Reaction progress variable conversion

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. 

The partial pressures of the various species are numerically equal to their mole fractions since the total pressure is one atmosphere. These mole fractions can be expressed in terms of a single reaction progress variable-the degree of conversion-as indicated in the following mole table. 

Apply rules that pertain to partial derivatives of the reaction-progress variable. As discussed in Example 4.4, the reaction-progress variable x is a measure of the extent to which a reaction has taken place. In the present case, the desired increase in equilibrium conversion to hydrogen and oxygen implies an increase in x. 

The checkers recovered a 1 1 mixture of tetraester and d1ketone from two runs conducted for 2.5 hr. When the reflux time was extended to 6 hr, complete conversion to product was attained. The reaction progress was monitored by gas evolution (Note 14). Some variability of reaction times is probably attributable to differences in stirring efficiency, temperature gradients, and/or particle size of the crystalline starting material. 

The fraction conversion/is an intensive measure of the progress of a reaction. It is a variable that is simply related to the extent of reaction. The fraction conversion of a reactant Aj in a closed system in which only a single reaction is occurring is given by... 

The Chemkin gas-phase subroutine library provides the evaluation of information about species, reactions, gas constants and units, equations of state, mole-mass conversion, thermodynamic properties, chemical production rates, equilibrium constants, rate of progress variables, and sensitivity parameters, along with the appropriate derivatives of the above quantities. 

In our search for favorable conditions for reaction we have considered how reactor type and size influence the extent of conversion and distribution of products. The reaction temperature and pressure also influence the progress of reactions, and it is the role of these variables that we now consider. 

For a single reaction this was called the fractional conversion X (or Xa), a number between zero and unity, because in a single reaction there is always a single variable that describes the progress of the reaction (we used Ca or X). For multiple reactants and multiple reactions there is not always a single species common to aU reactions to designate as A. However, there is fiequently a most valuable reactant on which to base conversion. We emphasize that by conversion Xj we mean the fractional conversion of reactant species j in all reactions. 

When the density varies, we need to find another variable to express the progress of a reaction. Earlier we defined the fractional conversion X for a single reaction, and in this chapter we defined the conversion of a reactant species for reactant A and Xj for reaction j. For the conversion in a reaction we need a different variable, and we shall use Xj (bold type), with the index i describing the reaction. We will first work our series and parallel reactions with these variables and then consider a variable-density problem. 

We divide the chapter into two parts Part 1 Mote Balances in Terms of Conversion, and Part 2 Mole Balances in Terms of Concentration, C,. and Molar Flow Rates, F,." In Pan 1, we will concentrate on batch reactors, CSTRs, and PFRs where conversion is the preferred measure of a reaction s progress for single reactions. In Part 2. we will analyze membrane reactors, the startup of a CSTR. and semibatch reactors, which are most easily analyzed using concentration and molar How rates as the variables rather than conversion. We will again use mole balances in terms of these variables (Q. f,) for multiple reactors in Chapter 6. 

Thus a in we see that the progress of a reaction can be completely described by the single variable of extent/degree of advancement or conversion. 

Different kinds of expressions for the molar ratio, n/no, can be used in Equation 3.118, depending on whether the extent of reaction or conversion is used as a variable and, whether one or several reactions are in progress in the system. For a system with a single chemical reaction, for instance, the alternative formulae 3.119 and 3.120 are available for the change in pressure ... 

Describing the Progress of a Reaction There are three variables that are commonly used to describe the composition of a reacting system, when a single reaction takes place. These three variables are the concentration of a species (usually the limiting reactant), the fractional conversion of a species (usually the limiting reactant), and the extent of reaction. The concentration of salicylic acid and the extent of reaction were used in Example 4-1. The application of each of these variables to Reaction (4-A) is discussed below. 

Once the value of the equilibrium constant K for the reaction under consideration - and the temperature of interest - is determined, the equilibrium conversion can be obtained. To this purpose we first express K in terms of compositions, which in turn are expressed in terms of the progress of the reaction variable (see Section 12.5.3). The latter is then calculated from the known K value and, consequently, the equilibrium conversion can be determined. 

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