Unidirectional reactions

Quantitatively, many observed deviations from simple equilibrium processes can be interpreted as consequences of the various isotopic components having different rates of reaction. Isotope measurements taken during unidirectional chemical reactions always show a preferential emichment of the lighter isotope in the reaction products. The isotope fractionation introduced during the course of an unidirectional reaction may be considered in terms of the ratio of rate constants for the isotopic substances. Thus, for two competing isotopic reactions... 

For the kinetics of a reaction, it is critical to know the rough time to reach equilibrium. Often the term "mean reaction time," or "reaction timescale," or "relaxation timescale" is used. These terms all mean the same, the time it takes for the reactant concentration to change from the initial value to 1/e toward the final (equilibrium) value. For unidirectional reactions, half-life is often used to characterize the time to reach the final state, and it means the time for the reactant concentration to decrease to half of the initial value. For some reactions or processes, these times are short, meaning that the equilibrium state is easy to reach. Examples of rapid reactions include H2O + OH (timescale < 67 /is at... 

Scheme 4.2 Parallel (competitive) first-order unidirectional reactions of a single reactant.

Desirable achiral derivatization reaction properties include fast, unidirectional reactions with no or minimal side reactions. In addition, both the reagent... 

Desorbed species are not removed and are allowed to accumulate in the inherently closed system of the batch reactor. Thus, unless a unidirectional reaction is being studied, reverse reactions must be taken into account in Ihe data analysis. The accumulation of desorbed... 

For the simplest of kinetic schemes, such as for unidirectional reactions, straightforward mathematical expressions exist that describe the rates at which the reagents are consumed in the process. In order to illustrate how digital simulation works, we will first tackle such simple examples, since they allow us to calibrate the method, and to discuss its constraints andlimi-tations. 

Next we consider some simple higher-order kinetic schemes, specifically the second- and third-order unidirectional reactions 2A — and 3A —> for which, again, closed-form solutions are available to validate our approach. (Since we omit any back reactions, we need not specify the products.) First we consider the unidirectional dimerization reaction... 

For the first-order unidirectional reaction (9.2-1) we therefore write the difference equation as... 

Special terms are also used to characterize the amplitude of isotopic fractionation caused by a given process. Isotope fractionation results from both equilibrium processes ( equilibrium fractionation ) and unidirectional reactions ( kinetic fractionation ). Nitrogen isotope variations in the ocean are typically dominated by kinetic fractionation associated with the conversions of N from one form to another. The kinetic isotope effect, , of a given reaction is defined by the ratio of rates with which the two N isotopes are converted from reactant to product ... 

Figure 1 The <5 N of reactant and product N pools of a single unidirectional reaction as a function of the fraction of the initial reactant supply that is left unconsumed, for two different models of reactant supply and consumption, following the approximate equations given in the text. The Rayleigh model (black lines) applies when a closed pool of reactant N is consumed. The steady-state model (gray lines) applies when reactant N is supplied continuously. The same isotopic parameters, an isotope effect e) of 5%o and a <5 N of 5%o for the initial reactant supply, are used for both the Rayleigh and steady-state models, e is approximately equal to the isotopic difference between reactant N and its product (the instantaneous product in the case of the Rayleigh model).

In SSITKA, it is assumed that the catalyst surface is a system made up of a number of interconnected compartments. Each compartment is a homogeneous or well-mixed system like a continuous stirred tank reactor (CSTR). A separate compartment is assumed to be present for each uniquely adsorbed reaction intermediate species. Based on this assumption, the response of a single unidirectional reaction step to a step change in the isotopic concentration of one of the reactants, which is made at time t = 0, is given as... 

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