Stoichiometry, variable

The less common lead oxides, Pb203 and Pb02, exhibit non-stoichiometry (variable oxygen content). 

The shift in the voltammogram for a metal ion in the presence of a ligand may be used to determine both the metal-ligand complex s stoichiometry and its formation constant. To derive a relationship between the relevant variables we begin with two equations the Nernst equation for the reduction of O... 

Sulfides are intermixed with iron oxides and hydroxides on carbon steels and cast irons. The oxides are also produced in the corrosion process (Reaction 6.6). Although theoretical stoichiometry of 1 to 3 is often suggested between sulfide and ferrous hydroxide, empirically the ratio of iron sulfide to ferrous hydroxide is highly variable. Sulfide decomposes spontaneously upon exposure to moist air. Additionally, corrosion-product stratification is marked, with sulfide concentration being highest near metal surfaces. 

Similar results are obtained for dre deposition of the carbides of these metals using methane as a source of carbon, atrd silicon tetrahalides for the preparation of silicides. These reactions are more complex than dre preparation of the diborides because of the number of carbides atrd silicides that the tratrsition metals form, some of which have wide ranges of non-stoichiometry. The control of the ratio of the partial pressures of dre ingoing gases is therefore important as a process variable. 

For symbolic convenience we make use of the reaction variable x, which is the decrease in concentration of reactant A in time t. Because of the reaction stoichiometry, X is also the decrease in B concentration. The mass balance expressions are... 

Transition elements, for which variable valency is energetically feasible, frequently show non-stoichiometric behaviour (variable composition) in their oxides, sulfides and related binary compounds. For small deviations from stoichiometry a thermodynamic approach is instructive, but for larger deviations structural considerations supervene, and the possibility of thermodynamically unstable but kinetically isolable phases must be considered. These ideas will be expanded in the following paragraphs but more detailed treatment must be sought elsewhere. " ... 

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. 

Schemes II and III can be solved only if [I] can be approximated at the steady-state value. If that approximation is not valid, then neither [A], nor [P], has a closed-form solution. Schemes II and III have a fixed stoichiometry, this being 2A = P for Scheme II and A + B = P + Q for Scheme III. Scheme I, on the other hand, has a variable stoichiometry, intermediate between the extremes A = P (when it fe tB]) and A + B = Q (when k k2[B]).

The stoichiometry of the redox reactions of conducting polymers (n and m in reactions 1 and 2) is quite variable. Under the most widely used conditions, polypyrroles and polythiophenes can be reversibly oxidized to a level of one hole per ca. 3 monomer units (i.e., a degree of oxidation, n, of ca. 0.3).7 However, this limit is dictated by the stability of the oxidized film under the conditions employed (Section V). With particularly dry and unreactive solvents, degrees of oxidation of 0.5 can be reversibly attained,37 and for poly-(4,4 -dimethoxybithiophene), a value of n = 1 has been reported.38 Although much fewer data are available for n-doping, it appears to involve similar stoichiometries [i.e., m in Eq. (2) is typically ca. 0.3].34,39"41 Polyanilines can in principle be reversibly p-doped to one... 

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. 

Solution This is a variable-velocity problem with u changing because of the reaction stoichiometry and the pressure drop. The flux marching equations for the various components are... 

The stoichiometry of transition metal oxides is more variable. Iron, for example, forms three binary oxides. In FeO the iron atoms have lost two electrons each (Fe, O ), and in Fc2 O3 they have lost three electrons each... 

An expansion of the solution TMP approach involves a cothermolytic strategy, whereby two or more molecular species that thermally convert to materials under mild heating are converted simultaneously in the same solution [83,128-130]. This cothermolysis method allows the composition of the final material to be tuned to variable stoichiometries, and has proven useful in the generation of catalytic materials where even small variations in elemental content can lead to dramatic performance changes. The remainder of this section serves to provide examples of the materials that can be formed via simple solid phase or solution TMP routes. 

Enynes are also especially effective in regioselective couplings, and the ligand structure and stoichiometry were both found to be important variables (Scheme 14) [31]. A model was proposed involving stereospecific ligand sub-... 

The electroneutrality condition decreases the number of independent variables in the system by one these variables correspond to components whose concentration can be varied independently. In general, however, a number of further conditions must be maintained (e.g. stoichiometry and the dissociation equilibrium condition). In addition, because of the electroneutrality condition, the contributions of the anion and cation to a number of solution properties of the electrolyte cannot be separated (e.g. electrical conductivity, diffusion coefficient and decrease in vapour pressure) without assumptions about individual particles. Consequently, mean values have been defined for a number of cases. 

Another possibility for the plasma device is the generation of N02 for the enhancement of NH3-SCR at low temperature, (the so-called fast SCR reaction) which occurs if there is a 1 1 N0 N02 stoichiometry over V-Ti02 type catalysts and with variable stoichiometry over Fe-beta zeolite. Being able to switch on and tune N02 production over a limited temperature range will help to avoid N02 slip issues, that can be an issue for oxidation catalysts. Also, if tuned correctly, plasma can do the NO oxidation without in turn doing S02 oxidation and so generate N02 without making sulphates (and associated particulates). 

At least for ethylene hydrogenation, catalysis appears to be simpler over oxides than over metals. Even if we were to assume that Eqs. (1) and (2) told the whole story, this would be true. In these terms over oxides the hydrocarbon surface species in the addition of deuterium to ethylene would be limited to C2H4 and C2H4D, whereas over metals a multiplicity of species of the form CzH D and CsHs-jD, would be expected. Adsorption (18) and IR studies (19) reveal that even with ethylene alone, metals are complex. When a metal surface is exposed to ethylene, selfhydrogenation and dimerization occur. These are surface reactions, not catalysis in other words, the extent of these reactions is determined by the amount of surface available as a reactant. The over-all result is that a metal surface exposed to an olefin forms a variety of carbonaceous species of variable stoichiometry. The presence of this variety of relatively inert species confounds attempts to use physical techniques such as IR to char-... 

One way to reduce the number of independent variables in the FRET-adjusted spectral equation is to use samples with a fixed donor-to-acceptor ratio. Under these conditions, the values of d and a are no longer independent, but rather the concentration of d is now a function of a and vice-versa. This approach is typical for the situation of FRET-based biosensor constructs. These sensors normally are designed to have a donor fluorophore attached to an acceptor by a domain whose structure is altered either as a result of a biological activity (such as proteolysis or phosphorylation), or by its interaction with a specific ligand with which it has high affinity. In general, FRET based biosensors have a stoichiometry of one... 

Widespread medicinal use of colloidal bismuth subcitrate (CBS) has prompted extensive studies of bismuth compounds involving the citrate anion. Bismuth citrate is essentially insoluble in water, but a dramatic increase in solubility with increasing pH has been exploited as a bio-ready source of soluble bismuth, a material referred to as CBS. Formulation of these solutions is complicated by the variability of the bismuth anion stoichiometry, the presence of potassium and/ or ammonium cations, the susceptibility of bismuth to oxygenation to Bi=0, and the incorporation of water in isolated solids. Consequently, a variety of formulas are classified in the literature as CBS. Solids isolated from various, often ill-defined combinations of bismuth citrate, citric acid, potassium hydroxide, or ammonium hydroxide have been assigned formulas on the basis of elemental analysis data or by determination of water and ammonia content, but are of low significance in the absence of complementary data other than thermal analysis (163), infrared spectroscopy (163), or NMR spectroscopy (164). In this context, the Merck index lists the chemical formula of CBS as KgfNHJaBieOafOHMCeHsCbh in the 11th edition (165), but in the most recent edition provides a less precise name, tripotassium dicitrato bismuthate (166). 

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