Stoichiometry complex reactions

Quantitative Calculations The stoichiometry of complexation reactions is given by the conservation of electron pairs between the ligand, which is an electron-pair donor, and the metal, which is an electron-pair acceptor (see Section 2C) thus... 

Mole-ratio plots used to determine the stoichiometry of a metal-ligand complexation reaction. 

Graphical determination of the stoichiometry and formation constant for a complexation reaction. 

For a reaction as complex as catalytic enantioselective cyclopropanation with zinc carbenoids, there are many experimental variables that influence the rate, yield and selectivity of the process. From an empirical point of view, it is important to identify the optimal combination of variables that affords the best results. From a mechanistic point of view, a great deal of valuable information can be gleaned from the response of a complex reaction system to changes in, inter alia, stoichiometry, addition order, solvent, temperature etc. Each of these features provides some insight into how the reagents and substrates interact with the catalyst or even what is the true nature of the catalytic species. 

It is possible to obtain fairly reliable values for many complexes of 1 1 (metal ligand) stoichiometry by using an extended empirical equation in which the dielectric constant is dependent on the cationic charge (21). For the complexation reaction ... 

Nickel and palladium react with a number of olefins other than ethylene, to afford a wide range of binary complexes. With styrene (11), Ni atoms react at 77 K to form tris(styrene)Ni(0), a red-brown solid that decomposes at -20 °C. The ability of nickel atoms to coordinate three olefins with a bulky phenyl substituent illustrates that the steric and electronic effects (54,141) responsible for the stability of a tris (planar) coordination are not sufficiently great to preclude formation of a tris complex rather than a bis (olefin) species as the highest-stoichiometry complex. In contrast to the nickel-atom reaction, chromium atoms react (11) with styrene, to form both polystyrene and an intractable material in which chromium is bonded to polystyrene. It would be interesting to ascertain whether such a polymeric material might have any catal3dic activity, in view of the current interest in polymer-sup-ported catalysts (51). 

Factor analysis is a statistical technique that has been used to interpret numerous types of data. Hamer (1989), Rastogi et al. (1990, 1991, 1992), Fotopoulos et al. (1994), and Bonvin and Rippin (1990) have used it successfully for the identification of stoichiometries of complex reactions. The technique is applied to Eqn. (A-1) which are rewritten in matrix form ... 

With a tetramacrocyclic ligand derived from four 1,4,7-triazacyclononane units that are attached to a central benzene ring, each two of the TACN subunits may sandwich one metal ion. Dinuclear, trinuclear, and tetranuclear Ni11 complexes (713)-(715) have been shown to form, depending on the stoichiometry and reaction conditions.1866... 

Several classes of discrete Ni/CS2 compounds have been prepared, usually by reaction of CS2 with Ni° phosphine complexes. Reactions of CS2, C02, and COS with Ni° complexes have been reviewed.2440 Compounds of varying stoichiometry have been obtained, depending on the phosphine used ... 

The second approach (Equation(3)) has a number of advantages over the first one (Equation(2)). The alkyl complexes are more reactive than the related alkoxides, the latter being for group 4 elements generally associated into dimers or trimers 48 also, reaction (2) liberates an alcohol which may further react with the surface of silica, whereas the alkane ( Equation(3)) is inert. It was demonstrated by various spectroscopic techniques and elemental analysis that with a silica dehydroxylated at 500 °C under vacuum, the stoichiometry of reaction (3) corresponds to n = 1.45,46 Moreover, a better control of the surface reaction was achieved with the procedure represented in Equation(3). 

A similar mechanism and stoichiometry underlie reactions of organic compounds with lithium and sodium borohydrides. With modified complex hydrides the stoichiometry depends on the number of hydrogen atoms present in the molecule. 

For the complex reaction with stoichiometry A + 3B 2R + S and with second-order rate expression... 

These rates are the rates of production of species A, B, and C (rj = Vjr) so these rates are written as negative quantities for reactants and positive quantities for products. This notation quickly becomes cumbersome for complex reaction stoichiometry, and the notation is not directly usable for multiple reaction systems. 

This set of relations between reaction orders and stoichiometric coefficients defines what we call an elementary reaction, one whose kinetics are consistent with stoichiometry. We later wiU consider another restriction on an elementary reaction that is frequently used by chemists, namely, that the reaction as written also describes the mechanism by which the process occurs. We will describe complex reactions as a sequence of elementary steps by which we will mean that the molecular collisions among reactant molecules cause chemical transformations to occur in a single step at the molecular level. 

The definitions in the previous section are simple for simple stoichiometry, but they become more comphcated for complex reaction networks. In fact, one frequently does not know the reactions or the kinetics by which reactants decompose and particular product form. The stoichiometric coefficients (the v,y) in the preceding expressions are complicated to write in general, but they are usually easy to figure out for given reaction stoichiometry. Consider the reactions... 

The stoichiometries of reactions 2 to 5 are based on the amounts of reagents used in reaction 1 and all yields are calculated on the basis of the platinum complex used in reaction 1. The complex trans-[PtHCl(PEt3)2] is prepared according to the procedure given in Ref. 11. 

TABLE 16-1 Stoichiometry of Coenzyme Reduction and ATP Formation in the Aerobic Oxidation of Glucose via Glycolysis, the Pyruvate Dehydrogenase Complex Reaction, the Citric Acid Cycle, and Oxidative Phosphorylation... 

Oxidation by dioxygen has a fundamental difficulty. The molecule has a diatomic structure, while in most cases only one atom is needed for selective oxidation of organic compounds. Even in the case of more complex reactions, the stoichiometry of which requires several (and sometimes many) oxygen atoms, the oxidation process on a catalyst surface is likely to proceed step by step, involving consecutively one oxygen atom after another. 

It should be stressed that the coding for the formation of these topologically complex molecules needs to be carefully controlled in order to obtain the desired structures. To illustrate this, consider ligand 7.59, which contains two didentate metal-binding domains. This might be expected to react with octahedral metal ions to give a triple-helical dinuclear complex. Reaction with iron(n) does indeed give a species of stoichiometry [Fe2(7.59)3]4+ however, the crystal structure reveals that an untwisted complex, 7.60, has been formed. 

Another classic example of a complex reaction is the decomposition of N2O5 which shows first order kinetics, but with the first order rate constant decreasing in value as the pressure is lowered. Superficially, this could be taken as evidence of a typical unimolecular decomposition. However, even a first glance at the stoichiometry of the reaction should suggest that it is unlikely that there is a simple one step breakdown of N2O5 into the products. 

Stoichiometry of Reaction. One of the factors that has made this a particularly attractive system for study has been the unambiguous identification and structural characterization of the starting tricoordinate dicopper(I) complex [Cu2(R—XYL—H)]2+ (10, R = H) and the green product... 

C0 = total amounts of 0 and H atoms in the system. It is evident that the equations of type (31) must fit any stoichiometry of complex reactions. 

Reactions that take place in a single step, that is, with a single transition state and no intermediates, are known as elementary reactions. They may represent an entire, kinetically simple reaction or a step in a more complex mechanism. In either case, the rate law for an elementary reaction is derived from its stoichiometry. This stands in contrast with more complex reactions, where the relationship between the overall stoichiometry and the rate law cannot be predicted, and both must be established experimentally. 

Aq,+, = Anywhere D represents the inerts. There is one equation for each component. It is perfectly feasible to retain each of these equations and to solve them simultaneously. Indeed, this is necessary if there is a complex reaction network or if molecular diffusion destroys local stoichiometry. For the current example, the stoichiometry is so simple it may as well be used. At any step j,... 

Chemical species involving molecular units in a repetitive structure to form a polymer are ubiquitous in soils. Multinuclear hydrolytic complexes, such as Al2(OH)2 or Fe2(OH>2, and biopolymers, such as proteins or polysaccharides, come to mind as familiar examples. The complexation reactions of hydrolytic and biological polymers are investigated in much the same way as described in Section 2.1, the principal issues being the characterization of the stoichiometry of the polymers, their metastability as aqueous species, and the effects of the close proximity among their functional groups on their reactivity.20... 

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