Calculation of equilibrium conversion

Whereas the equilibrium constant itself depends on the temperature only, the conversion at equilibrium depends on the composition of the original reaction mixture and, in general, on the pressure. If the equilibrium constant is very high, the reaction may be treated as being irreversible. If the equilibrium constant is low, however, it may be possible to obtain acceptable conversions only by using high or low pressures. Two important examples are the reactions  

in those cases in which reversibility of the reaction imposes a serious limitation, the equilibrium conversion must be calculated in order that the most advantageous conditions to be employed in the reactors may be chosen this may be seen in detail in the following example of the styrene process. A study of the design of this process is also very instructive in showing how the basic features of the reaction, namely equilibrium, kinetics, and suppression of byproducts, have all been satisfied in quite a clever way by using steam as a diluent. 

Let us suppose that we are setting out from first principles to investigate the dehydrogenation of ethylbenzene which is a well established process for manufacturing styrene  

There is available a catalyst which will give a suitable rate of reaction at 560°C. At this temperature the equilibrium constant for the reaction above is  

Feed pure ethylbenzene If a feed of pure ethylbenzene is used at 1 bar pressure, determine the fractional conversion at equilibrium. 

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Calculation of equilibrium conversions is based on the fundamental equations of chemical-reaction equilibrium, which in application require data for the standard Gibbs energy of reaction. The basic equations are developed in Secs. 15.1 through 15.4. These provide the relationship between the standard Gibbs energy change of reaction and the equilibrium constant. Evaluation of the equilibrium constant from thermodynamic data is considered in Sec. 15.5. Application of this information to the calculation of equilibrium conversions for single reactions is taken up in Sec. 15.7. In Sec. 15.8, the phase role is reconsidered finally, multireaction equilibrium is treated in Sec. I5.9.t... 

Calculation of Equilibrium Conversion. In practically all engineering calculations, the evaluation of the equilibrium constant is merely a means to an end. The ultimate goal is the calculation of how far a reaction can proceed—the equilibrium, conversion. 

Single Isothermal Reaction between Ideal Gases. One of the simplest cases involving a calculation of equilibrium conversion is for an isothermal reaction between ideal gases. Consider the reaction... 

Chang, T, Rousseau, R.W., and Kilpatrick, P.K. (1986) Methanol synthesis reactions calculation of equilibrium conversions using equations of state. Ind. Eng. Chem. Proc. Des. Dev., 25,477-481. 

Calculation of equilibrium conversions for heterogeneous systems and for multiple reactions is then outlined mostly through some typical examples. 

Assuming that the reaction mixture is an ideal solution, Eqn. (5.4-22) can be used to calculate the equilibrium conversion and composition of the reaction mixture ... 

Figure 6.4a shows the behavior of an endothermic reaction as a plot of equilibrium conversion against temperature. The plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as illustrated in Examples 6.1 and 6.2. If it is assumed that the reactor is operated adiabatically, a heat balance can be carried out to show the change in temperature with reaction conversion. If the mean molar heat capacity of the reactants and products are assumed constant, then for a given starting temperature for the reaction Ttn, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.4a. As the conversion increases, the temperature decreases because of the reaction endotherm. If the reaction could proceed as far as equilibrium, then it would reach the equilibrium temperature TE. Figure 6.4b shows how equilibrium conversion can be increased by dividing the reaction into stages and reheating the reactants...

Example 6.4 Following Example 6.2, the reactor temperature will be set to 700 K. Examine the effect of increasing the reactor pressure by calculating the equilibrium conversion of hydrogen at 1 bar, 10 bar, 100 bar and 300 bar. Assume initially ideal gas behavior. 

Assuming the reaction takes place at 1100 K and 20 bar, calculate the equilibrium conversion for a molar ratio of steam to methane in the feed of 3, 4, 5 and 6. Assume ideal gas behavior (K,p = 1, R = 8.3145 kJ-Kr -kmol-1). Thermodynamic data are given in Table 6.12. 

The equilibrium constant defined by eqn. (26) can be used to calculate the equilibrium conversion of reactants to products under specified conditions of temperature and pressure. The activity of a component X in a mixture of ideal gases, Ox, is given by... 

The data of Plank and Nace offer a convenient opportunity to investigate influences of the back reaction on the values of parameters, such as the value of the initial rate (dn/dt) and Ki obtained from Eqs. (28) and (29). Values of Kj for pyridine and styrene and values of initial rate were calculated from these equation with and without the back-reaction term (1 /K()PJPn- The results are summarized in Table X. Contrary to what might be anticipated, the integral reactor determination of dn/dt and Ki is surprisingly insensitive to the back reaction even at 85% of equilibrium conversion. This is in spite of the fact that this method of determination must become highly dependent on the back-reaction term when equilibrium conversion is approached sufficiently closely. An error... 

The calculated thermodynamic equilibrium conversions and product compositions for propylene disproportionation at 200 to 400 C were reported by Heckelsberg, Banks, and Bailey16). Atlar, Pis man, and Bakhshi-Zade 8S) made similar calculations for the 50 - 300 °C range. They noted that the equilibrium constants were independent of pressure. Banks and Regier 57) showed thermodynamic equilibrium conversions as a function of temperature for the various reactions involved in the synthesis of isoamylene via disproportionation (Fig. 3). A comparison of calculated equilibrium composition for... 

When the pressure of C02 in a carbonate-oxide system is equal to the equilibrium pressure pe, no net reaction occurs. When p < pe, the thermodynamic driving force favors oxide formation conversely, when p > pe, carbonate formation is favored. In the actual system the favored reaction may not occur, however, because kinetic factors prevent it. Particularly when p is not far from pe, the reaction may not proceed because some rate-limiting process, such as nucleus formation, is proceeding too slowly. The resulting spurious equilibria15 give rise to hysteresis effects, i.e., decomposition stops for some p < pe, recombination stops for some p > pe. It is for this reason that this work relies largely on thermodynamic methods for the calculation of equilibrium pressures. 

Related Calculations. While nothing is said above about kinetics, increasing the temperature very frequently changes the reaction rate favorably. Accordingly, in some exothermic-reaction situations, it may be worthwhile to sacrifice some degree of equilibrium conversion in favor of shorter reactor residence time by raising reaction temperature. Similarly, a pressure change may have an effect on kinetics that is contrary to its effect on equilibrium. 

P3-17g Calculate the equilibrium conversion and concentrations for each of the following reactions. 

The rate of energy transfer is important in determining the temperature distribution in reactors. Also, heats of reaction are significant in connection with equilibrium calculations. The following section deals with data and methods concerning heats of reaction, followed by a discussion of equilibrium conversion. 

Equation (5.58) enables the extent of conversion in a closed system below the upper limit of equilibrium conversion to be calculated as a function of time, when the rate constant and the equilibrium constant are known. It should be noted that Eq. (5.55) is applicable to reversible polymerization where the reacting monomers have equimolar initial concentrations and none of the reaction products is initially present in the reaction mixture. 

Assume that the reaction is reversible with Kq = 0.025 mol-/dm, and calculate the equilibrium conversion then redo (ai through (c) to achieve a conversion that is 90 of the equilibrium conversion. 

From the data of Tables II and III, it may be calculated that equilibrium conversion of hydrogen sulfide and sulfur dioxide to sulfur vapor in the secondary reactor is 78.0%. Cooling this gas stream to 140 °C (413 K) will lead to a liquid sulfur recovery of 76.1% of the secondary reactor output. Overall recovery in the two stages, then, may be calculated to be 94.9%. 

The results of this integral reactor study can be used to obtain information about the extent of the influence of the back reaction on the values of various parameters. The initial rate of cracking, dn/dt, where conversion was 56% of equilibrium conversion at 426° (800° F), has been calculated with and without the back reaction term (l/KE)PmPn in Equation (1). Neglecting the back reaction term leads to only an 8.6 % decrease in the calculated value of dn/dt] at 482° (900° F) at the highest conversion reported at 84% of equilibrium conversion, the rates differed by only 10.4%. Neglecting the back reaction term also gives only a small effect in the calculation of inhibitor equilibrium constants the constant for pyridine in the integral reactor in Table I would be only 4 % lower, while at 482° the constant for styrene where the conversion was 84% of equilibrium conversion (31 A. I. pellets) would be only 7.5% lower. 

The first question is one of thermodynamics the second is one of kinetics. The prediction of chemical reaction equilibria is one of the most useful aspects of thermodynamics. It is possible to calculate the equilibrium conversion of a given reaction from data taken on other reactions or from thermal data on the individual substances involved. 

The first step in reactor design is to calculate the equilibrium conversion as a function of temperature for a given pressure and feed ratio. For a bimolecular reversible reaction such as... 

In addition to the determination of enthalpies of reaction as a function of temperature and pressure, thermodynamics allows us to calculate the equilibrium conversion for single or complex reversible reactions at given conditions (temperature, pressure, and initial composition). 

Calculate the equilibrium conversion of the ammonia synthesis at 450 C and 600 atm taking into account the real behavior of the gas phase for stoichiometric amounts of nitrogen and hydrogen (N2/H2 = 1/3) ... 

It is required to scale up the reactor to process 600 m /h of fluid stream (at -196°C and 40 psi gauge pressure) containing 95% (mole) of O-H2 and achieve 95% of equilibrium conversion. The reactor diameter is 50 cm. Calculate the height of the packed bed reactor. Following correlations for packed bed hold good ... 

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