Conversion and Extent of Reaction

Conversions are often used in the rate expressions rather than concentrations, as follows  

An alternate, but related, concept to the conversion is the extent or degree of advancement of the general reaction Eq. (1.1-3), which is defined as 

either conversion or extent of reaction can be used to characterize the amount of reaction that has occurred. For industrial applications, the conversion of a feed is usually of interest, while for other scientific applications, such as irreversible thermodynamics (Prigogine [4]), the extent is often more useful both concepts should be known. Further details are given by Boudart [5] and Aris [6]. 

In terms of the extent of reaction, the reaction rate Eq. (1.1-4) can be written 

With this rate, the change in moles of any species is, for a single reaction. 

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Since the basis is 1 mole of ethylbenzene fed, the concepts of fraction conversion and extent of reaction are interchangeable (X -... 

The variable that describes composition in Eqn. (3-5) is Nu the total moles of species i . It sometimes is more convenient to work problems in terms of either the extent of reaction or the fractional conversion of a reactant, usually the limiting reactant. Extent of reaction is very convenient for problems where more than one reaction takes place. Fractional conversion is convenient for single-reaction problems, hut can he a source of confusion in problems that involve multiple reactions. The use of all three compositional variables, moles (or molar flow rates), fractional conversion, and extent of reaction, wiU be illustrated in this chapter, and in Chapter 4. 

For a given feed (fixed C o, . ) and using conversion of key component as a measure of the composition and extent of reaction, the versus T plot has the general shape shown in Fig. 9.3. This plot can be prepared either from a thermodynamically consistent rate expression for the reaction (the rate must be zero at equilibrium) or by interpolating from a given set of kinetic data in conjunction with thermodynamic information on the equilibrium. Naturally, the reliability of all the calculations and predictions that follow are directly dependent on the accuracy of this chart. Hence, it is imperative to obtain good kinetic data to construct this chart. 

For those cases where the permeability of reactant A is in between those of the two products, B and C, both the conversion and extent of separation increase with increasing permeation rate or permeation to reaction rate ratio (Table 11.9). The corresponding optimal compressor load (recycle flow rate to feed flow rate) also increases with the rate ratio. The top (permeate) stream is enriched with the most permeable product (i.e., B) while the bottom (retentate) stream is enriched with the least permeable product (i.e., C). It is noted from Table 11.9 that the optimal compressor loads for achieving the highest conversion and extents of separation can be quite different and a decision needs to be made for the overall objective. 

The feed to the reactor contains 7.80 mole% CHi, 19.4% O2, and 72.8% N2. The percentage conversion of methane is 90.0%, and the gas leaving the reactor contains 8 mol C02/mol CO. Carry out a degree-of-freedom analysis on the process. Then calculate the molar composition of the product stream using molecular species balances, atomic species balances, and extents of reaction. 

In this work, however, tests were desired to allow screening of hydrocaibon/catalyst combinations through measurenoenis of endotberm of reaction, extent of conversion, and identification of reaction products. However, the atmospheric-pressure bench scale test apparatus has been described elsewhere [11]. Parametric studies of the catalytic decomposition of n-heptane and cyclohexane were conducted to provide their stoichiometric analysis. The propo independent stoichiometric equations describing the catalytic decomposition of cyclohexane are ... 

Reactants are consumed and products are generated. If a reaction takes place within the system, you must be given (or look up) information about the reaction stoichiometry and extent of reaction. Or, perhaps the question is to calculate the extent of conversion given some of the process data. In any case, the fraction of feed converted to products is always an essential additional piece of information that helps determine values of the terms in Eq. (2.12). 

The reaction rates are kinetic equations, written in terms of measurement variables, such as concentration, partial pressure, and particularly, conversion or extent of reaction. The rate of product formation or transformation of the reactant is expressed in relation to the concentration of the limiting reactant and is valid for any closed or open system, at variable or constant volume. 

For viscous solutions, the assumptions of plug flow are not strictly valid. If the velocity profile is not flat, polymer solution near the tube wall will move more slowly than that near the center of the tube. Since the slow-moving polymer near the wall remains in the reactor longer, it will polymerize to a higher conversion (or extent of reaction) than the bulk material. This higher conversion will then compound the viscosity problem. Studies on the effect of this deviation from plug flow in tubular polymerization have to be carried out by Hamer and Ray [4,5]. 

Isothermal kinetic measurements fall into two categories method 1, in which the rate and extent of reaction at constant temperature are continuously monitored in the DSC and method 2, in which a partially cured sample is heated in the DSC to measure the residual heat of reaction. An advantage of method 1 is the simultaneous measurement of conversion and rate of conversion, which are necessary for some kinetic analyses. It should be noted that vitrification will occur during method 1 measurements if Tcure is less than Tg,. Method 2 has the advantage of simultaneous measurement of and conversion, from which the Tg-conversion relationship can be established. Both thermal and UV cure reactions can be measured by these methods. 

In the preceding chapters we developed a mathematical representation for the progress of gas-solid reactions and showed how the time-dependent conversion or extent of reaction can be related to the various parameters that characterize the system. Many of these parameters, such as the reaction rate constant (or more precisely the parameters appearing in the rate expression) and pore diffusion coefficients, are quite specific to both the chemical composition and physical structure of the solid reactants and thus must be determined experimentally. 

Fig. 2.6. Dependence of enanhomeric excess on relative rate of reaction and extent of conversion with a chiral reagent in kinetic resolution. [Reproduced from J. Am. Chem. Soc. 103 6237 (1981) by permission of the American Chemical Society.]...

It is important to note that and C2 are quantitative descriptors of the gel effect which depend only on the monomer, temperature and reaction medium. The full description of given by equation (11), requires g and g2 which are functions of the rate of initiation and extent of conversion. The kinetic parameters used in these calculations and their sources are given in Table 1. All data are in units of litres, moles and second. Figure 5 shows the temperature dependencies of and C2 and Table 2 lists these and other parameters determined by fitting the model to the data in Figures 1-4. 

The high conversion test is operated to ensure that essentially complete conversion of the HBr is possible, and to study the fate of the feed contaminants. In this test, the conditions are selected to ensure complete conversion of the HBr. Several reaction pathways are then available to feed contaminants. They may undergo combustion, react with HBr, or react with the bromine formed. The extent of reaction via any of these pathways will depend on the nature of the contaminants and the temperature. Information concerning the fate of the contaminants can then be gained by analyzing the gas, bromine, and aqueous phases exiting the reactor. 

In the context of this study, the extent of reaction refers to the conversion of sites from active to inactive, and is given by Equation 6 (i.e., x = 1 for no conversion, x = 0 for total conversion). For a single site mechanism it can be shown easily that F(x) reduces to 1.0. Solution of Equation 7 and substitution into Equation 3 yields the expected result ... 

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. 

One can relate the extent of reaction to the fraction conversion by solving equations 1.1.4 and 1.1.7 for the number of moles of the limiting reagent nlim and equating the resultant expressions. 

What is the order of the reaction and the reaction rate constant The reverse reaction may be neglected. The volume of the solution as determined by the height of the meniscus in the capillary may be assumed to be a measure of the fraction conversion (i.e., the volume change is proportional to the extent of reaction). 

For reactor design purposes, the distinction between a single reaction and multiple reactions is made in terms of the number of extents of reaction necessary to describe the kinetic behavior of the system, the former requiring only one reaction progress variable. Because the presence of multiple reactions makes it impossible to characterize the product distribution in terms of a unique fraction conversion, we will find it most convenient to work in terms of species concentrations. Division of one rate expression by another will permit us to eliminate the time variable, thus obtaining expressions that are convenient for examining the effect of changes in process variables on the product distribution. 

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