Analysis stoichiometric

The main use of stoichiometric equations is to express LAVOISIER S law in a mathematical form, that is the conservation of the elements (C, H, O...) during a chemical transformation. 

First of all, these equations confirm that the experimental results are not impaired by systematic errors, due to erroneous quantitative measurements or the failure to take into account one or other constituent. One can easily imagine that this is an essential 

But it will be seen that theory allows the number of equations for the reactions which are strictly necessary to describe the chemical system precisely to be defined in a rigorous way, when the nature and the number of the constituents to be taken into account are themselves well-defined. The theory therefore provides the necessary and sufficient number of chemical variables (or JOUGUET-de DONDER variables) and equations to calculate the composition of the reaction mixture during the transformation. In particular, these equations can be applied to chemical equilibria. 

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Under practical conditions, chemical reactions almost always produce smaller amounts of products than the amounts predicted by stoichiometric analysis. There are three major reasons for this. 

As the LiF example illustrates, the most direct way to determine the value of an equilibrium constant is to mix substances that can undergo a chemical reaction, wait until the system reaches equilibrium, and measure the concentrations of the species present once equilibrium is established. Although the calculation of an equilibrium constant requires knowledge of the equilibrium concentrations of all species whose concentrations appear in the equilibrium constant expression, stoichiometric analysis often can be used to deduce the concentration of one... 

The problem asks for a drawing that represents equilibrium conditions. We need a stoichiometric analysis of the reaction components. A table of amounts helps organize the information. The problem has two parts, and it best to treat them individually. 

The equilibrium concentration of Pb ions is stated to be 1.35 X 10 M, but the equilibrium concentration of iodide ions is not stated [Pb2- ],q = 1.35 X iO M[r]g(j — The equilibrium concentration of I is determined by stoichiometric analysis. Initially, the system contains only pure water and solid lead(II) iodide. Enough Pbl2 dissolves to make [Pb ]gq = 1.35 X 10 M. One formula unit of Pbl2 contains one Pb cation and two I" anions. Thus, twice as many iodide ions as lead ions enter the solution. The concentration of I at equilibrium is double that of Pb cations [r],q-2[Pb ],q-2.70 X lO M Substitute the values of the concentrations at equilibrium into the equilibrium expression and calculate the result ... 

Kwok, K. H., and Doran, P. M., Kinetic and Stoichiometric Analysis of Hairy Roots in a Segmented Bubble Column Reactor, Biotechnol. Prog., 11 429 (1995)... 

A stoichiometric table for keeping track of the amounts or flow rates of all species during reaction may be constructed in various ways, but here we illustrate, by means of an example, the use of , the extent of reaction variable. We divide the species into components and noncomponents, as determined by a stoichiometric analysis (Section 5.2.1), and assume experimental information is available for the noncomponents (at least). 

In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

A stoichiometric analysis based on the species expected to be present as reactants and products to determine, among other things, the maximum number of independent material balance (continuity) equations and kinetics rate laws required, and the means to take into account change of density, if appropriate. (A stoichiometric table or spreadsheet may be a useful aid to relate chosen process variables (Fj,ch etc.) to a minimum set of variables as determined by stoichiometry.)... 

A considerable improvement over purely graph-based approaches is the analysis of metabolic networks in terms of their stoichiometric matrix. Stoichiometric analysis has a long history in chemical and biochemical sciences [59 62], considerably pre-dating the recent interest in the topology of large-scale cellular networks. In particular, the stoichiometry of a metabolic network is often available, even when detailed information about kinetic parameters or rate equations is lacking. Exploiting the flux balance equation, stoichiometric analysis makes explicit use of the specific structural properties of metabolic networks and allows us to put constraints on the functional capabilities of metabolic networks [61,63 69]. 

Considering a trade-off between knowledge that is required prior to the analysis and predictive power, stoichiometric network analysis must be regarded as the most successful computational approach to large-scale metabolic networks to date. It is computationally feasible even for large-scale networks, and it is nonetheless far more predictive that a simple graph-based analysis. Stoichiometric analysis has resulted in a vast number of applications [35,67,70 74], including quantitative predictions of metabolic network function [50, 64]. The two most well-known variants of stoichiometric analysis, namely, flux balance analysis and elementary flux modes, constitute the topic of Section V. 

Despite its predictive power and successful application on a variety of large-scale metabolic networks, stoichiometric analysis also encompasses a few inadequacies. In particular, stoichiometric analysis largely relies on the steady-state assumption and is not straightforwardly applicable to analyze complex time-dependent dynamics in metabolic systems. Similarly, stoichiometric analysis does not allow us to account for allosteric regulation, considerably delimiting its capabilities to predict dynamic properties. See also Section V.C for a discussion of the limits of stoichiometric analysis. 

For our purposes, of particular interest are methods that aim to bridge the gap between stoichiometric analysis and explicit kinetic modeling [75]. A variety of... 

Nonetheless, the topological and stoichiometric analysis of metabolic networks is probably the most powerful computational approach to large-scale metabolic networks that is currently available. Stoichiometric analysis draws upon extensive work on the structure of complex reaction systems in physical chemistry in the 1970s and 1980s [59], and can be considered as one of the few theoretically mature areas of Systems Biology. While the variety and amount of applications of stoichiometric analysis prohibit any comprehensive summary, we briefly address some essential aspects in the following. 

Stoichiometric analysis goes beyond topological arguments and takes the specific physicochemical properties of metabolic networks into account. As noted above, based on the analysis of the nullspace of complex reaction networks, stoichiometric analysis has a long history in the chemical and biochemical sciences [59 62]. At the core of all stoichiometric approaches is the assumption of a stationary and time-invariant state of the metabolite concentrations S°. As already specified in Eq. (6), the steady-state condition... 

In this section, we describe a recently proposed approach that aims overcome some of the difficulties [23, 84, 296, 325] Structural Kinetic Modeling (SKM) seeks to provide a bridge between stoichiometric analysis and explicit kinetic models of metabolism and represents an intermediate step on the way from topological analysis to detailed kinetic models of metabolic pathways. Different from approximative kinetics described above, SKM is based on those properties that are a priori independent of the functional form of the rate equation. 

Specifically, SKM seeks to overcome several known deficiencies of stoichiometric analysis While stoichiometric analysis has proven immensely effective to address the functional capabilities of large metabolic networks, it fails for the most part to incorporate dynamic aspects into the description of the system. As one of its most profound shortcomings, the steady-state balance equation allows no conclusions about the stability or possible instability of a metabolic state, see also the brief discussion in Section V.C. The objectives and main requirements in devising an intermediate approach to metabolic modeling are as follows, a schematic summary is depicted in Fig. 25 ... 

Structural kinetic modeling keeps the advantages of the stoichiometric analysis, while incorporating dynamic aspects into the description of the system. 

Extending stoichiometric analysis, SKM allows to investigate the quantitative effects of allosteric regulation on the stability and dynamics of a metabolic system. 

Figure 25. Structural Kinetic Modeling seeks to keep the advantages of stoichiometric analysis, while incorporating dynamic properties into the description of the system. Specifically, SKM aims to give a quantitative account of the possible dynamics of a metabolic network.

Robert Urbanczik, SNA a toolbox for the stoichiometric analysis of metabolic networks. BMC Bioinformatics 7, 129 (2006). 

The purpose of stoichiometric analysis is to insure that element balance is maintained. In the present case the stoichiometry is fairly straightforward. In more complex cases linear algebra can be used to perform stoichiometric analysis in a generalized manner (1 ). 

For the assessment of the separation system a simple but realistic stoichiometric analysis is sufficient. Representative reactions are listed in Table 11.5 with stoichiometric coefficients from Table 11.4 at 2 bar. The resulting gas composition is given in Table 11.6 for a mixture of propene/ammonia/air of 1/1.2/9.5. 

Systems of linear equations are to be solved during the stoichiometric analysis of a reaction, but also on the occasion of the use of other numerical methods (see below). 

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