Extent of reaction defined

Whether A is the limiting reactant or not, it may be convenient to normalize by means of the extent of reaction, , defined for any species involved in the reaction by ... 

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... 

Although free energies are related to equilibrium constants, it is concentrations that are either ultimately desired or experimentally determined. There are many ways to perform equilibrium calculations. We will approach such calculations through the extent of reaction, , defined in Eq. (5), because all concentrations can be expressed in terms of this single variable. In addition, use of the extent of the reaction allows us to perform equilibrium calculations in a very systematic manner. At equihbrium, the extent of reaction becomes the extent of reaction... 

The subscript r is used to denote changes associated with a chemical reaction. Although symbols such as ArH should denote the integral enthalpy of reaction, ArH = H( 2) — H( i)> in practice this symbol is usually used to denote the change divided by the amount transferred, i.e. the change per extent of reaction, defined by the equation... 

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. 

Laplacian operator with rj as the position coordinate X local extent of reaction defined by Eq. (4.3.115)... 

The extent of reaction is defined in tenns of the amount n. of species B. (i.e. the amount of substance or enplethy n., usually expressed in moles [10]) ... 

In the reaction kinetics context, the tenn nonlinearity refers to the dependence of the (overall) reaction rate on the concentrations of the reacting species. Quite generally, the rate of a (simple or complex) reaction can be defined in temis of the rate of change of concentration of a reactant or product species. The variation of this rate with the extent of reaction then gives a rate-extent plot. Examples are shown in figure A3.14.1. In... 

It is convenient to define the fraction of reacted functional groups in a reaction mixture by a parameter p, called the extent of reaction. Thus p is the fraction of A groups which have reacted at any stage of the process, and 1 - p is the fraction unreacted ... 

As with other problems with stoichiometry, it is the less abundant reactant that limits the product. Accordingly, we define the extent of reaction p to be the fraction of A groups that have reacted at any point. Since A and B groups... 

For this reason, whenever there is a single reaction taking pldce in the yth MSA, no extent of reaction is defined. Instead the fractional saturation, uj, is employed. 

As mentioned earlier, the extent of reaction is defined for all reactions except the first one. Hence, we define 2 as the extent of reaction for Eq. (8.16). Equation (8.4) can now be used to describe the compositions of the reactive species as a function of I2 and the admissible compositions, i.e.. 

Let represent amount of substance i in moles. Then the extent of reaction is defined by Eq. (1-8)... 

Define the percentage extent of reaction for Scheme IX if F = cb + 2cc is the experimental measure of the progress of the reaction. 

Hulbert [77] points out that, in general, attempts to include an allowance for the influence of particle size variations in the reactant mixtures on kinetic analyses using the above equations have been unsatisfactory because some of the parameters are not readily defined. Kapur [42], working with powders of known crystal size distribution, indicated that the overall extent of reaction can be estimated by a summation of the individual contributions from each size fraction and thus the best kinetic fit determined. 

The extent of reaction, E, is defined by Eq. (2-59). It represents the fractional progress of reaction from beginning to end. As seen from the alternative form in Eq. (2-60), it is easily read off the profile of Y, versus time. 

An analogous situation occurs in the catalytic cracking of mixed feed gas oils, where certain components of the feed are more difficult to crack (less reactive or more refractory) than the others. The heterogeneity in reactivities (in the form of Equations 3 and 5) makes kinetic modelling difficult. However, Kemp and Wojclechowskl (11) describe a technique which lumps the rate constants and concentrations into overall quantities and then, because of the effects of heterogeneity, account for the changes of these quantities with time, or extent of reaction. First a fractional activity is defined as... 

The two time constants x and tV2 define time intervals in which a specific extent of reaction has been completed. In some applications one may wish to define a time point associated with a certain other extent of reaction completion. That is, how much time is required for the reaction to go to, say, 75% or 90% completion. This can be calculated using rearranged forms of Equations (A.16) through (A.21). For convenience, in Table Al.l we tabulate the extent of reaction completion for different time intervals, as multiples of x and ty2. 

The agreement between the experimental and calculated values of Ce, is excellent. The data shown in Figure 2 are for a constant bake time of 17 minutes. The upper and lower limits on define a cure window. The cure window for the low solids coating is 50 C. The model was further tested by measuring extents of reaction and temperature profiles for samples attached to different parts of a car body which passed through a pilot plant oven. This simulation tested the model under conditions where the substrate temperatures were far from constant. As shown in Table II, the agreement between the experimental and calculated values of Ce is again excellent. 

Consider a closed system (i.e., one in which there is no exchange of matter between the system and its surroundings) where a single chemical reaction may occur according to equation 1.1.3. Initially there are ni0 moles of constituent At present in the system. At some later time there are n moles of species At present. At this time the molar extent of reaction is defined as... 

The variable / depends on the particular species chosen as a reference substance. In general, the initial mole numbers of the reactants do not constitute simple stoichiometric ratios, and the number of moles of product that may be formed is limited by the amount of one of the reactants present in the system. If the extent of reaction is not limited by thermodynamic equilibrium constraints, this limiting reagent is the one that determines the maximum possible value of the extent of reaction ( max). We should refer our fractional conversions to this stoichiometrically limiting reactant if / is to lie between zero and unity. Consequently, the treatment used in subsequent chapters will define fractional conversions in terms of the limiting reactant. 

The reaction rate is properly defined in terms of the time derivative of the extent of reaction. It is necessary to define k in a similar fashion in order to ensure uniqueness. Definitions in terms of the various rt would lead to rate constants that would differ by ratios of their stoichiometric coefficients. 

Here, ac = papb> where pa and pb are the extents of reaction at gelation of A and B groups, respectively, and Xab is the ringforming parameter defined by the equation... 

---