). Thus, in this view, the hydrolysis occurs at external binding sites, while covalent binding occurs at intercalation sites. Furthermore, they reject the common intermediate model (Equation 2) on the basis of their belief that the rates of reaction for tetraol formation and adduct formation and the ratio of the products should be the same in such a model. While these rates of reaction are the same and the product ratios are observed to be different, this is fully consistent for a set of parallel pseudo-first order reactions involving a common intermediate (29) as pointed out above. Thus, the data of Meehan and Bond does not demonstrate the validity of the two-domain model (23). 

Two Different Reactants. A set of two or more first-order reactions, the reactants of which are independent of each other, generating at least one product that is common for each chemical reaction. For example, consider the following set of parallel reactions ... 

When reactions in series are considered, it is not possible to draw any very satisfactory conclusions without working out the product distribution completely for each of the basic reactor types. The general case in which the reactions are of arbitrary order is more complex than for parallel reactions. Only the case of two first-order reactions will therefore be considered ... 

In a parallel reaction network of first-order reactions, the selectivity does not depend upon reaction time or residence time, since both products are formed by the same reactant and with the same concentration. The concentration of one of the two products will be higher, but their ratio will be the same during reaction in a batch reactor or at any position in a PFR. The most important parameters for a parallel reaction system are the reaction conditions, such as concentrations and temperature, as well as reactor type. An example is given in the following section. 

The reactions can be described by two simple first order parallel reactions (route 1 of the scheme presented earlier) ... 

If one is computing the two changes separately (the parallel method), and given that the chemical reaction itself is usually tractable analytically, this component need not be simulated. For a first-order reaction as seen in (5.11) and (5.12), the last part in (5.12) has the general solution for a first-order reaction,... 

In its literal form, this reaction is only of academic interest because a molecule is unlikely to break up or isomerize irreversibly in two or more different ways. However, situations frequently encountered in practice are those of multistep parallel first-order decomposition reactions and of parallel reactions that involve coreactants but are pseudo-first order in the reactant A. An example of the first kind is dehydrogenation of paraffins, examples of the second kind include hydration, hydrochlorination, hydroformylation, and hydrocyanation of olefins and some hydrocarbon oxidation reactions. All these reactions are multistep, but the great majority are first order in the respective hydrocarbon, and pseudo-first order if any co-reactant concentration is kept constant. 

Consider the reaction network of two irreversible (one-way), first-order reactions in parallel ... 

The decomposition of many dmgs involves two or more pathways, the preferred route of reaction being dependent on reaction condition. Nitrazepam (VI) decomposes in two pseudo first-order parallel reactions giving different breakdown products in solution and in the solid state, as illustrated in Scheme 4.13. Decomposition of nitrazepam tablets in the presence of moisture will occur by both routes, the ratio of the two products being dependent on the amount of water present. 

The parameters in the model, which witb-rare exception should no exceed two in number, are obtained from the RTD data. Once the parame ters are evaluated, the conversion in the model, and thus in the real reactoi can be calculated. For typical tank-reactor models, this is the conversion i a series-parallel reactor system. For the dispersion model, the second-orde differential equation must be solved, usually numerically. Analytical soli tions exist for first-order reactions, but as pointed out previously, no mod has to be assumed for the first-order system if the RTD is available. 

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