Conversion variable

Each reactor was heated in an enclosing furnace controlled by an Omega temperature controller. All temperatures were monitored by l/16in Inconel-sheathed thermocouples mounted on the feed side Details regarding sampling and analysis are reported in [2]. The entire reactor/analytial system was configured to operate for long periods of time (lyr) under fixed-conversion variable-temperature conditions. 

The only experimental number which is properly referred to as the activation energy is that obtained from rate constants extrapolated to zero conversion. However, a reasonable approximation to this value can be obtained by comparing integral rate constants at constant conversion, variable temperature and residence time. Values of Eact so determined tend to be in the high range (65-80 kcal/mol). 

The conversion variable X does not have much meaning in flow systems not at steady state, owing to the accumulation of reactant. However, here the space time is relatively short (t = 0.02 h) in comparison with the time of decay t = 0.5 h. Consequently, we can assume a quasi-steady state and consider the conversion as defined by Equation (ElO-5.10) valid. Because the catalyst decays in less than an hour, a fluidized bed would not be a good choice to carry out this reaction. 

The above equation may also be written in terms of the conversion variable X since... 

HWI.12 DEGREE OF DISSOCIATION Express the Ky in terms of the equilibrium conversion variable z. Initially,... 

Note that the molar e.xtent of reaction is not a fractional conversion variable, and therefore its value is not restricted to lie between 0 and I. As defined here X, which has units of number... 

If we neglect distinctions among ortho-, meta- and para-products (no information given), then x is the total conversion variable. These reactions were carried out in the liquid phase, so volume changes associated with reaction are negligible. The rate equation to try first is second-order irreversible... 

Nomenclature is listed at the end of this chapter.) Equation 1 assumes that the volume of the reacting system remains constant, a reasonable assumption in Immoblllzed-catalyst studies. The rate is determined by taking the slope of a plot of concentration of substrate versus time. For reactions which Involve a gas phase and a liquid phase reactant, in which the gas phase reactant is held at a constant pressure, the total moles of liquid substrate can be related to the consumption of the gas phase reactant. The rate of substrate conversion is then found by making use of the conversion variable, X, defined as... 

Equation 14 can be solved analytically for the initial reaction rate of a metal ion catalyzed reaction between phenol and methanal. This yields an equation for both methanal and phenol consumption that is only dependent on one conversion variable. Figure 4 shows the dependence of the rate constants on the ionic radius of the hydrated cation, based on equation 14. The formation of the chelate complex between methanal, phenol and the metal ion is the slowest reaction step (see Scheme 3). Therefore, one can observe a second order kinetic law analyzing the kinetic data. 

Use is frequendy made of the conversion variable x related to -V by the relation ... 

Thus the rate of reaction at constant volume is seen to be equal to the derivative of the conversion variable x with respect to time. 

Lyapunov function (varies) volume of reaction mixture (m ) conversion (-) variables (varies)... 

IG, AH, zlS for chair-chair conversion variable temperature study spectrum reproduced, " i Energetics of ring conformational change estimated. 

There are numerous conversion variables that can be employed in developing solutions to rate equations. These as well as other conversion-related terms will be addressed in the next chapter. 

Cases 2 (Equation 4.21) and 3a (Equation 4.22) in the previous section are reviewed in order to present analytical solutions to the rate equation using a and X as the conversion variables. Several other rate expressions are also examined— some of which appeared in the previous section. 

Solutions to several rate expressions are presented below in terms of the conversion variable a. Note, however, that the conversion variable X will be primarily employed throughout the remainder of the text. For case (2), it was shown... 

Two subjects of concern to the practicing engineer involved with chemical reactions and/or chemical teactors are stoichiometry and (a topic briefly inboduced last chapter) conversion variables. The former topic is primarily concamed with the balancing" of the chemical reaction of concern. The latter topic provides information on the extent of the reaction, i.e., the degree to which the reactant has been converted in the product formed. Interestingly, the two topics are interrelated, and to a certain degree, complement each other. It is for this reason that both are discussed in this chapter. 

TTiis essentially places every quantity on a per mole of A" basis. The aforementioned conversion variable introduced in Chapter 4, can then be defined as the number of... 

This chapter serves to introduce the general subject of stoichiometry and conversion variables, which in a very real sense, is an extension of the material discussed in the previous chapter. To simplify the presentation to follow, some of the textual matter and illustrative examples will focus on combustion reactions because of the author s experience in this field. Topics to be reviewed include ... 

Stoichiometry Conversion Variables Volume Correction Factor Yield and Selectively... 

As discussed in the previous chapter, the two most common conversion variables employed in chemical reactor/kinetic studies are a and X. The term a is employed to represent the change in the number of moles of a particular species due to chemical reaction. The most conunonly used conversion variable is X, and it is used to represent the change in the number of moles of a particular species (say A) relative to the number of moles of A initially present or initially introduced (to a flow reactor). Thus,... 

Other conversion (related) variables include Na, the number of moles of species A at some later time (or position) C, the concentration of A at some later time (or position) X, the moles of A reacted/toto/ moles initially present Note that all of the above conversion variables can also be based on mass, but this is rarely employed in practice. All of these variables are further defined and considered in the development that follows. 

The author has defined other conversion variables that can be employed to describe the extent of the reaction. These are listed below for reactant/species A without any explanatory details ... 

To illustrate the difference between these conversion variables, consider once again—as in the previous chapter—the elementary irreversible first order reaction... 

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