Stoichiometric reactions defined

Another stoichiometric variable that may be used is the extent of reaction, , defined by equation 2.3-6 for a simple system. For a complex system involving N species and represented by R chemical equations in the form... 

A complete chemical reaction in which no fuel and no oxygen is left is called a stoichiometric reaction. This is used as a reference, and its corresponding stoichiometric oxygen to fuel mass ratio, r, can be determined from the chemical equation. A useful parameter to describe the state of the reactant mixture is the equivalence ratio, d, defined as... 

During the course of a chemical reaction, the number of moles of a particular reactant will change in a manner consistent with the stoichiometric relationships defined by the stoichiometric coefficients a, b, p, and q) ... 

This set of relations between reaction orders and stoichiometric coefficients defines what we call an elementary reaction, one whose kinetics are consistent with stoichiometry. We later wiU consider another restriction on an elementary reaction that is frequently used by chemists, namely, that the reaction as written also describes the mechanism by which the process occurs. We will describe complex reactions as a sequence of elementary steps by which we will mean that the molecular collisions among reactant molecules cause chemical transformations to occur in a single step at the molecular level. 

The reaction described above can also be carried out at higher concentration whereby the probability of intramolecular reaction (cyclization) vanishes. So called chain extension processes result from the stoichiometric reaction of a "living" bifunctional precursors with an efficient bifunctional electrophilic deactivator. This polycondensation reaction induces a very large increase of the molecular weight, but is also results in an enhanced polydispersity. - Fractionation is necessary if well defined substances are required. However the average distance between successive hinges along the chain fluctuates only very little. 

It is thus essential to specify the stoichiometric reaction equation when giving numerical values for such quantities in order to define the extent of reaction and the values of the stoichiometric numbers vB. 

To aid in the derivation of the stoichiometric flux relations, it is convenient to define a "stoichiometric reaction flux", r., for each of the s independent stoichiometric reactions, k = 1,2,. .. s. The reaction flux for a particular reaction, J<, when multiplied by the stoichiometric coefficient for a particular component, gives the rate of disappearance of the component i in the region (0-X) by the reaction J< per unit cross-sectional area. The net component flux is obtained by summing over all the stoichiometric reactions, i.e.,... 

Our understanding of organic reactions catalyzed by soluble metal complexes ( homogeneous catalysis ) is based on the properties and stoichiometric reactions of organometallic complexes, defined as molecules containing metal-carbon bonds. Significant aspects are summarized below, but for details the reader is recommended to one of the excellent texts cited at the end of this Appendix. 

Moreover, the discipline combines thermodynamics and chemical kinetics and thus may be helpful to researchers who are engaged in study ing complex chemical transformations—in particular, catalytic transforma tions. For example, some of the important concepts in this subject are the conditions of kinetic irreversibility of complex stepwise stoichiometric reactions and rate determining and rate limiting stages. The lecturers in traditional chemical kinetics recognize that these concepts are not simple ones and tend to conceal them in their courses. Fortunately, these con cepts appear to be consistently and properly defined in terms of thermody namics of nonequilibrium processes. 

Extent of reaction. A quantity not used in this book is the extent of reaction, defined as the number of moles formed or consumed, divided by the respective stoichiometric coefficient, vt ... 

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. 

This is a quahtative statement within a comparison therefore some rules have to be defined whether any possibly catalytic reaction fulfils this criterion or com-plexation of educt(s) or/and product(s) do(es) simply interfere with the stoichiometric reaction or some step thereof, also influencing the turnover kinetics. This means analyzing - measuring, calculating, predicting - the interaction of some metal ion within a metallo-protein on one hand and substrates, products on the other. Ostwald s definition of a catalyst implies the metal ion and with it its coordinative environment not be changed permanently by this transformation which in turn requires the metal binding properties of the substrate and product to differ from each other. 

The stoichiometry of the reaction defines the reaction elemental balance (atoms of H and Br, for instance) and therefore relates the number of molecules of reactants and products participating in the reaction. The stoichiometric coefficients are not unique for a given reaction, but their ratios are unique. For instance, for the FIBr synthesis above we could have written the stoichiometric equation Vs.H.2 + VaBrj <=> HBr as well. 

However, the number of unknowns and thus the mathematical problem to be solved is still quite large even for systems in which only a few reactions occur. To reduce the number of unknown variables, it is convenient to introduce the extent of reaction quantity. For a specific stoichiometric equation defining a particular reaction, the extent of reaction is defined by ... 

Usually when reaction paths are simulated, the irreversible reactant is an unstable mineral or a suite of unstable minerals that is, the stoichiometry of the irreversible reaction is fixed. Evaporation poses a special problem in reaction path simulation because the stoichiometry of the irreversible reaction (defined by the aqueous solution composition) continually changes as other minerals precipitate (or dissolve). In the second problem (above) evaporation of seawater was simulated by irreversible addition of "sea salt", that is, a hypothetical solid containing calcium, magnesium, sodium, potassium, chloride, sulfate and carbon in stoichiometric proportion to seawater. The approach used was valid as long as intermediate details of the reaction path are not required. The reaction path during evaporation could be solved in PHRQPITZ by changing the stoichiometry of the irreversible reactant (altered "sea salt") incrementally between phase boundaries, but this method would be extremely laborious. 

Consider a system with N chemical components undergoing a set of M reactions. Define the A x M matrix of stoichiometric coefficients as... 

Clearly equation (13.6) preserves the stoichiometric relationships of equation (13.1). Clhemical equation (13.6) tells us that whenever c kmol of C are produced in the reaction defined by chemical equation (13.1), a kmol of chemical A and b kmol of chemical B are used up. 

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