Stoichiometry and Reaction Coordinates

The reactor design equations in this book can be applied to all components in the system, even inerts. When the reaction rates are formulated using Equation 2.8, the solutions automatically account for the stoichiometry of the reaction. This is the simplest and preferred approach, but it has not always been followed in this book. Several examples have ignored product concentrations when they do not affect reactions rates and when they are easily found from the amount of reactants consumed. Also, some of the analytical solutions have used stoichiometry to ease the algebra. The present section formalizes the use of stoichiometric constraints. We begin with a matrix formulation for the reaction rates of the components in multiple reactions. The presentation is rather elegant from a mathematical viewpoint and does have some practical utility. 

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SnCU is effective in promoting the addition of nucleophiles to simple aldehydes. Among the most synthetically useful additions are allylstannane and -silane additions. The product distribution in the stannane reactions can be influenced by the order of addition, stoichiometry, and reaction temperature. The anti geometry of the tin-aldehyde complex is favored because of steric interactions. Furthermore, the six-coordinate 2 1 complex is most probably the reactive intermediate in these systems. The use of crotylstaimanes provides evidence for competing transmetalation pathways (Eq. 35) [60]. TiCU results in superior selectivity. 

The second use of Equations (2.36) is to eliminate some of the composition variables from rate expressions. For example, 0i-A(a,b) can be converted to i A a) if Equation (2.36) can be applied to each and every point in the reactor. Reactors for which this is possible are said to preserve local stoichiometry. This does not apply to real reactors if there are internal mixing or separation processes, such as molecular diffusion, that distinguish between types of molecules. Neither does it apply to multiple reactions, although this restriction can be relaxed through use of the reaction coordinate method described in the next section. 

In the general case of a piston flow reactor, one must solve a fairly small set of simultaneous, ordinary differential equations. The minimum set (of one) arises for a single, isothermal reaction. In principle, one extra equation must be added for each additional reaction. In practice, numerical solutions are somewhat easier to implement if a separate equation is written for each reactive component. This ensures that the stoichiometry is correct and keeps the physics and chemistry of the problem rather more transparent than when the reaction coordinate method is used to obtain the smallest possible set of differential... 

The first tt complexes of 1,3-diynes were reported by Greenfield. Shortly thereafter, Tilney-Bassett described the first heterometallic derivatives. This area has grown steadily since these initial reports and many complexes of this type are now known. Diyne complexes are often simply alkyne-substituted analogues of conventional jr-alkyne complexes. Indeed, transition metal compounds that form -complexes with mono-alkynes can be expected to form complexes with diynes. However, the thermal sensitivity of terminal diynes, especially 1,3-butadiyne, may limit the application of routine reaction conditions in some cases. Further coordination of the ynyl ligand by additional metal fragments is usually determined by the reagent stoichiometry and by steric effects. 

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. 

A further example of the use of this route to phospholyl complexes is given by Mathey <1996AGE1125>. Here, the P-P bonds of the macrocyclic tetraphosphole 230 are cleaved by elemental Na or K in a coordinating solvent (1,2-dimethoxyethane, DME) to afford new 2,2 -biphospholyl complexes. The exact composition of the product obtained is intimately linked to the nature of the metal and reaction stoichiometry (Scheme 103). With sodium a complex 301 is obtained in which just one of the P-P bonds has been ruptured, and the phospholyl moieties are bound in both an... 

The apparent contradiction between the empirical stoichiometry and the spectral characteristics of these new uranyl complexes was finally resolved by X-ray crystallography. Specifically, a single crystal X-ray structural analysis of the blue-black material formed from the reaction of the anhydrous uranyl chloride and o-dicyanobenzene [112] (Figures 22 and 23) revealed that the complex obtained was in fact an expanded five-subunit superphthalocyanine macrocycle in which a pentagonal bipyramidal coordination geometry pertains about the centrally-bound uranium atom. 

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