Stoichiometric equation, basic

The basic stoichiometric equation can be transformed somewhat so that for any... 

The life cycle of PLA starts with com production. All free energy used for such production is captured by photos3mthesis by following the basic stoichiometric equation ... 

The two basic principles permit the algebraic manipulation of chemical reactions (represented by their stoichiometric equations and associated enthalpy changes) in order to achieve desired thermochemical results. 

The concentrations of the various species can then be determined by solving equation 3.1.12 for and employing basic stoichiometric relations. 

In this case it is more convenient to rewrite equations 5.2.19 and 5.2.21 in terms of equilibrium concentrations and extents per unit volume. From basic stoichiometric principles... 

In general this equation must be solved using numerical methods. Once has been related to time in such fashion, equation 5.2.65 may be used to evaluate as a function of time. Basic stoichiometric principles may then be used to determine the corresponding concentrations of the various product and reactant species. 

If the number of basic overall equations, Q, is smaller than that of basic routes, P, it is expedient to use a stoichiometric basis of routes for a description of the reaction. In this case we need to know only Q rates along nonempty basic routes the remaining P — Q rates are not required (but this by no means implies that they equal zero). 

In this chapter, a reaction is considered acid or base catalyzed if its rate is proportional to the concentration of acid or base, respectively. According to Ostwald s definition of catalysis, however, it is required that the acid or base be not consumed in the reaction [12]. A true catalyst combines with the substrate to form a reactive intermediate, and the catalyst is regenerated in one of the final steps of the mechanism. In Bell s definition, a catalyst appears in the rate expression to a power higher than that to which it appears in the stoichiometric equation [1]. On the other hand, it merely depends on the acidity or basicity of the products (and also on the pH of the solution) whether or not the catalyst will be regenerated at the end. Therefore, it is not essential for the classification of reaction type and mechanism whether the acid or base is a true catalyst according to the more restricted definition, or a reactant which is consumed [12]. In both cases, the formation of an intermediate from substrate (S) and acid or base opens a low free energy pathway for the reaction. 

From the viewpoint of both a mass balance or a mole balance for elements themselves, such as C, H, or O, the generation and consumption terms are not involved in a material balance. Finally, Eq. (2.1) should not be applied to a balance on a volume of material unless ideal mixing occurs (see Sec. 3.1) and the densities of the streams are the same. In this chapter, information about the generation and consumption terms for a chemical compound will be given a priori or can be inferred from the stoichiometric equations involved in the problem. Texts treating chemical reaction engineering describe how to calculate from basic principles gains and losses of chemical compounds. 

The basic reaction of carbon with water vapour is endothermal and may be illustrated by the following stoichiometric equation ... 

A mechanistically different type of nitrosation was discovered by Keefer and Roller (1973), namely a nitrosation of secondary aliphatic amines with nitrite anions in alkaline solution, catalyzed by aldehydes. Although it is unlikely to be applicable to diazotization, i. e., to primary amines, it will be mentioned here because it is a good example of the fact that, in chemistry, particularly in organic chemistry, for a certain type of reaction, e. g., nitroso-de-protonation (which includes substitution of protons bonded to C, N, O, S, etc., atoms), practically all methods follow the same basic pattern (in the case of nitrosation substitution by an electrophilic nitrosating reagent). The Keefer-Roller nitrosation is apparently different if one looks at the stoichiometric equation (4-8). A careful kinetic investigation (Casado et al., 1981b, 1984 a) on the concentration and pH dependence of this reaction revealed that the nitrite anion and free amine base enter the substitution process and that formaldehyde is a true catalyst, as it is not required in equimolar amounts. 

The solution of the homogeneous set (45) of linear equations gives different sets of coefficients Aj. For a given set, the number of invariants is well defined, and it can indeed be higher than the number of elements, which gives to this method its optimal character (with respect to a balance of the elements only). On the contrary, the exact nature of the invariants is arbitrary, because, as for the stoichiometric equations, each linear combination of invariants is itself an invariant. This indetermination vanishes by fixing the basic vectors a priori. 

For semidiscontinuous processing, often used in fermentations for the production of yeast biomass or secondary metabolites, the basic balance equation is to be modified. Balancing in this case has to distinguish between components that are already present in the reactor at the beginning (number of moles nj q) and components that are fed later on to the reactor (flux of moles n°). The stoichiometric balance in this case of semidiscontinuous reactor operation is... 

In an effort to generalize the calculation scheme, Villars " adopted a somewhat different procedure. Again purely by intuition, he divided all constituents which can occur in equilibrium, into basic and derived ones. For each derived constituent he constructed a stoichiometric equation in the form of... 

There are three basic stoichiometric calculations mole-to-mole conversions, mole-to-mass conversions, and mass-to-mass conversions. All stoichiometric calculations begin with a balanced equation and mole ratios. 

Aiming to construct explicit dynamic models, Eqs. (5) and (6) provide the basic relationships of all metabolic modeling. All current efforts to construct large-scale kinetic models are based on an specification of the elements of Eq (5), usually involving several rounds of iterative refinement For a schematic workflow, see again Fig. 4. In the following sections, we provide a brief summary of the properties of the stoichiometric matrix (Section III.B) and discuss the most common functional form of enzyme-kinetic rate equations (Section III.C). A selection of explicit kinetic models is provided in Table I. TABLE I Selected Examples of Explicit Kinetic Models of Metabolisin 1 ... 

The last two catalytic systems available are intimately based on the stoichiometric ligands 22 and 23, derived from the dipeptide and the chiral phosphoric acid, respectively. The addition of basic additives to slow down or suppress the background reaction allowed the use of catalytic amounts of the ligand. In his initial report, Shi and coworkers have shown that adding 1 equivalent of ethyl methoxyacetate allowed the catalyst loading to be decreased to 0.25 equiv (equation 96) . Under these conditions, the enantioselectivities are similar to those reported in Figure 7. 

While the reaction is described by two overall equations, the number of basic routes is three. The basis of the routes in scheme (220) is chosen so that the overall equation of route Art3) is 0 = 0 i.e., A 3) is an empty route. Thus, the basis of routes is stoichiometric. Therefore, kinetic equations are required only for two rates namely that along routes AK1) and AK2). 

Many more recent stoichiometric studies of cobalt(III) complexes have been responsible for most of the developments in this area of research. Cobalt(III) ammine complexes effect hydrolysis of ethyl glycinate in basic conditions via intramolecular attack of a coordinated amide ion hydrolysis by external hydroxide ion attack also occurs (equation 74).341 Replacement of ammonia ligands by a quadridentate or two bidentate ligands allows the formation of aquo-hydroxo complexes and enables intramolecular hydroxide ion attack on a coordinated amino ester, amino amide... 

When the cluster [Pd4(C0)4(02CMe)4]-2MeC02H was dissolved in styrene and treated with methanol under an atmosphere of carbon monoxide, methyl cinnamate was formed.516 This reaction was also believed to occur by an alkoxycarbonyl route. The reaction became catalytic when [Pd(OAc)2] (106) was used in presence of NaOAc and a stoichiometric amount of copper(II) as reoxidant for the palladium(O) formed. Stille and co-workers have investigated this reaction, sometimes called carboalkoxylation, in detail. A basic difference between this reaction and the hydroesterification described above is that the oxidative nature of carboalkoxylation permits double functionalization of a double bond. Thus (E)- and (Z)-2-butene react readily with CO and methanol in the presence of a catalytic amount of PdCl2 and a stoichiometric amount of CuCl2 to give methyl 3-methoxy-2-methylbutanoate (equation 124).517,518... 

Temperature units/conversions Periodic table Basic atomic structure Quantum mechanical model Atomic number and isotopes Atoms, molecules, and moles Unit conversions Chemical equations Stoichiometric calculations Week 3 Atmospheric chemistry... 

Remark 7.6. The analysis framework we presented is also applicable if an inert component is used to increase the heat capacity of the reaction mixture. In this case, the model (7.2f) would be augmented by the equations corresponding to the model of the separation unit. However, the stoichiometric matrix S and reaction rates r would remain unchanged, since the inert component does not partake in any reaction. Furthermore, the analysis can be applied if more complex correlations are used for the physical parameters of the system (e.g., temperature dependence of heat capacities and densities), as long as the basic assumptions (7.27), (7.29), and (7.30) apply. 

Since AmG is sensitive to both the composition and concentration of electrolytes A and B, its calculation would be simplified considerably if the initial solutions and the final mixture were at the same stoichiometric ionic strength based on 1 kg of solvent in the final mixture. This suggests that for a given mixture of electrolytes in solution sufficient sets of common ion mixtures at the same I should be found which in sum describe the total solution, allowing the excess free energy of the mixture to be found using a series of calculations shown by equation 9. Basically, this is the approach used to calculate AmG in this study. 

Preparation of imines and enamines from carbonyl compounds and amines can be achieved with a dehydrating agent under acid/base catalysis [563]. Basically, primary amines afford imines unless isomerization to an enamine is favored as a result of conjugation, etc (see Eq. 252), and secondary amines afford iminium salts or enamines. These transformations can be conducted efficiently with a catalytic or stoichiometric amount of a titanium salt such as TiCU or Ti(0-/-Pr)4. Equation (247) illustrates an advantageous feature of this method in the imination of a hindered ketone. f-Butyl propyl ketone resisted the formation of the imine even by some methods reported useful for sterically hindered ketones [564,565]. The TiCU-based method works well, however, for this compound, giving the desired imine in high yield within a relatively short reaction period [566]. Imine derivatives such as iV-sulfonylimines could be... 

Promise is held in MPV reactions carried out under catalytic conditions. Instead of, for example, stoichiometric amounts of aluminum as the metal ion activator, catalytic quantities of complexes of rhodium and iridium can sometimes be used to bring about the same reactions. Although the catalytic mechanisms have not been established, postulation of the usual six-membered transition state in the critical step of hydride transfer appears reasonable. The strongly basic conditions of the MPV reaction are avoided. Reductions of aryl ketones (69 equation 30) using (excess) isopropyl alcohol as hydrogen donor and at partial conversions have led to the formation of alcohol (70) in modest enantiomeric excesses with various chiral ligands. " ... 

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