Stoichiometry from formulas

Until this point, a molecule has been formally described from a set of N nodes (nuclei) by three features only a labelling (composition stoichiometry, bruto formula), a topology (connection bonding skeleton), and a topography (constitution Lewis stmctures, resulting from the application of the labelling on the topology). 

As can be seen from equation 8.14, we may improve a method s sensitivity in two ways. The most obvious way is to increase the ratio of the precipitate s molar mass to that of the analyte. In other words, it is desirable to form a precipitate with as large a formula weight as possible. A less obvious way to improve the calibration sensitivity is indicated by the term of 1/2 in equation 8.14, which accounts for the stoichiometry between the analyte and precipitate. Sensitivity also may be improved by forming precipitates containing fewer units of the analyte. 

The familiar problem of misleading stoichiometries, and the frequent impossibility of deducing the correct structural formula from the empirical composition is well illustrated by the... 

The only crystalline phase which has been isolated has the formula Pu2(OH)2(SO )3(HaO). The appearance of this phase is quite remarkable because under similar conditions the other actinides which have been examined form phases of different composition (M(OH)2SOit, M=Th,U,Np). Thus, plutonium apparently lies at that point in the actinide series where the actinide contraction influences the chemistry such that elements in identical oxidation states will behave differently. The chemistry of plutonium in this system resembles that of zirconium and hafnium more than that of the lighter tetravalent actinides. Structural studies do reveal a common feature among the various hydroxysulfate compounds, however, i.e., the existence of double hydroxide bridges between metal atoms. This structural feature persists from zirconium through plutonium for compounds of stoichiometry M(OH)2SOit to M2 (OH) 2 (S0O 3 (H20) i,. Spectroscopic studies show similarities between Pu2 (OH) 2 (SOO 3 (H20) i, and the Pu(IV) polymer and suggest that common structural features may be present. 

Complex ions, also called coordination complexes, have well-defined stoichiometries and structural arrangements. Usually, the formula of a coordination complex is enclosed in brackets to show that the metal and all its ligands form a single structural entity. When an ionic coordination complex is isolated from aqueous solution, the product is composed of the complex ion and enough counter-ions to give a neutral salt. In the chemical formula, the counter-ions are shown outside the brackets. Examples include the sulfate salt of [Ni (NH3)g, ... 

Pyromellitate, the tetracarboxylate of benzene, forms red crystals of formula [Co2(C6H2 (C00)4)4]-18H20 from aqueous silica gel, and feature infinite chain-like polyanions with [Co(OH2)4[C6H2(COO)4)]2]ra2" stoichiometry where Co is in an octahedral environment of four waters and two traras-disposed carboxylates.436... 

Depending on the fabrication techniques and deposition parameters, the pH sensitive slope of IrOx electrodes varies from near-Nemstian (about 59 mV/pH) to super-Nemstian (about 70mV/pH or higher). Since the compounds in the oxide layers are possibly mixed in stoichiometry and oxidation states, most reported iridium oxide reactions use x, y in the chemical formulas, such as lr203 xH20 and IrOx(OH)y. Such mixed oxidation states in IrOx compounds may induce more H+ ion transfer per electron, which has been attributed to causing super-Nerstian pH responses [41],... 

New formulas, new stoichiometries, new structures, new reactants, new reducing agents, new oxidizing agents, and new areas of chemical research will result from the studies of chemical reactions in low-temperature matrices. 

Evidently, the most interesting materials are those in a fractional oxidation state, with general formula (cation)[M(dmit)2] (n > 1), since they can exhibit both electrical and magnetic properties. Only eight such complexes have been reported so far. All of them but (BDTA)[Ni(dmit)2]2 [89] have been obtained as powders. They have in general been poorly characterized, and their stoichiometries have been determined from elemental analysis. Among these powdered compounds, the... 

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). 

In cases where the antisite defects are balanced, such as a Ga atom on an As site balanced by an As atom on a Ga site, the composition of the compound is unaltered. In cases where this is not so, the composition of the material will drift away from the stoichiometric formula unless a population of compensating defects is also present. For example, the alloy FeAl contains antisite defects consisting of iron atoms on aluminum sites without a balancing population of aluminum atoms on iron sites. The composition will be iron rich unless compensating defects such as A1 interstitials or Fe vacancies are also present in numbers sufficient to restore the stoichiometry. Experiments show that iron vacancies (VFe) are the compensating defects when the composition is maintained at FeAl. 

There are over 100 different platinum group minerals. Some of the most common PGM are shown in Table 18.1. The stoichiometry of most of the PGM named [1] is known, but because these minerals are subject to a wide range of element substitution, as indicated in Table 18.1, there is little consistency between an ideal formula for the individual minerals and compositions of the given minerals from various locations. 

Complexes of TSO with lanthanide perchlorates which have the formula Ln(TS0)9(C104)3 have been reported by Edwards et al. (266) (Ln = Ce or Y). Later, Vicentini and Perrier (267) have prepared the whole series of complexes of TSO with lanthanide perchlorates and have shown that the L M in these complexes gradually decreases from 9 1 to 7 1 as the cationic size decreases. These authors could not prepare Y(TS0)g(C104)3 reported by Edwards et al. (266). Instead, they obtained the complex of the composition Y(TS0)7(C104)3. Two series of complexes of TSO with lanthanide hexafluorophosphates are known (268, 269). While the L M in one of the series is 7.5 1, in the other series it is found to be 8 1. The change in the stoichiometry of the two series of compounds is attributed to the preparative procedures adopted. In both the series of complexes, the PFg ion remains ionic. Lanthanide nitrates (270), chlorides (270), and isothiocyanates (271) also yield complexes with TSO. In all these complexes, changes in the stoichiometry could be observed when the lanthanide series was traversed. In all these complexes the anions are coordinated to the metal ion. 

In the constitutional model of Ugi, rather than molecules, "ensemble of molecules (EM) are used in which the molecules can be either chemically different or identical. Like molecules, an EM has an empirical formula, which is the sum of the empirical formulae of the constiment molecules and describes the collection A of atoms within the EM under consideration. All the EM s which can be formed from A have the same empirical formula . Therefore, an EM(A) consists of one or more molecules which can be obtained from A using each atom which belongs to A only once. Moreover, a FIEM(A) or a family of isomeric EM, is the collection of all EM(A) and it is determined by the empirical formula . On the other hand, a chemical reaction, or a sequence of chemical reactions, is the conversion of an EM into an isomeric EM, and therefore a FIEM contains all EMs which are chemically interconvertible, as far as stoichiometry is concerned. In summary, a FIEM(A) contains, at least in principle, the whole chemistry of the collection A of atoms and since any collection of atoms may be chosen here, Ugi concludes that a theory of FIEM is, in fact, a theory of all chemistry. 

In magnesia-stabilised / "-alumina, the formula is Na, (Mg2 Al5 (08 and X is essentially fixed at 0.175. An alternative way of representing it is in terms of a derivation from the stoichiometry NaAlnOi, with the formula Nai+2Mg2Aln jOi7. Various values of 2 are quoted in the literature, between 0.5 and 0.8. The value 0.747 which is in this range coincides with that obtained using the alternative, spinel-like formula given above, with x = 0.175. 

In both P- and j9"-alumina, the conduction planes contain a nonintegral number of Na ions and there are considerably more sites available than Na ions to fill them. The structures are often described in terms of the supposedly ideal 1 11 stoichiometry with the formula NaAliiOi7. In such a case, of the three out of four oxide ions that are missing from the conduction planes, only one half of their vacant sites would contain a Na ion, as indicated schematically in Fig. 2.10. In practice, excess Na" ions are almost always present (e.g. ion A in Fig. 2.1(c)) but rarely in suflBcient quantities to fill all the available vacancies this then gives rise to the high carrier concentrations in these phases. 

Samples 6 and 7 in table 5.32 are from the Zabargad peridotite (Red Sea) and are representative of the chemistry of upper mantle pyroxenes (Bonatti et al., 1986). The absence of Fe203 in these samples is due to the fact that microprobe analyses do not discriminate the oxidation state of iron, which is thus always expressed as FeO. It must be noted here that the observed stoichiometry (based on four oxygen ions) is quite consistent with the theoretical formula and that no Fe is required to balance the negative charges of oxygen. 

To overcome this problem an extension of the sublattice model was proposed by Hillert et al. (1985) which is now known as the ionic two-sublattice model for liquids. As in the previous case it uses constituent fractions as composition variables, but it also considers that vacancies, with a charge corresponding to the charge of the cations, can be introduced on the anion sublattice so that the composition can move away from the ideal stoichiometry and approach an element with an electropositive character. The necessary neutral species of an electronegative element are added to the anion sublattice in order to allow the composition to approach a pure element. The sublattice formula for the model can then be written as... 

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