Extents of reaction

For most of the reactor models in the flowsheet simulators, it is necessary to provide R chemical reactions involving C chemical species  

Consider a single reaction. In the stoichiometric reactor models, one specifies the fractional conversion, of key reactant k. 

For example, for the conversion of CO and H2 to CH3OH, assuming an initial feed of 100 kmol/hr CO and 600 kmol/hr H2 and 70% conversion of CO (the key component), using Eq. (6.4), the molar flow rates of the three components in the reactor effluent are  

For multiple reactions, the reactions must be specified as series or parallel. The former is equivalent to having reactors in series with the feed to each reactor, except the first, being the product from the previous reactor. Each reaction can have a different key reactant. For parallel reactions, it is preferable to specify the extent of reaction for each reaction, which results in  

A chemical reaction can be written as a general stoichiometric equation, in terms of reactants A, B, etc. and products R, S, etc.. 

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 

If the R equations are in canonical form with one noncomponent in each equation, it is convenient to calculate from experimental information for the noncomponents. The utility of this is illustrated in the next section. 

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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... 

One important application of the variable-time integral method is the quantitative analysis of catalysts, which is based on the catalyst s ability to increase the rate of a reaction. As the initial concentration of catalyst is increased, the time needed to reach the desired extent of reaction decreases. For many catalytic systems the relationship between the elapsed time, Af, and the initial concentration of analyte is... 

To verify the method a 1.00-mL aliquot of a standard solution of 40.0-ppm glucose was added to 1.00 ml of the combined reagents, requiring 34.6 s to produce the same extent of reaction. Determine the calculated concentration of glucose in the standard and the percent error for the analysis. 

By line 5, the reaction has reached 80% completion and the number average value of the degree of polymerization is 5. Although we have considered this slowly evolving polymer in terms of the extent of reaction, another question starts to be worrisome How long is this going to take ... 

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 ... 

The foregoing conclusion does not mean that the rate of the reaction proceeds through Table 5.1 at a constant value. The rate of reaction depends on the concentrations of reactive groups, as well as on the reactivities of the latter. Accordingly, the rate of the reaction decreases as the extent of reaction progresses. When the rate law for the reaction is extracted from proper kinetic experiments, specific reactions are found to be characterized by fixed rate constants over a range of n values. 

The question posed in Sec. 5.2-how long will it take to reach a certain extent of reaction or degree of polymerization —is now answered. As is often the case, the answer begins, It all depends. . . . ... 

In this section we turn our attention to two other questions raised in Sec. 5.2, namely, how do the molecules distribute themselves among the different possible species and how does this distribution vary with the extent of reaction Since a range of species is present at each stage of the polymerization, it is apparent that a statistical answer is required for these questions. This time, our answer begins, On the average. . . . ... 

Note that N /N gives the mole fraction of n-mers in a mixture at an extent of reaction p. As we have seen before, N = (1 - p) Aq, since each molecule in the mixture contains one unreacted A group. Incorporating this result into Eq. (5.25) yields... 

This compound is sometimes called a nylon salt. The salt polymer equilibrium is more favorable to the production of polymer than in the case of polyesters, so this reaction is often carried out in a sealed tube or autoclave at about 200°C until a fairly high extent of reaction is reached then the temperature is raised and the water driven off to attain the high molecular weight polymer. 

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... 

The extent of reaction p is again based on the group present in limiting amount. For the system under consideration, p is the fraction of A groups that have reacted. 

For an extent of reaction corresponding to a> a, gelation is predicted to occur. 

This equation describes the extent of reaction at which the system is predicted to gel. 

Equation (5.47) is of considerable practical utility in view of the commercial importance of three-dimensional polymer networks. Some reactions of the sort we have considered are carried out on a very large scale Imagine the consequences of having a polymer preparation solidify in a large and expensive reaction vessel because the polymerization reaction went a little too far Considering this kind of application, we might actually be relieved to know that Eq. (5.47) errs in the direction of underestimating the extent of reaction at... 

As an example of the quantitative testing of Eq. (5.47), consider the polymerization of diethylene glycol (BB) with adipic acid (AA) in the presence of 1,2,3-propane tricarboxylic acid (A3). The critical value of the branching coefficient is 0.50 for this system by Eq. (5.46). For an experiment in which r = 0.800 and p = 0.375, p = 0.953 by Eq. (5.47). The critical extent of reaction, determined by titration, in the polymerizing mixture at the point where bubbles fail to rise through it was found experimentally to be 0.9907. Calculating back from Eq. (5.45), the experimental value of p, is consistent with the value =0.578. 

For a fixed extent of reaction, the presence of multifunctional monomers in an equimolar mixture of reactive groups increases the degree of polymerization. Conversely, for the same mixture a lesser extent of reaction is needed to reach a specified with multifunctional reactants than without them. Remember that this entire approach is developed for the case of stoichiometric balance. If the numbers of functional groups are unequal, this effect works in opposition to the multifunctional groups. 

Use the molecular weight ratio to calculate the apparent extent of reaction of the caprolactam in these systems. Is the variation in p qualitatively consistent with your expectations of the effect of increased water content in the system Plot p versus moisture content and estimate by extrapolation the equilibrium moisture content of nylon-6 at 255 C. Does the apparent equilibrium moisture content of this polymer seem consistent with the value given in Sec. 5.6 for nylon-6,6 at 290°C ... 

At 270°C adipic acid decomposesf to the extent of 0.31 mol % after 1.5 hr. Suppose an initially equimolar mixture of adipic acid and diol achieves a value of p = 0.990 after 1.5 hr. Compare the expected and observed values of n in this experiment. Criticize or defend the following proposition The difference between the observed and expected values would be even greater than calculated above if, instead of the extent of reaction being measured analytically, the value of p expected (neglecting decomposition) after 1.5 hr were calculated by an appropriate kinetic equation. 

This situation is expected to apply to radical termination, especially by combination, because of the high reactivity of the trapped radicals. Only one constant appears which depends on the diffusion of the polymer radicals, so it cannot cancel out and may be the source of a dependence of the rate constant on the extent of reaction or degree of polymerization. 

Waste Destruction by Combustion Reaction. At the simplest level, waste destmction can be thought of as a first-order process involving the thermally excited mpture of a chemical bond. The time to achieve a given extent of reaction, T, can be found from... 

Vanadium phosphoms oxide-based catalysts ate unstable in that they tend to lose phosphoms over time at reaction temperatures. Hot spots in fixed-bed reactors tend to accelerate this loss of phosphoms. This loss of phosphoms also produces a decrease in selectivity (70,136). Many steps have been taken, however, to aHeviate these problems and create an environment where the catalyst can operate at lower temperatures. For example, volatile organophosphoms compounds are fed to the reactor to mitigate the problem of phosphoms loss by the catalyst (137). The phosphoms feed also has the effect of controlling catalyst activity and thus improving catalyst selectivity in the reactor. The catalyst pack in the reactor may be stratified with an inert material (138,139). Stratification has the effect of reducing the extent of reaction pet unit volume and thus reducing the observed catalyst temperature (hot... 

Effect of Structure. The rate at which different alcohols and acids are esterified as weU as the extent of the equiHbrium reaction are dependent on the stmcture of the molecule and types of functional substituents of the alcohols and acids. Specific data on rates of reaction, mechanisms, and extent of reaction are discussed in the foUowing. More details concerning stmctural effects are given in References 6, 13—15. 

Continuous esterification of acetic acid in an excess of -butyl alcohol with sulfuric acid catalyst using a four-plate single bubblecap column with reboiler has been studied (55). The rate constant and the theoretical extent of reaction were calculated for each plate, based on plate composition and on the total incoming material to the plate. Good agreement with the analytical data was obtained. 

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