Conversion, fractional equilibrium

The conversion to equilibrium is effected in the presence of a catalyst at a pressure of 300 bar. Assuming the behavior to remain ideal, calculate the fractional conversion for each reaction and hence the volume composition of the equilibrium mixture. 

Conversions between equilibrium constants and fractionation factors are more complicated, as it is often necessary to accoimt for molecular stoichiometry and symmetry. For a generic balanced isotopic exchange reaction,... 

C10-6)(T2-2982) +0.2599C10-9)(T3-2983) In terms of fractional conversion, the equilibrium constant is... 

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

Feed ethylbenzene with steam If the feed to the process consists of ethylbenzene diluted with steam in the ratio 15 moles steam 1 mole ethylbenzene, determine the new fractional conversion at equilibrium a e. 

The various symbols have the same meaning as in equation 6.7 X is the equilibrium concentration in solution of the ion originally in the exchanger, and k represents the reaction rate constant for the chosen direction of exchange. The fractional attainment of equilibrium is given by X/X whilst the fractional equilibrium conversion of the resin is equal to Xja. 

Similarly, the conversion (fraction of reactant transformed or converted) calculated from thermodynamic data would be the end point on a curve of conversion vs time such as that shown in Fig. 1-2. Again, curve A represents the case where the time required to reach equilibrium conditions is great, while in case B the equilibrium conversion is approached more rapidly and is attained essentially at a finite time. Curves A and B could apply to the same reaction the difference between them reflects the fact that in case B the rate has beeAjncreased, for example, by use of a catalyst. The rate of the reaction is initially increased over that for the uncatalyzed reaction, but the equilibrium conversion as shown in Fig. 1-2 is the same for both cases. 

Fructose Fructose, in the ketohexose form jS-o-fruc-tose (CgHi206), is produced from glucose by an isomerase enzyme (glucose-fructose isomerase), which converts glucose to fructose, and subsequent enrichment of the fructose fraction (equilibrium conversion is 50%), or isolation of fructose and crystallization. Products are high-fructose corn syrup, the most widely used monosaccharide sweetener, at 42, 55, and 90% fructose (with glucose, the other major component) and crystalline fructose. 

A catalyst is a material that accelerates a reaction rate towards thennodynamic equilibrium conversion without itself being consumed in the reaction. Reactions occur on catalysts at particular sites, called active sites , which may have different electronic and geometric structures than neighbouring sites. Catalytic reactions are at the heart of many chemical industries, and account for a large fraction of worldwide chemical production. Research into fiindamental aspects of catalytic reactions has a strong economic motivating factor a better understanding of the catalytic process... 

Equimolal proportions of the reactants are used. Thermodynamic data at 298 K are tabulated. The specific heats are averages. Find (1) the enthalpy change of reaction at 298 and 573 K (2) equilibrium constant at 298 and 573 K (3) fractional conversion at 573 K. 

Olefin metatheses are equilibrium reactions among the two-reactant and two-product olefin molecules. If chemists design the reaction so that one product is ethylene, for example, they can shift the equilibrium by removing it from the reaction medium. Because of the statistical nature of the metathesis reaction, the equilibrium is essentially a function of the ratio of the reactants and the temperature. For an equimolar mixture of ethylene and 2-butene at 350°C, the maximum conversion to propylene is 63%. Higher conversions require recycling unreacted butenes after fractionation. This reaction was first used to produce 2-butene and ethylene from propylene (Chapter 8). The reverse reaction is used to prepare polymer-grade propylene form 2-butene and ethylene ... 

After phase separation, two sets of equations such as those in Table A-1 describe the polymerization but now the interphase transport terms I, must be included which couples the two sets of equations. We assume that an equilibrium partitioning of the monomers is always maintained. Under these conditions, it is possible, following some work of Kilkson (17) on a simpler interfacial nylon polymerization, to express the transfer rates I in terms of the monomer partition coefficients, and the iJolume fraction X. We assume that no interphase transport of any polymer occurs. Thus, from this coupled set of eighteen equations, we can compute the overall conversions in each phase vs. time. We can then go back to the statistical derived equations in Table 1 and predict the average values of the distribution. The overall average values are the sums of those in each phase. 

Intelligent engineering can drastically improve process selectivity (see Sharma, 1988, 1990) as illustrated in Chapter 4 of this book. A combination of reaction with an appropriate separation operation is the first option if the reaction is limited by chemical equilibrium. In such combinations one product is removed from the reaction zone continuously, allowing for a higher conversion of raw materials. Extractive reactions involve the addition of a second liquid phase, in which the product is better soluble than the reactants, to the reaction zone. Thus, the product is withdrawn from the reactive phase shifting the reaction mixture to product(s). The same principle can be realized if an additive is introduced into the reaction zone that causes precipitation of the desired product. A combination of reaction with distillation in a single column allows the removal of volatile products from the reaction zone that is then realized in the (fractional) distillation zone. Finally, reaction can be combined with filtration. A typical example of the latter system is the application of catalytic membranes. In all these cases, withdrawal of the product shifts the equilibrium mixture to the product. 

For AG = AH — TAS = 0 the conversion between the two spin states has achieved thermal equilibrium, and the fractions of both states have become equal, % = = 2 - The transition temperature may be thus defined as = AH/AS. 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

The degree of dissociation a is the equilibrium degree of conversion, i.e. the fraction of the number of molecules originally present that dissociated at the given concentration. The degree of dissociation depends directly on the given dissociation constant. Obviously a = [Bz+]/v+c = [Az ]/v c, [Bv+Av ] = c(l - a) and the dissociation constant is then given as... 

Fig. 5.65 Dependence of the solar conversion efficiency (CE) on the threshold wavelength (Ag) for a quantum converter at AM 1.2. Curve 1 Fraction of the total solar power convertible by an ideal equilibrium converter with no thermodynamic and kinetic losses. Curve 2 As 1 but the inherent thermodynamic losses (detailed balance and entropy production) are considered. Continuous line Efficiency of a regenerative photovoltaic cell, where the thermodynamic and kinetic losses are considered. The values of Ag for some semiconductors are also shown (according to J. R. Bolton et al.)... 

Table 6.14 Equilibrium conversions and product mole fractions for the manufacture of hydrogen.

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. 

If nonstoichiometric amounts of reactants are present in the initial system, the presence of excess reactants tends to increase the equilibrium fractional conversion of the limiting re-... 

If converted into plots of fraction conversion versus time, these forms give rise to a characteristic S shape. These plots first rise, showing autoacceleration as the rate increases, then pass through an inflection point as the rate reaches a maximum, and finally taper off so that the fraction conversion approaches unity or its equilibrium value as the time approaches infinity. 

Other reactions will have somewhat different forms for the curve of Qq versus T. For example, in the case of a reversible exothermic reaction, the equilibrium yield decreases with increasing temperature. Since one cannot expect to exceed the equilibrium yield within a reactor, the fraction conversion obtained at high temperatures may be less than a subequilibrium value obtained at lower temperatures. Since the rate of energy release by reaction depends only on the fraction conversion attained and not on the position of equilibrium, the value of Qg will thus be lower at the higher temperature than it was at a lower temperature. Figure 10.2 indicates the general shape of a Qg versus T plot for a reversible exothermic reaction. For other reaction networks, different shaped plots of Qg versus T will exist. 

---