Independent Species Composition Specifications

In the preceding section, we discussed how to determine the number of independent chemical reactions and how to select a set of independent reactions. The number of independent reactions indicates the number of equations that we should solve to determine the composition of the reactor. To solve these equations. 

Let US examine more closely the nature of the problem. Consider first a chemical reactor where the following two reactions take place  

Since each chemical reaction has at least one species that does not participate in the other, both reactions are independent. Hence, we need to specify two species compositions to determine the extents of the two reactions. At first glance, it seems that we can specify the composition of any two species. However, a closer examination of the reactions reveals that none of the species participates in both reactions. By specifying the amount of two species from the same chemical reaction, we cannot determine the extents of the second reaction and the reactor composition. Hence, we have to specify two independent compositions such that each relates to a distinct independent chemical reaction. Similar situations may arise when we deal with more complex sets of chemical reactions, where the identification of independent compositions is not so obvious. Consider the hydrogenation of toluene where the following two reactions take place  

These two chemical reactions are independent, yet if we specify the amounts of toluene and methane, we cannot determine the composition of the other species. The reason is that, while the two reactions are independent, we cannot select any two species compositions to provide information on all other species. In this case, compositions of the toluene and methane do not provide us with a relationship on the amount of diphenyl and hydrogen. This becomes evident if we multiply Reaction 2.8.1 by 2 and subtract Reaction 2.8.2  

It is clear that specifications of the amounts of toluene and methane do not provide any information on the amounts of diphenyl and hydrogen. 

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To identify independent species composition specifications, we adopt the following procedure ... 

Independent composition specifications depend on the relationships among individual species and the chemical reactions taking place in the reactor, but they are invariant of the specific set of independent reactions selected. Since the set of independent reactions generated by the reduced matrix of the Gaussian elimination... 

Firstly, when relating (gravimetrically determined) equilibrium film composition to solution composition, activity effects must be taken into account. These effects may cause solvent and other neutral molecules, as well as the target species, to enter/leave the film. The importance of medium effects cannot be overemphasised here. A special case is a co-ordination model, where favourable interaction between polymer and target species results in saturation of the film except at very low concentration. The film mass is then independent of solution composition. This situation is likely for systems where a strong, specific polymer/analyte interaction has been synthetically designed into the polymer. 

The traditional pulp/paper composition metrics (e.g. specific lignin and cellulose contents) are based on chemical reaction (depolymerization) of the native biomass into fractions. Each separated fiaction is then independently pyrolysed, and the pyrolysis yields are fit to models, and the composite used to predict other woody species ... 

Other studies have indicated that PG and PLD are a major source of PA in cells stimulated with various agonists [197-200] and several studies have confirmed biphasic formation of DAG, with the first phase derived from PIP2 and the second from PC via PA [201-205]. Analyses of the specific fatty acid composition of PA and PtdBut derived from cells treated with butanol and stimulated by bombesin or LPA also showed a predominance of saturated and mono-unsaturated fatty acids in the lipids derived from PLD action [206]. The fatty acid composition was very different from that found in DAG generated by PLC action on PIP2, in which polyunsaturated fatty acids predominate. The key issue is whether the DAG species derived from PC can activate PKC. Although studies indicate that this species is active on PKC in vitro, this has not been demonstrated in vivo. As described above [196], PC-derived DAG can activate Ca +-independent PKC isozymes but, because of the lack of a Ca rise, it cannot activate ( a -dcpcridcril PKC isozymes. 

I loss of ecosystem functions Reactions are very site specific and independant of species, e.g., -/1 NPP of vegetation, changes in stocks and site composition (C,-, Q-plants), species-related changes in population of herbivores Changes in site composition, loss of biodiversity,... 

The equations you have written down provide a mathematical description of the reaction mechanism. In fact, if we focus on the rate of production of the product P then all the equations are seen to be interlinked the formation of P depends on the decomposition of Y, which in turn depends on the decomposition of X, which in turn depends on the decomposition of A. In principle, the equations can be solved to find how the concentrations of all of the species present (A, X, Y and P) vary with time but, overall, it is not possible to find a simple form of the rate equation. In fact, these comments need not be specific to the model mechanism we have chosen to discuss in general, they will apply to any form of mechanism. However, we know from experimental investigations that many composite reactions which have time-independent stoichiometry have relatively simple rate equations. This must mean that it is legitimate to simplify the analysis of reaction mechanisms. But how A clue to one approach can be taken from the unlikely source of an article in the Daily News (London) 26 December 1896 ... 

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