Dependent and Independent Reactions

Basis components of the solution interact between themselves forming secondary components, which, in turn, may interact both with the basis components and between themselves. As a result, the relaxation process in a multi-component solution includes a multitude of chemical reactions of different nature and direction. For the determination of equilibrium water composition it is necessary to have equilibrium constants of these reactions, therefore, it is necessary to establish the number and nature of participating reactions. 

It is customary to separate all reactions in water into two large groups linearly independent and dependent. With the linearly independent reactions belong reactions with participation of the basis components, and with linearly dependent ones - reactions between secondary components. Independent reactions are actually reactions of the formation of secondary components from the basis ones. 

For instance, if reactions of the secondary CO and HCOj formation from the basis H O, H and CO look Hke 

Then the reaction with the participation of two secondary components  

Their stoichiometric coefficients may be streamlined in the format of a matrix table. For this purpose we will place components in columns and reactions, in lines. We will assign to stoichiometric coefficients of the reactants a minus sign, and of the products, plus sign. We will equate stoichiometric coefficients of the absent components to zero. Then the above reactions will be  

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As already discussed, at equilibrium only the reaction rates wr of the R linearly independent reactions can initially be assumed to vanish. To handle the correspondence between the linearly dependent and independent reactions we relate the A, and Ar affinities through linear equations of the form... 

As early as the 1980s, it was indicated that some proteins such as cytochrome oxidase in the membranes and mitochondria were a target for the action of qin-ghaosu. Meshnick et al. have performed a series of experiments about the interaction between qinghaosu and proteins in the presence of heme and have concluded that the binding between qinghaosu and albumin probably involves thiol and amino groups via both iron-dependent and -independent reactions. However, they have not isolated and confirmed such covalent adducts and have presented the ques-... 

To determine the relationships between the dependent and independent reactions, let ttfon denote the scalar factor relating the Ath dependent reaction to the mth independent reaction. Thus, afa is the multiplier of the mth independent reaction to obtain the Mr independent reaction. To determine the numerical values of the factors, we conduct species balances for each dependent reaction. For the Ml dependent reaction, the following set of linear equations should be satisfied for each species ... 

Kinetic studies have concentrated on the glycine system.1174,1175,1176 In the pH range 3.0-3.8 (40 °C), the reaction proceeds by acid-dependent and -independent paths reaction via the hydroxy complex is probably la, whereas the aqua complex appears to undergo /a substitution. 

A comparison of this equation with Equation 1) demonstrates that functional relationships between dependent and independent variables can be quite different for CSTR s and batch reactors, even with the same reaction system and the same kinetic mechanisms. 

Supramolecules 63-65 were designed to exploit the well-known redox chemistry of electronically excited [Ru(bpy)3] +-type complexes with nitroaromatics [164]. For both systems (R = H and Me), the excited-state lifetime of the Ru(II) polypyridyl donor is sufficiently long that concentration-dependent and -independent kinetics were observed. The concentration-dependent rate arises from the bimo-lecular electron transfer reaction between uncomplexed Ru(II) polypyridyl donor and the 3,5-DNB acceptor. The measured bimolecular rate constants were in ac-... 

The screen for each chemical kinetic calculation simultaneously displays a variety of characterizations in multiple windows and allows analysis of time/temperature-dependent species and reaction information including species concentrations, species steady-state analysis, individual reaction rates, net production/destruction rates, reaction equilibrium analysis and the temperature/time history of the system. The interactive user-sorting of the species and reaction information from the numerical simulations is mouse/cursor driven. An additional feature also allows interactive analysis and identification of dependent and independent species and reaction pathways, on-line reaction network analysis and pathway/flowchart construe-... 

Note that the summation on the left-hand side of Eq. 4.3.4 is over independent reactions only, whereas the summation on die right-hand side is over all reactions that take place in the reactor. Using Eq. 2.4.8, we write the right-hand side of Eq. 4.3.4 as a sum of dependent reactions and independent reactions,... 

Solution The purpose of this example is to illustrate the design formulations for chemical reactions where the dependency between dependent reactions and independent reactions is not due to reversible reactions. First, we determine the number of independent reactions and select a set of independent reactions. We construct a matrix of stoichiometric coefficients for the given reactions ... 

The first two of these reactions describe, respectively, the acid-dependent and -independent pathways for the oxidation of I. The second-order dependence on [Br ] and [H" ] can be explained by the latter reaction if the dominant reactive Ce(IV) hydrolyzed species (in 0.2 2.0 M HCIO4) is Ce(OH). ... 

Tsuji, R.F., Hoshino, K., Noro, Y., Tsuji, N.M., Kurokawa, T., Masuda, T., Akira, S. Nowak, B. (2003) Suppression of allergic reaction by A-carrageenan Toll-like receptor 4/MyD88-dependent and -independent modulation of immunity, din. Exp. Allergy 33, 249-258. 

A list of typical dependent and independent variables for a furnace simulation is shown in Table VI. Coal particles typically are treated in a procedure that couples the continuum (Eulerian or fixed reference fame) gas-phase grid and the discrete (Lagrangian or moving reference frame) particles. Numerical solutions are repeated until the gas flow field is converged for the computed particle source terms, radiative fluxes, and gaseous reactions. Lagrangian particle trajectories are then calculated. After solving all particle-class trajectories, the new source terms... 

The common approach to downturn a dimension of system of the equations of any nature is the method of unknowns exclusion. With a reference to chemical systems, the simple example of its use is the concept of so-called dependent and independent substances, relations between them beeing defined by the laws of conservation of atoms quantity. For catalytic reactions always there is one such law - law of conservation of amount of atoms of the catalyst in each of elementary stages. This law is linear and allows easily to exclude one of unknowns, that is to express quantity of any one of intermediate substances through others. Generally in chemical systems can exist both linear and nonlinear conservation laws (CL). 

A Posteriori Modei Discrimination. Several discrimination criteria can be used in the case no additional experimental information can be acquired. A first criterion has already been discussed in Section 3.1.2, that is, investigating the total pressure effect on the initial reaction rate potentially allows identifying the RDS in a reaction mechanism. Similar tests can be defined in which the rate equation is rearranged into a particular form to give a linear relationship between dependent and independent variables. 

Figure 3.4. Initial velocity versus substrate concentration plot for an enzyme-catalyzed reaction. Notice the first- and zero-order regions of the curve, where the reaction velocity is, respectively, linearly dependent and independent of substrate concentration.

There is a general agreement on the reaction rate. It is a fast reaction, the rate has a negative temperature dependence, and the reaction rate constant is independent of pressure in a wide pressure range (0.5

values obtained in flow reactors, using NH3 F-> NH2 HF as a radical source, are significantly... 

HMnOi - + MnOi" + OH accounts for the major reaction pathway. In the reaction with hydroxy-cyclohexanecarboxylic acids,a complex pH dependence is observed, the mechanism involving complex formation between the neutral hydroxy-acid and the permanganate. The intermediate complex is, however, considered to undergo a (reversible) deprotonation prior to the rate-determining electron transfer step. Acid-dependent and -independent paths have also been described in the oxidation of ethyl acetate in perchloric acid. The mechanism of the fast reaction between Mn " and nitrite has been investigated in glycine and phthalic acid buffers. The rate law may be expressed as... 

The distinction between dependent and independent variables is that the independent variable is the one being changed, x, and the dependent variable, y, is the observed variable caused by this change, e g. y = x. Parameters represent physical quantities that characterize the system and model such as density, thermal conductivity, viscosity, reaction rate constants, or activation energies. Parameters are not necessarily constants, and can be described as ftmctions of the dependent (or independent) variables, e g. heat capacity Cp(r) and density p(p,T). 

The development of combustion theory has led to the appearance of several specialized asymptotic concepts and mathematical methods. An extremely strong temperature dependence for the reaction rate is typical of the theory. This makes direct numerical solution of the equations difficult but at the same time accurate. The basic concept of combustion theory, the idea of a flame moving at a constant velocity independent of the ignition conditions and determined solely by the properties and state of the fuel mixture, is the product of the asymptotic approach (18,19). Theoretical understanding of turbulent combustion involves combining the theory of turbulence and the kinetics of chemical reactions (19—23). 

FIGURE 22.4 The light-dependent and light-independent reactions of photosynthesis. Light reactions are associated with the thylakoid membranes, and light-independent reactions are associated with the stroma. 

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