First-order chemical kinetics series reaction

The death of a single microbial cell is a biochemical process (or series of processes) the entrapment of individual microbial cells in or on filters is due to physical forces. These effects on individual cells are peculiar to individual sterilization processes. On the other hand, the effects of inactivating processes and filtering processes on populations of microbial cells are sufficiently similar to be described by one general form—exponential death. Exponential kinetics are typical of first-order chemical reactions. For inactivation this can be attributed to cell death arising from some reaction that causes irreparable damage to a molecule or molecules essential for continuing viability. 

Laplace transformation is particularly useful in pharmacokinetics where a number of series first-order reactions are used to model the kinetics of drug absorption, distribution, metabolism, and excretion. Likewise, the relaxation kinetics of certain multistep chemical and physical processes are well suited for the use of Laplace transforms. 

Wu and Gschwend (1986) reviewed and evaluated several kinetic models to investigate sorption kinetics of hydrophobic organic substances on sediments and soils. They evaluated a first-order model (one-box) where the reaction is evaluated with one rate coefficient (k) as well as a two-site model (two-box) whereby there are two classes of sorbing sites, two chemical reactions in series, or a sorbent with easily accessible sites and difficultly accessible sites. Unfortunately, the latter model has three independent fitting parameters kx, the exchange rate from the solution to the first (accessible sites) box k2, the exchange rate from the first box to the... 

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 ... 

Also shown in Fig. 40 is the ILim 1/3 behaviour for the first reduction wave alone (at the detector electrode). Extrapolation of this data to zero current produces a positive intercept on the x ( 71/3) axis, indicating that the electrode reaction is influenced by following chemical kinetics. The data in Fig. 40 can be used to calculate Nk as a function of 7, which in turn can be converted to the corresponding values of the kinetic parameter A via eqns. (121) and (122). It follows from eqn. (103) that a plot of A against 7"1/3 allows the lst-order rate constant for the chemical step to be elucidated. Figure 41 shows the A- 7 1/3 behaviour for the reduction of the oxidized ADM A at the detector electrode at a series of basic conditions. As predicted by eqn. (103), a linear relationship between A and 7 1/3 holds and intercepts the origin. The data in Fig. 41 allowed Aoki and Matsuda [125] to evaluate the 2nd-order rate constant, k2, for the deamination of oxidized ADMA... 

The chemical kinetics in a packed reactor have been studied in a detail by Reijn, Poppe, and van der Linden [554] with the aid of the tanks-in-series model. They based their theory on three assumptions that the number of tanks N in the reactor is constant that the chemical reactions are (pseudo) first order and that adequate mixing is ensured. 

Chemical vapor deposition (CVD) of tetraethoxysilane on HZSM5 was performed stepwise under well-controlled, mild conditions. Several test reactions were performed over the series of modified samples. Under mild conditions, CVD follows first order kinetics with respect to uncovered external sites on the zeolite crystals. The external surface is homogeneous with regard to both CVD and catalytic activity. Reactions, which are controlled by strong internal mass transfer restrictions, do respond in a way, which indicates that CVD causes pore mouth plugging rather than pore mouth narrowing. 

For the situation in which each of the series reactions is irreversible and obeys a first-order rate law, eqnations (5.3.4), (5.3.6), (5.3.9), and (5.3.10) describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For consecutive reactions in which all of the reactions do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time at which the concentration of a particular intermediate passes through a maximum. If interested in designing a continuous-flow process for producing this species, the chemical engineer must make appropriate allowance for the flow conditions that will prevail within the reactor. That disparities in reactor configurations can bring about wide variations in desired product yields for series reactions is evident from the examples considered in Illustrations 9.2 and 9.3. 

Therefore we attempted to simulate advanced pyrolysis using a multi-step model (MSM). This model was developed using TGA- and DSC-derived kinetic coefficients, determined for chemically and thermally treated oil shale samples by modelling particular reaction steps. The MSM is based on the reaction scheme shown in Fig. 4-116 which displays a series of parallel and consecutive first order reactions. K and B denote the kerogen and bitumen originally present in the oil shale B, B, and to /Jj are non-volatilized intermediates and products (solids and liquids) to are volatilized products (gases and vapors) and/j to/jg are the stoichiometric coefficients that fulfil the condition ... 

A sequence of chemical reactions with a first-order kinetics is the archetype of chain processes in which the concepts of intermediate species, transition state, and activation energy barrier find a thorough application. This is for saying that the study of such a system with this case study of two reactions in series is of paramount importance. 

It has been stated by Boudart that the steady-state approximation (SSA) can be considered as the most important general technique of applied chemical kinetics [9]. A formal proof of this hypothesis that is applicable to all reaction mechanisms is not available because the rate equations for complex systems are often impossible to solve analytically. However, the derivation for a simple reaction system of two first-order reactions in series demonstrates the principle very nicely and leads to the important general conclusion that, to a good approximation, the rate of change in the concentration of a reactive intermediate, X, is zero whenever such an intermediate is slowly formed and rapidly disappears. 

The acyl-enzyme is an ester which was shown by both chemical and physical methods to result from the attachment of the acyl moiety of the substrate to Ser-195 of the enzyme. 2. A base of pX, = 7 is required for the reaction. 3. This base is the imidazole ring of His-57. 4. The deacylation is a nucleophilic reaction and a series of substituents in the acyl group yields a Hammett p-constant of +1.6 [18]. 5. The reaction is first order with respect to the nucleophile, as determined from the kinetics of the methanolysis reaction [19]. 6. The nucleophile reacts in the protonated form with the acyl-enzyme, as evidenced by the pH-dependence of the reaction of acetyl-, iso-... 

An essential property of a catalyst is that it is regenerated in its original state after each reaction cycle from reactants to products. In order to appreciate this, one should realize that a catalyst provides sites for a reactant molecule to adsorb. In its adsorbed state the molecule undergoes chemical changes and finally the product molecule desorbs, and regenerates a vacant site for adsorption of the next molecule. The overall result is a conversion of reactant to product molecules by a series of reactions in which the catalyst is first consumed but regenerated at the end. In this section we analyze the kinetics of such a self-regenerating catalytic system. 

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