Nonstoichiometric method

In 10.3 we introduce two fundamental approaches to reaction equilibrium calculations the traditional stoichiometric method and a nonstoichiometric method, which is useful when many reactions are occurring and when products and reactants are known but the reactions are unknown. In setting up both kinds of calculations, we must again confront issues related to standard states, and we must select appropriate computational forms. These issues are discussed in 10.4 for reacting systems. 

How do we use the nonstoichiometric method to set up equations for computing the equilibrium composition at the completion of a single reaction ... 

The typical reaction-equilibrium problem is to determine the equilibrium composition when species are allowed to react under specified conditions. In previous sections we have addressed various aspects of such problems now we summarize the computational forms usually used in solving them. Common forms used for the stoichiometric method are presented here those for the nonstoichiometric method are presented in 10.4.5. 

In this nonstoichiometric method, part of the solution is the set of values for the Lagrange multipliers In most situations these multipliers have little physical significance they merely serve to ensure conservation of atoms, so their values are a necessary but nonphysical by-product of the calculation. When the number of elements Mg is less than the number of species C, the C equations (10.4.35) could be combined to eliminate the nig multipliers X, so their values would not obtained explicitly. However, if such a combination is done, the result is equivalent to the stoichiometric expression for the equilibrium constant, and the computational advantages of the nonstoichiometric method are lost. 

Note that in the nonstoichiometric approach, we do not obtain values for stoichiometric coefficients and we have no parameters, such as the extent that track the progress of individual reactions. Moreover, the computational forms (10.4.32)-(10.4.35) contain no quantities that are specific to a particular reaction (e.g., no subscripts appear). So although the nonstoichiometric equations (10.4.32)-(10.4.35) were derived with one reaction in mind, they actually apply to situations involving any number of reactions. In fact, we can use the nonstoichiometric method without knowing how many reactions are occurring or even what those reactions might be we only need a complete identification of all reactants and products. This constitutes a principal advantage of the nonstoichiometric development. 

In contrast, the nonstoichiometric approach is generally better for complicated situations involving many reactions, including those many situations, such as combustion and biological processes, in which all reactions caimot be explicitly identified. This method involves many fewer preparatory steps no stoichiometric coefficients need be computed, no reactions are identified or balanced, and no equilibrium constants are evaluated. The principal price paid for this convenience is the larger number of equations to be solved. But, even though the nonstoichiometric method produces more equations than the stoichiometric method, the nonstoichiometric development is more systematic and its general form can often be more readily implemented on a computer. 

For reaction-equilibrium computations, we have discussed only stoichiometric methods, in which the elemental balances are imposed explicitly through F sets of stoichiometric coefficients. For one-phase systems, these formulations require us to solve only F algebraic equations for F extents of reaction therefore, they require us to identify F independent reactions. Such stoichiometric methods appear to be most effective when the number of species C is not much greater than the number of elements (C nig). Otherwise, when C m, nonstoichiometric methods may be more computationally efficient [16,18], though this comment probably depends on the particular algorithms being compared. 

Detailed specification of aU the chemical reactions and species involved in the model Nonstoichiometric method... 

Various preparative methods are adopted at nonstoichiometric formulations, incomplete dehydration or using oxide additives to obtain boron phosphate of varying purity for its catalytic applications. The compound also forms hydrates (tri- tetra-, penta-, and hexahydrates) which readily decompose in water to phosphoric acid and boric acid. 

Manes, L. A new method of statistical thermodynamics and its application to oxides of the lanthanide and actinide series, in Nonstoichiometric oxides (Sprensen, O. T. ed.). Academic Press, New York, Chapt. 3, 99 (1981)... 

For any heterotype solid solution, or a nonstoichiometric compound, EDX analysis in the AEM on a large number of crystals is required. In a typical laboratory situation 30 to 40 crystals are routinely analyzed for each preparation. This sampling is adequate to establish trends in stoichiometric variations in a heterogeneous material. Fine gradations in compositions of a seemingly phase-pure material by the criterion of bulk diffraction techniques, can also be revealed. For quantitative microanalysis, a ratio method for thin crystals (16) is used, given by the equation ... 

Nonstoichiometric composition producing impurity levels can arise in two ways, either (1) excess atoms in interstitial positions or (2) holes in the lattice. Both methods [(1) and (2)] are theoretically possible in n- and p-type semiconductors. 

A comparable spectrum of polycrystalline nickel that was taken with an ISS by Goff and Smith (19) (Figure 3) shows the presence of carbon and oxygen on the surface, resulting from adsorbed hydrocarbons, CO, or possibly nonstoichiometric NiOx, as indicated by the other methods. 

The basis of most of these methods is comparative in nature, that is, results are compared to known pure compounds. The inference is that if the catalyst resembles some property of the known compound, then that compound is present in the catalyst. However, caution must be exercised in this interpretation because we may be dealing with indefinite and nonstoichiometric surface complexes which may have some properties in... 

Although the electrochemical method is widely employed for producing monocrystalline nonstoichiometric salts, it does have some disadvantages, such as long reaction times (up to several weeks) and drastic limitations imposed on the solvents and the amount of the target product (a few milligrams). In contrast, the chemical approach does not suffer from these restrictions and can theoretically afford unlimited quantities of materials. 

To prove the above statement on the determining effect of electric charge of both the CdS colloidal particle surface and the quencher molecule on the adsorption of these molecules from aqueous solution, we have modified the surface of colloidal CdS during its preparation. The most efficient method of such modification consists in changing the surface charge of the colloidal particle via the preparation of nonstoichiometric colloid. In this case, the surface charge is determined by the charge of excessive ion (either S 2 or Cd2+). 

Ying, X Y., and Tschope, A., Gas phase synthesis of nonstoichiometric nanocrystalline catalysts, in Advanced Catalysts and Nanostructured Materials Modern Synthetic Methods (W. R. Moser, Ed.), p. 231, Academic Press, San Diego (1996). 

Abstract. Nanopowders of nonstoichiometric tungsten oxides were synthesized by method of electric explosion of conductors (EEC). Their electronic and atomic structures were explored by XPS and TEM methods. It was determined that mean size of nanoparticles is d=10-35 nm, their composition corresponds to protonated nonstoichiometric hydrous tungsten oxide W02.9i (OH)o.o9, there is crystalline hydrate phase on the nanoparticles surface. After anneal a content of OH-groups on the surface of nonstoichiometric samples is higher than on the stoichiometric ones. High sensitivity of the hydrogen sensor based on WO2.9r(OH)0.09 at 293 K can be connected with forming of proton conductivity mechanism. 

In the work an electronic structure of nanoparticles of nonstoichiometric oxide WO, was investigated by XPS-method at room and work temperatures. Hydrogen sensor based on these nanoparticles showed a good sensitivity at room temperature. 

Abstract. The interaction of hydrogen with nonstoichiometric Tio.9Zro.iMnL3Vo.5 Laves phase compound at pressure up to 60 atm and in temperature range from 150 to 190°C has been studied by means of calorimetric and P-X isotherm methods. The obtained results allow us to propose the existence of one hydride phase, 0-hydride, in the Ti0 9Zr0 jMnj 3V0 5 - H2 system in the temperature range 150-170°C. It has been found that temperature 190°C is close to critical temperature (182°C) above which hydride phases does not exist. 

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