Reactions with Multiple Species

When there are many species involved, the problem becomes much more complex and species partial pressures have to be calculated by approximate numerical techniques. As an illustration, consider the Si-CI-H system3 with only eight gaseous species (H2, HCI, SiH4, SiH3CI, SiH2Cl2, SiHCU, SiCI4 and Si Cl ) allowed, where the deposition of solid Si on the surface of the container must be allowed for. 

It must also be made clear that the accuracy of this approach depends on the skill with which the significant species are selected. For example, Si2H6 may be a significant species in this reaction, but it has been neglected. 

To treat this problem along the lines we have been discussing, we choose six reactions as follows  

A seventh equation is derived from the fact that the sum of the partial pressures must equal the total pressure (in this example, 1 atmosphere). 

A final (eighth) relationship is obtained when we specify the Cl/H ratio. For this system. Si may leave the gas phase in going from one equilibrium to another (deposit as a thin film), but the Cl and H will remain the same. Therefore, we can write 

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Table 9.4 Standard Apparent Reduction Potentials E ° (in volts) at 298.15 K of Half-reactions Involving Reactants with Multiple Species...

For q multiple reactions with ni species occurring in either a semibatch or batch reactor. Equation (13-15) can be generalized in the same manner a.s the steady-state energy balance, to give... 

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). 

Bis(trifluoromethyl)-substituted heterodienes are electron-deficient species They therefore react preferentially with electron-rich multiple bond systems to give [4+2] cycloadducts (Diels-Alder reaction with inverse electron demand) [238]... 

Of the many reagents, both heterogeneous and homogeneous, that can facilitate chemical reactions, the cycloamyloses stand out. Reactions can be catalyzed with many species such as hydronium ions, hydroxide ions, general acids, general bases, nucleophiles, and electrophiles. More effective catalysis can sometimes be achieved by combinations of catalytic species as in multiple catalysis, intramolecular catalysis, and catalysis by com-plexation. Only the latter catalysis can show the real attributes of an efficient catalytic system, namely speed and selectivity. In analogy to molecular sieves, selectivity can be attained by stereospecific complexation and speed can be likewise attained if the stereochemistry within the complex is correct. The cycloamyloses, of any simple chemical compound, come the closest to these goals. 

Steefel, C. I. and A.C. Lasaga, 1994, A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. American Journal of Science 294, 529-592. 

As with any modern review of the chemical Hterature, the subject discussed in this chapter touches upon topics that are the focus of related books and articles. For example, there is a well recognized tome on the 1,3-dipolar cycloaddition reaction that is an excellent introduction to the many varieties of this transformation [1]. More specific reviews involving the use of rhodium(II) in carbonyl ylide cycloadditions [2] and intramolecular 1,3-dipolar cycloaddition reactions have also appeared [3, 4]. The use of rhodium for the creation and reaction of carbenes as electrophilic species [5, 6], their use in intramolecular carbenoid reactions [7], and the formation of ylides via the reaction with heteroatoms have also been described [8]. Reviews of rhodium(II) ligand-based chemoselectivity [9], rhodium(11)-mediated macrocyclizations [10], and asymmetric rho-dium(II)-carbene transformations [11, 12] detail the multiple aspects of control and applications that make this such a powerful chemical transformation. In addition to these reviews, several books have appeared since around 1998 describing the catalytic reactions of diazo compounds [13], cycloaddition reactions in organic synthesis [14], and synthetic applications of the 1,3-dipolar cycloaddition [15]. 

We also need to describe the rates of multiple-reaction systems. We do this in the same way as for single reactions with each of the i reactions in the set of R reactions being described by a rate r,-, rate coefficient ki, order of the forward reaction with respect to species j, etc. 

For a batch reactor with multiple reactions the mass-balance equation on species j is... 

Most multiple-reaction systems are more comphcated series-parallel sequences with multiple reactants, some species being both reactant and product in different reactions. These simple rules obviously will not work in those situations, and one must usually solve the mass-balance equations to determine the best reactor configuration. 

For conversions with multiple reactions we encounter a problem we have escaped previously. In a multiple-reaction system we need a symbol for the conversion of each reaction and also a symbol for the conversion of each reactant. In Chapter 4 we defined the conversion of a species as Za for reactant A and as Xj for thejth reactant. If we are talking about the conversion of each reaction, we need a symbol such as X for the ith reaction. We should therefore not use Xs for both of these quantities. However, rather than introducing a new variable, we will simply use Xj to specify the conversion of a species and X to indicate the conversion of a reaction. We will not use these quantities enough to make this ambiguity too confusing. 

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