Simple stoichiometry

Most of these compounds react readily with available oxygen, including H2O. These compounds have simple stoichiometries, iategral values of x,y, and exhibit conductivities ranging from iasulatiag to metal-like. 

The efficiencies which may be obtained can consequently be calculated by simple stoichiometry from the equilibrium data. In the ease of countercurrent-packed columns, the solute can theoretically be completely extracted, but equilibrium is not always reached because of the poorer contact between the phases. The rate of solute transfer between phases governs the operation, and the analytical treatment of the performance of such equipment follows closely the methods employed for gas absorption. In the ease of two immiscible liquids, the equilibrium concentrations of a third component in each of the two phases are ordinarily related as follows ... 

However, simple stoichiometry often conceals structural complexity as in the many alkali metal tellurides MTe (jc = 1, 1.5, 2.5, 3,... 

Compounds whose molecular compositions are multiples of a simple stoichiometry are polymers, stricdy, only if they are formed by repetition of the simplest unit. However, the name polymerization isomerism is applied rather loosely to cases where the same stoichiometry is retained but where the molecular arrangements are different. The stoichiometry PtCl2(NH3)2 applies to the 3 known compounds, [Pt(NH3)4][PtCU], [Pt(NH3)4][PtCl3(NH3)]2, and [PtCl(NH3)3]2[PtCl4] (in addition to the cis and trans isomers of monomeric [PtCl2(NH3)2]). There are actually 7 known compounds with the stoichiometry Co(NH3)3(N02)3. Again it is clear that considerable differences are to be expected in the chemical properties and in physical properties such as conductivity. 

Oxides of the actinides are refractory materials and, in fact, Th02 has the highest mp (3390°C) of any oxide. They have been extensively studied because of their importance as nuclear fuels. However, they are exceedingly complicated because of the prevalence of polymorphism, nonstoichiometry and intermediate phases. The simple stoichiometries quoted in Table 31.5 should therefore be regarded as idealized compositions. 

Some redox reactions have relatively simple stoichiometry and can be balanced by inspection. Others are much more complicated. Because redox reactions involve the transfer of electrons from one species to another, electrical charges must be considered explicitly when balancing complicated redox equations. 

The oxidation by Co(III) to chlorate in an acidic perchlorate medium has a simple stoichiometry... 

A constant volume batch reactor is used to convert reactant. A, to product, B, via an endothermic reaction, with simple stoichiometry, A —> B. The reaction kinetics are second-order with respect to A, thus... 

The extraction equilibrium in the CUPREX process is dependent on the activity of CU in the feed solutions which in turn is dependent on the stability of chlorometallate complexes [MCIJ2 and [MC1X]3 X for the di- and tri-valent metals present149,150, rather than the simple stoichiometry represented by the equation shown in Figure 6.151,152... 

Step 3 Calculate the theoretical yield of product in grams or moles, based on the limiting reactant using simple stoichiometry. 

Comparison shows that,in the case of the 02-pulse, co-production of C02 and C2Hi,0 was observed whereas withN20, C02 was mainly formed. One can roughly estimate the total amount of each oxygen species,taken up by the catalyst surface from each pulse, by the application of simple stoichiometry to the amount of the produced C02 and C2Hi,0 and an intermediate (In) in the complete oxidation. Here the existence of the intermediate (In) was demonstrated in our previous papers (jy l ). The amount of (In) is obtained from the amount of C02 formed by the decomposition of it in an 02-He stream (see Run 2 in Figs.7 and 8). In addition it is assumed that (In) keeps the carbon-carbon bond and retains four atomic oxygen (1J0. Fig. 

Searching for other oscillatory autoxidation reactions led Druliner and Wasserman to use cyclohexanone as a substrate instead of benzalde-hyde (168). Unlike the simple stoichiometry found for the benzaldehyde reaction, the ketone gives at least six or more products, and the relative amounts of these vary substantially with the experimental conditions (Scheme 7). 

The sulfuric acid that is generated on the moist sewer surfaces may react with the alkaline cement in the concrete. A simple stoichiometry of this reaction is given by the following expression ... 

However, if reaction is not of a simple stoichiometry but involves different number of moles of reactants or products, the rate should be divided by corresponding stoichiometric coefficient in the balanced chemical equation for normalizing it and making it comparable. For example, for a general reaction aA + bB — cC + dD... 

It is clear that many reactions, particularly those without simple stoichiometry, will have mechanisms containing several steps, one or more of which may include reversible equilibria (consider for example (1.118) to (1.120)). The number of separate terms in the rate law will indicate the number of paths by which the reaction may proceed, the relative importance of which will vary with the conditions. The complex multiterm rate laws, although tedious to characterize, give the most information on the detailed mechanism. 

The simple stoichiometry in (8.72) belies simple kinetics. The dynamics are... 

These relations assume that there is no B or C in the feed, Cbo Cco 0- With this simple stoichiometry the definitions become simpler compared to more complex sets of reactions. 

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... 

As is well known, simple stoichiometry of a compound is not a good guide to the coordination number of the central atom. This is well shown in (BiCl3)3-7tu (tu = thiourea), where bismuth is octahedrally coordinated to thiourea via the sulfur atom.240 The structure was found to consist of bismuth cations and anions, [Bi2Cl4tu6]2+[BiCl5tu]2- (82). 

Even compounds with deceptively simple stoichiometries may be more complex, as in the case of XcF -. sF which has both bridged canons, ind anions. 

In applying a rate equation to a situation where the volume of a given reaction mixture (i.e. the density) remains constant throughout the reaction, the treatment is very much simplified if the equation is expressed in terms of a variable X, which is defined as the number of moles of a particular reactant transformed per unit volume of reaction mixture (e.g. Cao Ca) at any instant of time t. The quantity X is very similar to a molar concentration and has the same units. By simple stoichiometry, the moles of the other reactants transformed and products generated can also be expressed in terms of x, and the rate of the reaction can be expressed as the rate of increase in X with time. Thus, by definition,... 

Anionic clusters are good nucleophiles (see Section III,A) and are often easy to make. On the other hand, the electrophilic nature of most monometallic complexes is obvious from ligand substitutions. The combination of these properties makes a strategy for cluster expansion. This strategy was used for the first time by Hieber (130) in making Fe4(CO)fc from Fe3(CO),7 and Fe(CO)s. It is probably active in many syntheses of large metal carbonyl clusters because the Re, Os, Rh, Ir, Ni, and Pt clusters involved are almost always anionic. However, simple stoichiometries can rarely be written for such reactions (122). This route makes mixed metal clusters accessible, e.g.,... 

In a subsequent paper, the action of mercuric salts on allylgermanium compounds was described. Solvents acetonitrile and ethanol were used, and the simple stoichiometry (13) (R = H, Me) found to obtain3. 

Expressing the Rate in Terms of Reactants or Products for Non-simple Stoichiometry... 

Since HC1 and NaOH are completely dissociated in dilute solutions, and the reaction goes to completion, this is really a simple stoichiometry problem in which we convert the HsO+ concentration to pH. If the initial... 

Similar to other binary /(-p-clcment systems, the formation of binary rare earth - antimonides with a simple stoichiometry is a characteristic feature of these systems. The largest number of structure types formed was encountered for the group of RSb2 compounds (4 members). The polymorphic modifications were observed for GdSb2 and TbSb2 as well as the RSb (R = La, Ce) and RsSb (R = Yb, Y and Sc) compounds were noted to undergo the solid state transformations. 

All these annihilation signals share the property of being proportional to the square of the neutralino density. This follows from the fact that the neutralino is a Majorana fermion, i.e. is identical to its antiparticle. Two neutralinos can annihilate to produce standard model particles. Simple stoichiometry then tells us that the annihilation rate, being proportional to the product of the densities of the initial particles, is proportional to the square of the neutralino density. In more detail, we have... 

Hydrides, nitride and carbides are known for some of the elements. Some have simple stoichiometry and structure, such as TiN and TiC with the rock salt structure. Many are non-stoichiometric with metallic properties, and some can be regarded as interstitial compounds with the non-metal atom occupying sites between metallic atoms in the normal elemental structure. 

A complex network of reactions is hidden behind the simple stoichiometry of -butane oxidation (Equation 35). Butene, butadiene and furan have been suggested to be intermediates in a cascade of reactions eventually producing the anhydride. Carboxylic acids and carbon oxides are formed in parallel and consecutive oxidations. 

Let us take as a simple example the following set of first-order chemical reactions of simple stoichiometry ... 

The simple stoichiometry of the salts often obscmes the complexity found in many polytellurides, the stractures of which find few analogs in lighter chalcogen congeners sulfur and selenium. Spirocyclic Tev and Tes both show a square-planar tellurium atom (see Figure 7(a) and (b)). A similar motif is found in Rb2Tes that exhibits a continuous... 

In superchlorination, breakpoint reactions like Eqs. (17.37) to (17.42) will transpire. A host of other reactions may also occur such that all these, as shown by the preceding reactions, produce acids. The number of reactions are many, therefore, it is not possible to predict the amount of acids produced by using simple stoichiometry. The only way to determine this amount is to run ajar test as is done in the determination of the optimum alum dose. Metcalf Eddy, Inc. wrote that in practice it is found that 15.0 mg/L of alkalinity is needed per mg/L of ammonia nitrogen (Metcalf Eddy, Inc., 1972). But, again, the best method would be to run the jar test. 

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