Reaction thermodynamic equilibrium limited

All of the above reactions are reversible, with the exception of hydrocracking, so that thermodynamic equilibrium limitations are important considerations. To the extent possible, therefore, operating conditions are selected which will minimize equilibrium restrictions on conversion to aromatics. This conversion is favored at higher temperatures and lower operating pressures. 

The second reaction studied using lipase as catalyst was the reversible re-gioselective esterification of propionic acid and 2-ethyl- 1,3-hexanediol [180]. While the previously described reaction was almost irreversible, this reaction is equilibrium limited with an apparent equilibrium constant of 0.6 0.1. In addition, the accumulated water inhibits the enzyme. Therefore, only the removal of the water from the reaction zone assures high enzymatic activity as well as drives the reaction beyond thermodynamic equilibrium. Experiments with two... 

Combining chromatography with a chemical reactor can be used to achieve reaction and separation within the same reactor, and this can be used to generate products beyond the normal thermodynamic equilibrium limitation. 

Finally, there may be a few opportunities for closecoupling of reaction and adsorption systems to overcome thermodynamic-equilibrium limitations or to enhance selectivity by operating with low conversions per pass. Reaction types... 

Thermodynamic equilibrium limitations exist for the first reaction, but the other reactions can be considered as irreversible, at least in the region where the conversion to styrene is attractive. Only reaction 3 is considered in the first stage calculations because there is considerable experimental evidence that the other reactions occur to only a very small extent. 

Because of these factors, typical reactions occur in a limit of strong thermodynamic disequilibrium exactly opposite to the near thermodynamic equilibrium limit of the slow variable models. Consequently, forces acting... 

The reaction is further complicated by thermodynamic equilibrium limitations, as indicated in Table I. The condensation/dehydration of acetone to MO is limited to about 20% conversion at 120 C (16). However, there is no equilibrium limitation to the overall acetone-to-MIBK reaction. This, coupled with the possibility of numerous thermodynamically favorable side reactions that are also acid/base-catalyzed (Fig. 1), suggests the need to balance the acid/base and hydrogenation properties of the selected catalyst. 

Generally, three phase fixed bed reactors are operated with concurrent downflow of gas and liquid in the trickling regime (trickle-bed reactor). Countercurrent operation is less frequent as in this case, the possible ranges of liquid and gas flow rates are very narrow. It is used when thermodynamic equilibrium limits the extent of reaction. 

Methane is unique among hydrocarbons in being thermodynamically stable with respect to its elements. It follows that pyrolytic reactions to convert it to other hydrocarbons are energetically unfavourable and will be strongly equilibrium-limited. This is in marked contrast to the boranes where mild thermolysis of B2H6 or B4H10, for example, readily yields mixtures of the higher boranes (p. 164). Vast natural reserves of CH4 gas exist but much is wasted... 

The synthetic utility of the alkene metathesis reaction may in some cases be limited because of the formation of a mixture of products. The steps of the catalytic cycle are equilibrium processes, with the yields being determined by the thermodynamic equilibrium. The metathesis process generally tends to give complex mixtures of products. For example, pent-2-ene 8 disproportionates to give, at equilibrium, a statistical mixture of but-2-enes, pent-2-enes and hex-3-enes ... 

Membranes can be applied to catalysis in different ways. In most of the literature reports, the membrane is used on the reactor level (centimeter to meter scale) enclosing the reaction mixture (Figure 10.3). In most cases, the membrane is used as an inert permselective barrier in an equilibrium-limited reaction where at least one of the desired products is removed in situ to shift the extent of the reaction past the thermodynamic equilibrium. 

If a detailed reaction mechanism is available, we can describe the overall behavior of the rate as a function of temperature and concentration. In general it is only of interest to study kinetics far from thermodynamic equilibrium (in the zero conversion limit) and the reaction order is therefore defined as ... 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

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. 

For reversible reactions one normally assumes that the observed rate can be expressed as a difference of two terms, one pertaining to the forward reaction and the other to the reverse reaction. Thermodynamics does not require that the rate expression be restricted to two terms or that one associate individual terms with intrinsic rates for forward and reverse reactions. This section is devoted to a discussion of the limitations that thermodynamics places on reaction rate expressions. The analysis is based on the idea that at equilibrium the net rate of reaction becomes zero, a concept that dates back to the historic studies of Guldberg and Waage (2) on the law of mass action. We will consider only cases where the net rate expression consists of two terms, one for the forward direction and one for the reverse direction. Cases where the net rate expression consists of a summation of several terms are usually viewed as corresponding to reactions with two or more parallel paths linking reactants and products. One may associate a pair of terms with each parallel path and use the technique outlined below to determine the thermodynamic restrictions on the form of the concentration dependence within each pair. This type of analysis is based on the principle of detailed balancing discussed in Section 4.1.5.4. 

The hydrogen producing reactions are limited by thermodynamic equilibrium. The reactions must take place under carefully controlled external firing, with heat transfer taking place from the combustion gas in the firebox to the process gas in the catalyst-filled tubes. Carbon monoxide in the product gas is converted almost completely to hydrogen in the downstream catalytic reactor. 

Natural gas is reacted with steam on an Ni-based catalyst in a primary reformer to produce syngas at a residence time of several seconds, with an H2 CO ratio of 3 according to reaction (9.1). Reformed gas is obtained at about 930 °C and pressures of 15-30 bar. The CH4 conversion is typically 90-92% and the composition of the primary reformer outlet stream approaches that predicted by thermodynamic equilibrium for a CH4 H20 = 1 3 feed. A secondary autothermal reformer is placed just at the exit of the primary reformer in which the unconverted CH4 is reacted with O2 at the top of a refractory lined tube. The mixture is then equilibrated on an Ni catalyst located below the oxidation zone [21]. The main limit of the SR reaction is thermodynamics, which determines very high conversions only at temperatures above 900 °C. The catalyst activity is important but not decisive, with the heat transfer coefficient of the internal tube wall being the rate-limiting parameter [19, 20]. 

Finally, we present the results of the case studies for Eley-Rideal and LH reaction mechanisms illustrating the practical aspects (i.e. convergence, relation to classic approximations) of application of this new form of reaction rate equation. One of surprising observations here is the fact that hypergeometric series provides the good fit to the exact solution not only in the vicinity of thermodynamic equilibrium but also far from equilibrium. Unlike classical approximations, the approximation with truncated series has non-local features. For instance, our examples show that approximation with the truncated hypergeometric series may supersede the conventional rate-limiting step equations. For thermodynamic branch, we may think of the domain of applicability of reaction rate series as the domain, in which the reaction rate is relatively small. 

In converter passes downstream of the first pass, exit temperatures are limited by thermodynamic equilibrium to around 500°C or less. To obtain optimum conversion, the heats of reaction from succeeding converter passes are removed by superheaters or air dilution. The temperature rise of the process gas is almost direcdy proportional to the S02 converted in each pass, even though S02 and 02 concentrations can vary widely. 

So far this discussion has covered the effect of kinetics on reaction selectivity. However, it is important to realise that selectivity can also be determined by thermodynamics. It is thus necessary to write kinetics expressions that ensure the thermodynamic limitations are fulfilled for reactions where thermodynamic limitation is likely. For example, if the experiment shown in Fig. 12 were continued to higher the temperature, the CO conversion would eventually fall off with increasing temperature due to the water gas shift reaction reaching equilibrium. 

The NO oxidation to N02 is a reversible reaction limited by thermodynamic equilibrium. The typical dependence of the N02 outlet concentration on temperature is shown in Fig. 13. At low temperatures, N02 is thermodynamically more stable than NO but the reaction rate is rather slow. At higher temperatures, the reaction rate increases, but concurrently the N02 formation becomes limited by thermodynamic equilibrium. Thus, the outlet N02 concentration from the DOC typically exhibits a maximum at intermediate temperatures. 

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