Two Species with Coupled Reactions

Up to this point, the treatments have involved reactions for which the discrete form of the reaction-diffusion equations involve only terms in concentration of the species to which the discrete equation applies. That is, if there were two substances involved, O and R as above, then the discrete equation at a point i had terms only in C 0 for species O, and only C R for species R. This made it possible to use the Thomas algorithm to reduce a system like (6.27) to (6.28), treating the two species systems separately. They then get coupled through the boundary conditions. 

When homogeneous reactions take place, it often happens that some of the discrete equations contain terms in concentration for more than the one species, and it is then not generally possible to use the Thomas algorithm to reduce the systems. These systems are said to be coupled. An example will illustrate this situation. 

Consider the catalytic or EC7 reaction pair as described in Sect. 2.4, page 23, (2.76). For generality, the species designations A and B are now written as O and R, and the reaction pair then is 

The derivation of the discrete equations corresponding to this reaction pair will be given in Chap. 8 and it will suffice here to provide the general form they will take  

The coefficients o.,i(i) and a arise from the particular spatial approximation of the second derivative, while the a,k(i) come from the homogeneous chemical reaction rate, as will be described in Chap. 8. 

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Osajaxanthone 257 possesses antimicrobial and antifish poison activities and was isolated from Calophyllum enervo-sum [111] nigrolineaxanthone F 256 was isolated from the Garcinia nigrolineata species [112]. They can be synthesized from xanthone 255 by two different regioselective coupling reactions with prenal. 

The reaction shown above for the steam reforming of methatie led to die formation of a mixture of CO and H2, die so-called synthesis gas. The mixture was given this name since it can be used for the preparation of a large number of organic species with the use of an appropriate catalyst. The simplest example of this is the coupling reaction in which medrane is converted to ethane. The process occurs by the dissociative adsorption of methane on the catalyst, followed by the coupling of two methyl radicals to form ethane, which is then desorbed into the gas phase. 

Micellar catalysis of azo coupling reactions was first studied by Poindexter and McKay (1972). They investigated the reaction of a 4-nitrobenzenediazonium salt with 2-naphthol-6-sulfonic and 2-naphthol-3,6-disulfonic acid in the presence of sodium dodecylsulfate or hexadecyltrimethylammonium bromide. With both the anionic and cationic additives an inhibition (up to 15-fold) was observed. This result was to be expected on the basis of the principles of micellar catalysis, since the charges of the two reacting species are opposite. This is due to the fact that either of the reagents will, for electrostatic reasons, be excluded from the micelle. 

This new impurity proved to be derived from the Pd-catalyzed oxidation of DIPA to the enamine via P-hydride elimination. In fact, mixing Pd(OAc)2 with DIPA in DMF-d7 readily formed Pd black along with two species, primary amine and acetone, presumably derived from the enamine through hydrolysis. The resulting enamine or acetone then underwent a coupling reaction with iodoaniline 28. Heterocyclization through the arylpalladium(II) species provided 2-methyl indole 71, as shown in Scheme 4.19. 

A zinc-mediated carbon-carbon coupling reaction can be carried out on the metallated form of (t-butyldimethylsilyl)(2-pyridylmethyl)amine, formed in reaction with dimethylzinc. The isolated dimeric species can be reacted with further dimethyl zinc to give bis(methylzinc)-l,2-dipyridyl-l,2-bis(t-butyldimethylsilylamido)ethane, which contains two N3C coordinated zinc centers.89... 

A flexible method for modeling redox disequilibrium is to divide the reaction database into two parts. The first part contains reactions between the basis species (e.g., Table 6.1) and a number of redox species, which represent the basis species in alternative oxidation states. For example, redox species Fe+++ forms a redox pair with basis species Fe++, and HS- forms a redox pair with SO4. These coupling reactions are balanced in terms of an electron donor or acceptor, such as 02(aq). Table 7.1 shows coupling reactions from the llnl database. 

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