Selectivity stoichiometric coefficient

Repeat the analysis in the example of 7.4.2, but for the one arbitrarily selected stoichiometric coefficient, use Vji = -1. Create a table of compositions vs. extent of reaction and compare it with the one in the example. Which quantities change and which remain unaffected by the way the reaction is balanced Discuss. 

To select stoichiometric coefficients so as to obtain whole non-codivisible numbers only. In the example given by equation (2.3) this condition would be satisfied by the first-named equation. 

The task now is to select the linear combinations that will most probably correspond to independent parts of the reaction network with easily interpretable stoichiometry. A simplification of the data in the matrix can be achieved by such a rotation that the axes go through the points in Fig. A-2 (this is equivalent to some zero-stoichiometric coefficients) and that the points of Fig. A-3 are in the first quadrant (this corresponds to positive reaction extents) if possible. Rotations of the abscissa through 220° and the ordinate through 240° lead to attaining both objectives. The associated rotation matrix is ... 

Figure 19 shows the stoichiometric coefficient y versus time. The y-coefficient is the molar ratio between the amount of hydrogen in the conversion gas and the amount of carbon in the conversion gas. In this particular selection of y-graphs the dynamic ranges for the different wood fuels during a batch are fuel wood 3 0, wood pellets 2.6 0, and wood chips 2.4 0. These dynamic ranges are quite representative of the whole range of volume fluxes tested. 

This is a number that goes from zero to unity as the selectivity improves. We can use the number of moles Nj, chosen on some basis for each species such that we divide each Nj by its stoichiometric coefficient to normalize them. For a steady-state flow system the molar flow rates Fj are appropriate. 

Stoichiometric coefficients of selected antioxidants in reactions with... 

Click the box under Reactant Components and use the dropdown menu to select component E (ethylene). Set the stoichiometric Coefficient at — 1 (reactant is consumed) and the Exponent at 1 (first-order reaction) (see Fig. 2.50). Repeat for the other reactant B (benzene). In a similar way, define the product as EB with a coefficient of 1... 

The use of the stoichiometric coefficient v, guarantees that the reaction rate does not depend on the concrete component i considered. There are several possibilities regarding the selection of an appropriate scale. Frequently, the reaction volume Vr is used leading to a reaction rate rv which has the dimension [mol m-3 s]. 

Brinkley (4 postulated C species at equilibrium, p species, referred to as "components," were selected to have linearly independent formula vectors, where p is the rank of the atom matrix, (mjk), and Yj is the formula vector for the jth species, [mj, mj2f...mjE]. Given the choice of components, the stoichiometric coefficients for an independent set of chemical reactions are computed ... 

The user has to specify a split ratio for each branching module and a distribution coefficient for each component entering a distribution module. The conversion module requires a stoichiometric coefficient for each component involved and the fractional conversion of a selected key component. Each recycle has to be defined by the originating and destination modules, computational sequence, and convergence tolerance of a key component. 

Whenever the kinetics of a chemical transformation can be represented by a single reaction, it is sufficient to consider the conversion of just a single reactant. The concentration change of the remaining reactants and products is then related to the conversion of the selected key species by stoichiometry, and the rates of production or consumption of the various species differ only by their stoichiometric coefficients. In this special case, the combined influence of heat and mass transfer on the effective reaction rate can be reduced to a single number, termed the catalyst efficiency or effectiveness factor rj. From the pioneering work of Thiele [98] on this subject, the expressions pore-efficiency concept and Thiele concept have been coined. 

Fractional conversion of a reactant is defined as the ratio of the amount consumed to that charged. In this book, the following definitions of yield, yield ratio, and selectivity are used The yield of a product is the ratio of the amount of reactant (or reactants) converted to the product to the total amount of reactant (or reactants) charged. The cumulative yield ratio of two products is the ratios of their yields. The instantaneous yield ratio is the ratio of the momentary rates of conversion to these products. The cumulative selectivity to a product is the ratio of the amount of reactant (or reactants) converted to that product to the amount consumed. The instantaneous selectivity is the ratio of the momentary rate of reactant conversion to the product to that of reactant consumption. Not used in this book is the extent of reaction, defined as the number of moles consumed or formed, divided by the stoichiometric coefficient of the respective participant. 

The cracking severity and selectivity parameters are used to correlate product yields. The stoichiometric coefficients in Equation 9 are modeled via a simple power series in CSI. 

For a given waste stream, series of reactions Bjk, components A, and cell retention time 6c, the concentration of all components in the reactor effluent stream and gas discharge can be determined. This requires that the stoichiometric coefficients Vik be known, including the value for organism synthesis. Also required are the coefficients kk and Kk for each reaction. The method used for selection of appropriate values are discussed in the following. 

Selectivity S of a product is the ratio of the rate of production of that product to the rate of production of all products combined. For a single reaction selectivity is trivial—if more than one product occurs, then the selectivity of each product is the ratio of the stoichiometric coefficient of that product to the sum of stoichiometric coefficients of all the products. Thus for reaction (7-1)... 

Once the specific chemical formula is selected, the stoichiometric coefficients of the individual species are defined as follows For each product species, the stoichiometric coefficient is identical to the coefficient of that species in the chemical formula. For each reactant, the stoichiometric coefficient is the negative value of the coefficient of that species in the chemical reaction. If a species does not participate in the reaction, its stoichiometric coefficient is zero. 

Solution We select the written chemical reaction as the chemical formula hence, the stoichiometric coefficients are... 

Since Matrix (b) has three nonzero rows, there are three independent chemical reactions. We select Reactions 1, 3, and 5 as a set of independent reactions, and their stoichiometric coefficients are... 

Note fliat flie argon is an inert species, and its stoichiometric coefficient is zero, a. Selecting the entire process as the system (the inlet is stream 1 and the outlet is stream 4) hence, (F,ot)in = Ei = 60 mol/min and (EtoOcut = F. Writing an argon balance using Eq. 2.3.3,... 

Solution First we have to determine the number of independent reactions, and to select a set of independent reactions. We construct a matrix of stoichiometric coefficients for the given reactions ... 

Select a species (a nonzero stoichiometric coefficient) to relate to the first reaction, and then remove the colunrn and the row from the redueed matrix. 

Selection of a chemical reaction as a basis for the calculation and defining its stoichiometric coefficients... 

We can construct the matrix of stoichiometric coefficients and reduce it to a diagonal form to determine the number of independent reactions. However, in this case, we have three reversible reactions, and, since each of the three forward reactions has a species that does not appear in the other two, we have three independent reactions and three dependent reactions. We select the three forward reactions as the set of independent reactions. Hence, the indices of the independent reactions are m = 1, 3, 5, and we describe the reactor operation in terms of their dimensionless extents, Zi, Z3, and Z5. The indices of the dependent reactions are = 2, 4, 6. Since this set of independent reactions consists of chemical reactions whose rate expressions are known, the heuristic rule on selecting independent reactions is satisfied. The stoichiometric coefficients of the selected three independent reactions are... 

Solution First, we determine the number of independent reactions and select a set of independent reactions. The matrix of stoichiometric coefficients for these reactions was constructed and reduced to a reduced matrix in Example 2.12. Since there are three nonzero rows in the reduced matrix, there are three independent reactions. The nonzero rows in the reduced matrix represent the following set of independent reactions ... 

We select the forward reaction as the independent reaction and the reverse reaction as the dependent reaction. Hence, the index of the independent reaction is m = 1, the index of the dependent reaction is k = 2. Since Reaction 2 is the reverse of Reaction 1, a2i = — 1. The stoichiometric coefficients of the independent reaction are... 

Solurion The reactor design formulation of these chemical reactions was discussed in Example 4.2. Recall that there are two independent reactions and one dependent reaction, and, following the heuristic rule, we select Reactions 1 and 2 as a set of independent reactions hence, m = 1,2, and = 3. The stoichiometric coefficients of the independent reactions are... 

The number of components C in a mixture equals the number of constituents N minus the number of independent reactions R. It is always possible to select R independent reactions which are so-called formation reactions A formation reaction is one which yields only one constituent, from all the components. For the formation-reaction of constituent B, the stoichiometric coefficient of B is unity the stoichiometric coefficient of component a is denoted by -vga, a = 1,..., C. 

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