Stoichiometry from balanced

Stoichiometry (from the Greek stoikeion—element) is the practical application of the law of multiple proportions. The stoichiometric equation for a chemical reaction states unambiguously the number of molecules of the reactants and products that take part from which the quantities can be calculated. The equation must balance. 

Concentration-Time Data. We will now use nonlinear regression to determine the rate law parameters from concemraiion-time data obtained in batch experiments. We recall that the combined rate law-stoichiometry-mole balance for a constant-volume batch reactor is... 

At the end, we summarize the results of the model of a reacting mixture of fluids with linear transport properties from Sects. 4.5 and 4.6 (properties such as kinematics, stoichiometry and balances of mass, momentum and their moment, energy and entropy inequality are as in Sects. 4.2, 4.3 and 4.4). Constitutive equations, their properties and final form of entropy production are given in the end of Sect. 4.5 (from Eq. (4.156)), further thermodynamic quantities and properties are given at the... 

We can use the mole ratios (stoichiometry) from the balanced equation to determine the rates of change of other products and reactants. The rate of reaction can then be derived from any one of these individual rates. 

The outcome of the analysis of the integrated peak intensities shown in Fig. 6 is shown in Table 1 after corrections for different photoelectron cross sections and for the different inelastic mean free paths for the photoelectrons. The C l.s peak was not included in the quantitative balance since it was felt to represent a contamination overlayer which was not an integral part of the corrosion film. Previous XPS intensity studies of reference oxides showed reasonably good agreement with expected stoichiometries [9]. From the analysis, it can be seen that this film contained more oxygen than was accountable by stoichiometry the balance is believed to be water of hydration. 

The reaction center has either to be spedfied when inputting a reaction into a database, or it has to be determined automatically. Specification on input is time-consuming but it can benefit from the insight of the human expert, particularly so if the reaction input is done by the primary investigator as is the case in an electronic notebook. Automatic determination of reaction centers is difficult, particularly so when incomplete readion equations are given where the stoichiometry of a reaction is not balanced see Section 3.1). One approach is to try first to complete the stoichiometry of a reaction equation by filling in the missing molecules such as water, N2, etc. and then to start with reaction center determination. A few systems for automatic reaction center specification are available. However, little has been published on this matter and therefore it is not discussed in any detail here. 

Since the volume depends on conversion or time in a constant pressure batch reactor, consider the mole balance in relation to the fractional conversion X. From the stoichiometry. 

Sometimes we need to know how much product to expect from a reaction, or how much reactant we need to make a desired amount of product. The quantitative aspect of chemical reactions is the part of chemistry called reaction stoichiometry. The key to reaction stoichiometry is the balanced chemical equation. Recall from Section H that a stoichiometric coefficient in a chemical equation tells us the relative amount (number of moles) of a substance that reacts or is produced. Thus, the stoichiometric coefficients in... 

To construct an overall rate law from a mechanism, write the rate law for each of the elementary reactions that have been proposed then combine them into an overall rate law. First, it is important to realize that the chemical equation for an elementary reaction is different from the balanced chemical equation for the overall reaction. The overall chemical equation gives the overall stoichiometry of the reaction, but tells us nothing about how the reaction occurs and so we must find the rate law experimentally. In contrast, an elementary step shows explicitly which particles and how many of each we propose come together in that step of the reaction. Because the elementary reaction shows how the reaction occurs, the rate of that step depends on the concentrations of those particles. Therefore, we can write the rate law for an elementary reaction (but not for the overall reaction) from its chemical equation, with each exponent in the rate law being the same as the number of particles of a given type participating in the reaction, as summarized in Table 13.3. 

Most students demonstrated the abihty to translate from the sub-micro to the symbolic level by writing a balanced equation for the reaction in the question shown in Fig. 8.8. In determining the hmiting reagent, however, there were a lower number of correct responses than for the question in Fig. 8.9 based on stoichiometry. The difference in performance is even greater for part (c) of both questions... 

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. 

Since Br2 (gas) is the driving force for defect formation, we need also to consider deviation from stoichiometry, 8. Thus, we also set a Agi=6 Br balance ... 

Material-balance problems are particular examples of the general design problem discussed in Chapter 1. The unknowns are compositions or flows, and the relating equations arise from the conservation law and the stoichiometry of the reactions. For any problem to have a unique solution it must be possible to write the same number of independent equations as there are unknowns. 

A proper set of chemical equations provides an aid in chemical book-keeping to determine composition as reaction proceeds. This is the role of chemical stoichiometry. On the one hand, it prescribes elemental balances that must be obeyed as constraints on reaction on the other hand, in prescribing these constraints, it reduces the amount of other information required (e g., from kinetics) to determine the composition. 

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. 

As depicted in Figure 2.3, electrons are transferred from the oxidation step to the reduction step of the redox reaction. The number of electrons exchanged is the fundamental basis for establishing the stoichiometry of the redox process. This fact is crucial when establishing a mass balance, as will be done by modeling sewer processes (cf. Chapters 5 and 6). The OX value is, by definition, a key element in determination of this number. 

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

Disturbance of H Balance from Temporal or Spatial Decoupling of the Production and Mineralizatbn of the Biomass. In a most general way the synthesis (assimilation) and the decomposition (respiration) of biomass can be written stoichiometri-cally as... 

Each of these dissociation reactions also specifies a definite equilibrium concentration of each product at a given temperature consequently, the reactions are written as equilibrium reactions. In the calculation of the heat of reaction of low-temperature combustion experiments the products could be specified from the chemical stoichiometry but with dissociation, the specification of the product concentrations becomes much more complex and the s in the flame temperature equation [Eq. (1.11)] are as unknown as the flame temperature itself. In order to solve the equation for the n s and T2, it is apparent that one needs more than mass balance equations. The necessary equations are found in the equilibrium relationships that exist among the product composition in the equilibrium system. 

A chemical reaction is in most cases the result of an overall balance of a number of steps, called elementary reactions, whose rate law can be deduced from the stoichiometry. The rate law of an elementary reaction has the form... 

Apart from hydrocarbons and gasoline, other possible fuels include hydrazine, ammonia, and methanol, to mention just a few. Fuel cells powered by direct conversion of liquid methanol have promise as a possible alternative to batteries for portable electronic devices (cf. below). These considerations already indicate that fuel cells are not stand-alone devices, but need many supporting accessories, which consume current produced by the cell and thus lower the overall electrical efficiencies. The schematic of the major components of a so-called fuel cell system is shown in Figure 22. Fuel cell systems require sophisticated control systems to provide accurate metering of the fuel and air and to exhaust the reaction products. Important operational factors include stoichiometry of the reactants, pressure balance across the separator membrane, and freedom from impurities that shorten life (i.e., poison the catalysts). Depending on the application, a power-conditioning unit may be added to convert the direct current from the fuel cell into alternating current. 

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. 

In the reaction, one mole of hydroxide generates one mole of alcohol and one mole of carboxylate ion from one mole of ester. Based on this stoichiometry (the mole relationship as defined by the balanced chemical equation), if the number of moles of base is known, then the amount of ester is known. 

Non-stoichiometry, which originates from various kinds of lattice defect, can be derived from the phase rule. As an introduction, let us consider a trial experiment to understand non-stoichiometry (this experiment is, in principle, analogous to the one described in Section 1.4.8). Figure 1.1 shows a reaction vessel equipped with a vacuum pump, pressure gauge for oxygen gas, pressure controller for oxygen gas, thermometer, and chemical balance. The temperature of the vessel is controlled by an outer-furnace and the vessel has a special window for in-situ X-ray diffraction. A quantity of metal powder... 

This is the rate at which the hydrogen reacts. From the stoichiometry of the reaction, the rate at which the thiophene reacts is Thus this term replaces the >/4 k°CAL term in equation 4.45 for the thiophene material balance which then becomes ... 

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