Equilibrium Conversion Liquid-Phase Reactions

To establish the relationship between conversion and the equilibrium constant in this case, we follow the same approach as for gas-phase reactions. The activity of component i of a liquid mixture is given by  

Except close to the critical point, the ratio of the two standard state fugacities can be calculated from  

While for a gas-phase reaction can be estimated from an equation of state, evaluation of requires knowledge of the values of the neces- 

If these parameters are not available, activity coefficients can be estimated with the UNIFAC method (see Problem 15.51). 

Evaluation of equilibrium conversions requires, because of the nonlinear character of the equation, an iterative scheme which can be initialized by assuming ideal solution behavior. 

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The equilibrium conversion can be increased by employing one reactant in excess (or removing the water formed, or both). b. Inerts concentration. Sometimes, an inert material is present in the reactor. This might be a solvent in a liquid-phase reaction or an inert gas in a gas-phase reaction. Consider the reaction system... 

The effect of external pressure on the rates of liquid phase reactions is normally quite small and, unless one goes to pressures of several hundred atmospheres, the effect is difficult to observe. In terms of the transition state approach to reactions in solution, the equilibrium existing between reactants and activated complexes may be analyzed in terms of Le Chatelier s principle or other theorems of moderation. The concentration of activated complex species (and hence the reaction rate) will be increased by an increase in hydrostatic pressure if the volume of the activated complex is less than the sum of the volumes of the reactant molecules. The rate of reaction will be decreased by an increase in external pressure if the volume of the activated complex molecules is greater than the sum of the volumes of the reactant molecules. For a decrease in external pressure, the opposite would be true. In most cases the rates of liquid phase reactions are enhanced by increased pressure, but there are also many cases where the converse situation prevails. 

The law of mass action, the laws of kinetics, and the laws ol distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equilibrium values otherwise, hydrolysis must occur The equations governing the rate of the reaction and the variation of the rale constant (as a function of such variables as temperature, catalyst strength, and proponion of reactants) describe Ihe kinetics of the liquid-phase reaction. The usual distillation laws must he modified, since must esterifications arc somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after Ihe extent of conversion has been determined. See also Distillation. 

Measurements of kinetic parameters of liquid-phase reactions can be performed in apparata without phase transition (rapid-mixing method [66], stopped-flow method [67], etc.) or in apparata with phase transition of the gaseous components (laminar jet absorber [68], stirred cell reactor [69], etc.). In experiments without phase transition, the studied gas is dissolved physically in a liquid and subsequently mixed with the liquid absorbent to be examined, in a way that ensures a perfect mixing. Afterwards, the reaction conversion is determined via the temperature evolution in the reactor (rapid mixing) or with an indicator (stopped flow). The reaction kinetics can then be deduced from the conversion. In experiments with phase transition, additionally, the phase equilibrium and mass transport must be taken into account as the gaseous component must penetrate into the liquid phase before it reacts. In the laminar jet absorber, a liquid jet of a very small diameter passes continuously through a chamber filled with the gas to be examined. In order to determine the reaction rate constant at a certain temperature, the jet length and diameter as well as the amount of gas absorbed per time unit must be known. 

As an example of a more complicated case than the two step sequence, we will discuss the esterification of a carboxylic acid with an alcohol. This is a very old and well-known category of homogeneous liquid-phase reactions. The esters of carboxylic acids are of an enormous practical importance for example, millions of tons of polyesters are produced via the reaction of dicarboxylic acids with diols and a wide variety of mono- and di-esters are used in the production of fine and specialty chemicals, such as pharmaceuticals, herbicides, pesticides and fragrances. The esterification reaction is a homogenous liquid-phase process where the limiting conversion of the reactants is determined by equilibrium. Typically the equilibrium constants of esterification reactions have values of 1-10, which implies that considerable amounts of reactants exist in the equilibrium mixture. 

NaA/polyelectrolyte multilayer-pervaporation membrane showing a greater stability under acidic conditions in comparison with a pure zeolite A membrane and maintaining a high selectivity for water over alcohols. For the same purpose, Kita et al. [181-183] proposed a zeolite T membrane, prepared by ex situ crystallization, for the per-vaporation-aided or vapor-permeation-aided esterification of acetic acid with ethanol. This membrane has a higher acid resistance and can be directly immersed in the liquid-phase reaction mixture. The conversions achieved exceed the equilibrium limit and reached to almost 100% after a stabilization period of 8 h. 

For the calculation of the chemical equilibrium conversion of reversible reactions in the liquid phase, the corresponding fugacities are required. For the description of fugacities in the liquid phase, in most cases activity coefficients yi are used (see Section 5.2) ... 

Is the reaction kinetically or equilibrium controlled The answer affects both the maximum sin e-pass conversion and the reactor configuration. The majority of gas- and liquid-phase reactions in the CPI are kinetically controlled. The most notable exceptions are the formation of methanol from synthesis gas, synthesis of ammonia from nitrogen and hydrogen, and the production of hydrogen via the water-gas shift reaction. 

Consider a gas-phase and a liquid-phase reaction of your choice and describe, in each case, the modifications that you would use in order to increase the equilibrium conversion. 

Product removal during reaction. Sometimes the equilibrium conversion can be increased by removing the product (or one of the products) continuously from the reactor as the reaction progresses, e.g., by allowing it to vaporize from a liquid-phase reactor. Another way is to carry out the reaction in stages with intermediate separation of the products. As an example of intermediate separation, consider the production of sulfuric acid as illustrated in Fig. 2.4. Sulfur dioxide is oxidized to sulfur trioxide ... 

The metathetic reaction occurs in the gas phase at relatively high temperatures (150°-350°C) with molybdenum or tungsten supported catalysts or at low temperature (=50°C) with rhenium-based catalyst in either liquid or gas-phase. The liquid-phase process gives a better conversion. Equilibrium conversion in the range of 55-65% could be realized, depending on the reaction temperature. ... 

The novel approach finally taken was to conduct the reaction and purification steps in a reactor-distillation column in which methyl acetate could be made with no additional purification steps and with no unconverted reactant streams. Since the reaction is reversible and equilibrium-limited, high conversion of one reactant can be achieved only with a large excess of the other. However, if the reacting mixture is allowed to flash, the conversion is increased by removal of the methyl acetate from the liquid phase. With the reactants flowing countercurrently in a sequence of... 

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. 

The volumetric ratio of the two liquid phases (j6 = Forg/ Faq) can affect the efficiency of substrate conversion in biphasic media. The biocatalyst stability and the reaction equilibrium shift are dependent on the volume ratio of the two phases [29]. In our previous work [37], we studied the importance of the nonpolar phase in a biphasic system (octane-buffer pH 9) by varying the volume of solvent. The ratio /I = 2/10 has been the most appropriate for an improvement of the yield of the two-enzyme (lipase-lipoxygenase) system. We found that a larger volume of organic phase decreases the total yield of conversion. Nevertheless, Antonini et al. [61] affirmed that changes in the ratios of phases in water-organic two-phase system have little effect upon biotransformation rate. 

The equilibrium conversion can be calculated from knowledge of the free energy, together with physical properties to account for vapor and liquid-phase nonidealities. The equilibrium conversion can be changed by appropriate changes to the reactor temperature, pressure and concentration. The general trends for reaction equilibrium are summarized in Figure 6.8. 

Due to chemical conversion in the liquid-phase mass transfer film the mass flux of A at the vapour-liquid interface and the mass flux of A at the boundary between this film and the liquid bulk will differ. Figures 9(a) and (b) show the values of these fluxes as a function of the reaction rate constant ko for equilibrium constants K = 1 and X = 100. The... 

When lipases are used for enzymatic conversions, the enzyme is mainly active at a phase boundary, which can effectively be provided by a membrane. Additionally, for conversions requiring two phases (e.g. fat splitting [84—86] and esterifications [87]), the membrane also keeps the two liquid phases (an oil and an aqueous phase, respectively) separated. This is schematically depicted in Fig. 13.11. The equilibrium reactions involved are... 

Reaction 1 is highly exothermic. The heat of reaction at 25°C and 101.3 kPa (1 atm) is in the range of 159 kj/mol (38 kcal/mol) of solid carbamate (9). The excess heat must be removed from the reaction. The rate and the equilibrium of reaction 1 depend gready upon pressure and temperature, because large volume changes take place. This reaction may only occur at a pressure that is below the pressure of ammonium carbamate at which dissociation begins or, conversely, the operating pressure of the reactor must be maintained above the vapor pressure of ammonium carbamate. Reaction 2 is endothermic by ca 31.4 kj/mol (7.5 kcal/mol) of urea formed. It takes place mainly in the liquid phase the rate in the solid phase is much slower with minor variations in volume. 

In this condenser, part of the stripper off-gases are condensed (the heat of condensation is used to generate low pressure steam). The carbamate formed and noncondensed NH3 and C02 are put into the reactor bottom and conversion of the carbamate into urea takes place. The reactor is sized to allow enough residence time for the reaction to approach equilibrium. The heat requited for the urea reaction and for heating the solution is supplied by additional condensation of NH3 and C02> The reactor which is lined with 316 L stainless steel, contains sieve trays to provide good contact between the gas and liquid phases and to prevent back-mixing. The stripper tubes are 25-22-2 stainless steel. Some strippers are still in service after almost 30 years of operation. 

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