Stoichiometric definition

The (molar) notion of pure substance has an important function in providing anchoring points in chemical space, but (homogeneous) solutions and (quasi-homogeneous) conglomerates are also substances. A strict separation between stoichiometric and non-stoichiometric definite compounds, as well as that between compounds and solutions, should not be insisted upon. Strictly speaking there are only impure substances and pure substance is an ideal-limit-concept. In practice mixed or impure phases (Aristotle s mixts) may be the preferred stuff. 

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). 

Because the metal structure is locked by these atoms, the resulting compound is often much harder than the original metal, and some of the compounds are therefore of industrial importance (see under iron). Since there is a definite ratio of holes to atoms, filling of all the holes yields compounds with definite small atom-metal atom ratios in practice, all the holes are not always filled, and compounds of less definite composition non-stoichiometric compounds) are formed. 

Normality makes use of the chemical equivalent, which is the amount of one chemical species reacting stoichiometrically with another chemical species. Note that this definition makes an equivalent, and thus normality, a function of the chemical reaction in which the species participates. Although a solution of 1T2S04 has a fixed molarity, its normality depends on how it reacts. 

The chemical reactions that occnr in flames transform an initial reactant mixtnre into final reaction prodncts. In the case of fnel-oxygen combns-tion, the final prodncts are principally water vapor and carbon dioxide, althongh nnmerons other prodncts snch as carbon monoxide may be formed, depending on the reactant composition and other factors. If the ratio of fnel-to-oxygen is stoichiometric, the final reaction prodncts, by definition, contain no excess fnel or oxygen. Theoretically, this means that partial oxidation prodncts snch as CO (itself a fnel) are not formed. In reality, partial oxidation prodncts snch as CO or OH are formed by high tem-peratnre reactions. For example, the molar stoichiometric reaction of methane is written ... 

Obviously dc dt = 2 dcpjtk), because for each molecule of A that reacts, two molecules of B react, so it is necessary to include the stoichiometric coefficient or at least to specify clearly what definition of rate is being used. 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

For definiteness, the oxidation of copper to copper(l) oxide may be considered. Our picture of the process is that cation vacancies and positive holes formed at the Cu O/Oj interface by equation, 1.166 are transported to the Cu/CujO interface where they are destroyed by copper dissolving in the non-stoichiometric oxide. We require an expression for the rate of oxidation. 

The respiratory quotient (RQ) is often used to estimate metabolic stoichiometry. Using quasi-steady-state and by definition of RQ, develop a system of two linear equations with two unknowns by solving a matrix under the following conditions the coefficient of the matrix with yeast growth (y = 4.14), ammonia (yN = 0) and glucose (ys = 4.0), where the evolution of C02 and biosynthesis are very small (o- = 0.095). Calculate the stoichiometric coefficient for RQ =1.0 for the above biological processes ... 

The careful worker explicitly states the usage chosen for v. This choice defines the rate constant, which may otherwise be uncertain by a small numerical factor. When the definition is obvious, as in a reaction in which all the stoichiometric coefficients are unity, the definition of the numerical factor can be omitted. 

The negative ion concentrations all show very definite maxima on the fuel-rich side of stoichiometric flame composition. 

This definition for reaction order is directly meaningful only for irreversible or forward reactions that have rate expressions in the form of Equation (1.20). Components A, B,... are consumed by the reaction and have negative stoichiometric coefficients so that m = —va, n = —vb,. .. are positive. For elementary reactions, m and n must be integers of 2 or less and must sum to 2 or less. 

An ordered distribution of spheres of different sizes always allows a better filling of space the atoms are closer together, and the attractive bonding forces become more effective. As for the structures of other types of compound, we observe the validity of the principle of the most efficient filling of space. A definite order of atoms requires a definite chemical composition. Therefore, metal atoms having different radii preferentially will combine in the solid state with a definite stoichiometric ratio they will form an inter-metallic compound. 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

The reaction rate is properly defined in terms of the time derivative of the extent of reaction. It is necessary to define k in a similar fashion in order to ensure uniqueness. Definitions in terms of the various rt would lead to rate constants that would differ by ratios of their stoichiometric coefficients. 

Definitions for the variables and constants appearing in eqns. 1 and 2 are given in the nomenclature section at the end of this paper. The first of these equations represents a mass balance around the reactor, assuming that it operates in a differential manner. The second equation is a species balance written for the catalyst surface. The rate of elementary reaction j is represented by rj, and v j is the stoichiometric coefficient for component i in reaction j. The relationship of rj to the reactant partial pressures and surface species coverages are given by expressions of the form... 

Attempts to define operationally the rate of reaction in terms of certain derivatives with respect to time (r) are generally unnecessarily restrictive, since they relate primarily to closed static systems, and some relate to reacting systems for which the stoichiometry must be explicitly known in the form of one chemical equation in each case. For example, a IUPAC Commission (Mils, 1988) recommends that a species-independent rate of reaction be defined by r = (l/v,V)(dn,/dO, where vt and nf are, respectively, the stoichiometric coefficient in the chemical equation corresponding to the reaction, and the number of moles of species i in volume V. However, for a flow system at steady-state, this definition is inappropriate, and a corresponding expression requires a particular application of the mass-balance equation (see Chapter 2). Similar points of view about rate have been expressed by Dixon (1970) and by Cassano (1980). 

Since (—mcii4.r) is equal to the fuel supply rate (wch4) by definition for a stoichiometric reaction, then the exit mass flow rate is... 

Since at the flame sheet Yq2 = Yf = 0, this is the definition of a stoichiometric system so that... 

Fe 2S], a [4Fe-4S] and a [3Fe-4S] center. The enzyme catalyzes the reversible redox conversion of succinate to fumarate. Voltammetry of the enzyme on PGE electrodes in the presence of fumarate shows a catalytic wave for the reduction of fumarate to succinate (much more current than could be accounted for by the stoichiometric reduction of the protein active sites). Typical catalytic waves have a sigmoidal shape at a rotating disk electrode, but in the case of succinate dehydrogenase the catalytic wave shows a definite peak. This window of optimal potential for electrocatalysis seems to be a consequence of having multiple redox sites within the enzyme. Similar results were obtained with DMSO reductase, which contains a Mo-bis(pterin) active site and four [4Fe 4S] centers. 

These activities can be verified if It can he shown that the solubility data of (8) are at stoichiometric saturation, but as mentioned above, this requires independent thermodynamic definition of K(x). 

The characterization, the full identification, of a phase requires a complete and detailed description of its structure. As examples, consider the data, obtained from X-ray diffraction experiments, reported in Table 3.2 for stoichiometric and variable composition phases. An explanation of the various symbols used will be given in the following paragraphs. For a general reference to symbols, definitions and... 

While CMC is assumed to be an observable and definite value in the case of surfactant monomers, there are frequent reports in the literature of the formation of aggregates or micelle-like associations in solutions of organic solutes so dilute as to preclude apparently the formation of micelles [208, 267-269, 272, 275,278]. Work with different types of commercial surfactants has indicated that molecularly non-homogeneous surfactants do not display the sharp inflection in surface tension associated with CMC in molecularly homogeneous monomers, but rather the onset of aggregation is broad and indistinct [253,267,268]. The lack of well-defined CMCs for non-homogeneous surfactants is speculated to result from the successive micellization of the heterogeneous monomers at different stoichiometric concentrations of the surfactant, which results in a breadth of the monomeric-micelle transition zone. 

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