Stoichiometry and Kinetics

In a chemical reactor, one or several simultaneous chemical reactions take place. In an industrial context, some of the reactions tend to be desirable, whereas others are undesirable side reactions yielding by-products. 

In case several reactions take place simultaneously in the system, these are called multiple reactions. 

An example of a desirable main reaction is methanol synthesis 

These reactions in the methanol synthesis are parallel reactions in H2, since H2 reacts simultaneously with CO2 and CO to yield CO and CH3OH. On the other hand, the reaction scheme can be interpreted to be consecutive in CO, as CO is produced by the latter reaction and consumed by the first one. 

A classical example of coupled reactions is illustrated by a reaction scheme that is parallel in one reactant and consecutive in another. For instance, in the chlorination of p-cresol, mono- and dichloro-p-cresols are produced according to the following scheme 

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Kredich NM, EJ Eoote, BS Keenan (1973) The stoichiometry and kinetics of the inducible cysteine desulfhy-drase from Salmonella typhimurium. J Biol Chem 248 6187-6196. 

The stoichiometry and kinetics of gas phase epoxidation of cyclohexene by silica-supported Ti(0 Pr)4 upon treatment with /< r/-butyl hydro peroxide were the... 

Kim C., Q. Zhou, B. Deng, E. C. Thornton and H. Xu, 2001, Chromium(VI) reduction by hydrogen sulfide in aqueous media stoichiometry and kinetics. Environmental Science and Technology 35, 2219-2225. 

In previous chapters, we deal with simple systems in which the stoichiometry and kinetics can each be represented by a single equation. In this chapter we deal with complex systems, which require more than one equation, and this introduces the additional features of product distribution and reaction network. Product distribution is not uniquely determined by a single stoichiometric equation, but depends on the reactor type, as well as on the relative rates of two or more simultaneous processes, which form a reaction network. From the point of view of kinetics, we must follow the course of reaction with respect to more than one species in order to determine values of more than one rate constant. We continue to consider only systems in which reaction occurs in a single phase. This includes some catalytic reactions, which, for our purpose in this chapter, may be treated as pseudohomogeneous. Some development is done with those famous fictitious species A, B, C, etc. to illustrate some features as simply as possible, but real systems are introduced to explore details of product distribution and reaction networks involving more than one reaction step. 

The structure of HRP-I has been identified as an Fe(IV) porphyrin -ir-cation radical by a variety of spectroscopic methods (71-74). The oxidized forms of HRP present differences in their visible absorption spectra (75-77). These distinct spectral characteristics of HRP have made this a very useful redox protein for studying one-electron transfers in alkaloid reactions. An example is illustrated in Fig. 2 where the one-electron oxidation of vindoline is followed by observing the oxidation of native HRP (curve A) with equimolar H202 to HRP-compound I (curve B). Addition of vindoline to the reaction mixture yields the absorption spectrum of HRP-compound II (curve C) (78). This methodology can yield useful information on the stoichiometry and kinetics of electron transfer from an alkaloid substrate to HRP. Several excellent reviews on the properties, mechanism, and oxidation states of peroxidases have been published (79-81). 

We wish to treat 10 liters/min of liquid feed containing 1 mol A/liter to 99% conversion. The stoichiometry and kinetics of the reaction are given by... 

On a molecular level, reactions occur by coUisions between molecules, and the rate is usually proportional to the density of each reacting molecule. We will return to the subject of reaction mechanisms and elementary reactions in Chapter 4. Here we define elementary reactions more simply and loosely as reactions whose kinetics agree with their stoichiometry. This relationship between stoichiometry and kinetics is sometimes called the Law of Mass Action, although it is by no means a fundamental law of nature, and it is frequently invalid. 

When a second sulfite or SO2, if you like, or H2SO3 attacks 03Cr0S02 2, it goes all in one fell-swoop to chromic ion, to which sulfate is attached at the end of the reaction, and an SCV - radical. One can t precipitate sulfate with barium immediately after the reaction. Coordination of the chromium (111) stabilizes the radical until it can react with another as was mentioned by Dr. Halpern. This mechanism accounts for both the stoichiometry and kinetics. 

When n = 2 this represents the second-order reaction scheme aikAt + Ak -> products with certain constraints on the stoichiometry and kinetic constants. When there is a single component this reduces to a second-order reaction. This cooperative element in the Astarita kinetics is, of course, no defect—indeed it may be its strength. 

Chen XZ, Zhu T, Smith DE, et al. Stoichiometry and kinetics of the high-affinity H+-coupled peptide transporter PepT2. J Biol Chem 1999 274 2773-2779. 

Table I. Stoichiometry and Kinetics of the Reaction Between Formaldehyde and Some Flavan-3-ols (pH 8.0 and 30 °C)...

Stoichiometry and Kinetics. The starting point in studies of ligand-DNA complexes is usually a titration experiment to es-... 

Hammond D. E., McManus 1., Berelson W. M., Kilgore T. E., and Pope R. H. (1996) Early diagenesis of organic material in equatorial Pacific sediments stoichiometry and kinetics. Deep-Sea Res. II. 43, 1365-1412. 

Finally, mention should be made of the investigations of Collin and Delplace which were carried out at very low pressures (10 —10 torr). It appears that at these low pressures completely different stoichiometry and kinetics prevail. 

VoU, M. and Boehm, H.-P. (1970). Basic surface oxides on carbon — II. Stoichiometry and kinetics of the formation reaction thermal decomposition (in German). Carbon, 8, 741-52. 

The stoichiometries and kinetics for the reaction of 02 - with halogenated hydrocarbons (alkanes, alkenes, and aromatics) are summarized in Table 7-1.18-24 [The normalized first-order rate constants, fcj / [S], were determined by the rotated ring-disk electrode method under pseudo-first-order conditions ([substrate] > [O2-)]. ... 

Table 7-3 Stoichiometries and Kinetics for the Reaction of 0.1-5.0 mM Cb - with Substituted Hydrazines, Catechol, and Ascorbic Acid in Dimethylformamide (or Dimethylsulfoxide) at 25°C...

Stoichiometry and Kinetics of Gas Phase Cyclohexene Epoxidation by a Silica-Supported terr-Butylperoxidititanium Complex... 

Figure 3 illustrates different relations of Foxygen to Fcarbon, which depend on stoichiometry, and kinetics of reaction. The normal calc-silicate decarbonation trend applies if all minerals in the rock are fully equilibrated during a reaction such as 4 or 5, in which case all carbon in the rock is liberated as CO2 (Fcarbon 0), while only 40% of the oxygen is released (Foxygen 0.6). However, if the rock has (for example) 50% excess silicates that are not involved in the reaction, but which still equilibrate isotopically, then F xy 0.8 as Fcarbon 0.0 along the 50% inert oxygen trend and the amount of Or°0 depletion will be smaller. Likewise, if 50% of a rock s carbon does not participate due to stoichiometric excess, a 50% inert carbon trend will be followed and the depletion of will also be less. In practice any trend is possible from -100%... 

The synthesis problem of a chemical reactor network may be defined as follows. Given the reaction stoichiometry and kinetic expressions, initial feeds, reactor targets (productivity, selectivity, flexibility), technological constraints, the optimal reactor network structure, as well as sub-optimal alternatives. The following elements should be determined ... 

Toby, S. (2000). The relationship between stoichiometry and kinetics. Journal of Chemical Education, 77, 188-190. 

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