Series reactions, first-order intermediate

Schematic representation of the time dependence of the concentration of the first intermediate in a series of first-order reactions. Initial intermediate concentration is nonzero.

A series of first order irreversible reactions is one in which an intermediate is formed that can then further react. A generalized series reaction is... 

Series of First-Order Reections The phenyl rearrangement (reaction 4, Scheme 7.2) proceeds through an intermediate rather than a transition state. In this case, the unimolecular reaction becomes a series of first-order reactions ... 

Another very common kinetic scheme involves a series of first-order reactions, leading first to the formation of an intermediate B, which subsequently reacts to give the final product... 

Concentration-time curves. Much of Sections 3.1 and 3.2 was devoted to mathematical techniques for describing or simulating concentration as a function of time. Experimental concentration-time curves for reactants, intermediates, and products can be compared with computed curves for reasonable kinetic schemes. Absolute concentrations are most useful, but even instrument responses (such as absorbances) are very helpful. One hopes to identify characteristic features such as the formation and decay of intermediates, approach to an equilibrium state, induction periods, an autocatalytic growth phase, or simple kinetic behavior of certain phases of the reaction. Recall, for example, that for a series first-order reaction scheme, the loss of the initial reactant is simple first-order. Approximations to simple behavior may suggest justifiable mathematical assumptions that can simplify the quantitative description. 

Consecutive Reactions Where an Inter-mediate Is the Desired Product. Consecutive reactions in which an intermediate species (V) is the desired product are often represented as a series of pseudo first-order reactions... 

As a simple model for the enzyme penicillinase, Tutt and Schwartz (1970, 1971) investigated the effect of cycloheptaamylose on the hydrolysis of a series of penicillins. As illustrated in Scheme III, the alkaline hydrolysis of penicillins is first-order in both substrate and hydroxide ion and proceeds with cleavage of the /3-lactam ring to produce penicilloic acid. In the presence of an excess of cycloheptaamylose, the rate of disappearance of penicillin follows saturation kinetics as the cycloheptaamylose concentration is varied. By analogy to the hydrolysis of the phenyl acetates, this saturation behavior may be explained by inclusion of the penicillin side chain (the R group) within the cycloheptaamylose cavity prior to nucleophilic attack by a cycloheptaamylose alkoxide ion at the /3-lactam carbonyl. The presence of a covalent intermediate on the reaction pathway, although not isolated, was implicated by the observation that the rate of disappearance of penicillin is always greater than the rate of appearance of free penicilloic acid. 

Equations (5.16) of Table 5.1 refer to series first-order reactions. Of interest for the solvent extraction kinetics is a special case arising when the concentration of the intermediate, [Y], may be considered essentially constant (i.e., d[Y]/dt = 0). This approximation, called the stationary state or steady-state approximation, is particularly good when the intermediate is very reactive and present at very small concentrations. This situation is often met when the intermediate [Y] is an interfacially adsorbed species. One then obtains... 

Gurden et al. studied the monitoring of batch processes using spectroscopy. As a case study, they followed a pseudo first-order biochemical reaction with an intermediate using UV-vis spectroscopy. Following statistical process monitoring, process disturbances could be detected in a series of batches. 

Fig. 1.25. Reaction in series—batch or tubular plug-flow reactor. Concentration Cr of intermediate product P for consecutive first order reactions, A -> P -> Q...

In the reaction scheme in series (sixth row in Table 2.1), the required product is often the intermediate I, and its concentration has a maximum at time t, which can be taken as the optimal batch time, When the system follows a first-order kinetics not affected by chemical equilibrium (Fig. 2.5), it can be easily shown that t depends on the values of the rate constants through the following expression ... 

Figure 7.3 also compares the evolution of the concentrations of the intermediate Q and the product in case of two first-order reactions in series in a CSTR with that in a batch or plug flow reactor. For constant density, the mass balance for the reaction components in a CSTR are ... 

A priori, the mechanism of hydrogenation of benzene may be represented as a series of hydrogen transfers from the catalyst to the adsorbed benzene and the adsorbed intermediates (Scheme 5)." The often observed first order reaction in H2 suggests that the addition of the second hydrogen atom is the more difficult step, indicating that the largest energy barrier lies between adsorbed arene and adsorbed diene. However, no cyclohexadienes have been detected as intermediates. 

Figure 6-3.2 Yield of acetaldehyde as a function of ethanol conversion. Data were obtained at 518 K. Data points (in order of increasing ethano conversion) were obtained at space velocities of 26,000,52,000,104,000, and 208,000 h"h The curves were calculated for a first-order series reaction in a plug-flow reactor and show yield of the intermediate species B as a function of the conversion of reactant for various ratios of rate constants and. [Reprinted with permission fiom Ind. Eng. Chan. Prod. Res. Dev., 22, 212 (1983). Copyright 1983 American Chemical Society.]...

The reaction of dimethylmagnesium with excess ketone consists of a series of pseudo first-order reactions involving the formation of two intermediate products. Pi and P2 before the formation of the final product P3. Interpretation of the kinetic data did not necessarily lead to the conclusion that a complex between the ketone and the organomagnesium species was required to bring about a reaction (case II) a bimolecular collision not involving a complex (case I) also fit the data. Nevertheless, in the abstract of the paper the authors showed the three equations that did involve complex formation, which may reflect their preference for the traditional concept of the preliminary formation of a "Meisenheimer complex. The paper continued as follows Inability to distinguish between case I and case II is relatively minor compared to the more essential features of the reaction path which have been clearly established. A four-center concerted mechanism was presented in each of the carbon carbon bond formation steps in the detailed mechanism depicted in the final scheme. 

With two electrocatalytic steps in series, the concentration of the intermediate B (Eq. 70) goes through a maximum with time (or space-time for a flow reactor). Solution of the kinetic equations for each species (60) yields for the simple case of first-order reactions... 

Series first-order reactions may be referred to the cases when the mechanism goes through an intermediate Sorg, for example, at an interfaciaUy adsorption of the solute ... 

The reaction is first order in molecular oxygen and first order in methanol therefore, we say both the reaction and the rate law are elementary. This forn of the rate law can be derived from Collision Theory as shown in the Profes- sion Reference Shelf 3A on the CD-ROM. There are many reactions where the stoichiometric coefficients in the reaction are identical to the reaction orders but the reactions are not elementary owing to such things as pathways involving active intermediates and series reactions. For these reactions that are not elementary but whose stoichiometric coefficients are identical to the reaction orders in the rate law. we say the reaction follows on elememary rate /aw. For example, the oxidation reaction of nitric oxide discussed earlier. 

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