Second-order irreversible system

As discussed later, the reaction-enhancement factor ( ) will be large for all extremely fast pseudo-first-order reac tions and will be large tor extremely fast second-order irreversible reaction systems in which there is a sufficiently large excess of liquid-phase reagent. When the rate of an extremely fast second-order irreversible reaction system A -t-VB produc ts is limited by the availabihty of the liquid-phase reagent B, then the reac tion-enhancement factor may be estimated by the formula ( ) = 1 -t- B /VCj. In systems for which this formula is applicable, it can be shown that the interface concentration yj will be equal to zero whenever the ratio k yV/k B is less than or equal to unity. 

Figure 14-10 illustrates the gas-film and liquid-film concentration profiles one might find in an extremely fast (gas-phase mass-transfer limited) second-order irreversible reaction system. The solid curve for reagent B represents the case in which there is a large excess of bulk-liquid reagent B. The dashed curve in Fig. 14-10 represents the case in which the bulk concentration B is not sufficiently large to prevent the depletion of B near the liquid interface and for which the equation ( ) = I -t- B /vCj is applicable. 

The F(t) curve for a system consisting of a plug flow reactor followed by a continuous stirred tank reactor is identical to that of a system in which the CSTR precedes the PFR. Show that the overall fraction conversions obtained in these two combinations are different when the reactions are other than first-order. Derive appropriate expressions for the case of second-order irreversible reactions and indicate how the reactors should be ordered so as to maximize the conversion achieved. 

The occurrence of steady-state multiplicity in gas-liquid CSTRs has been demonstrated in experimental (9) and theoretical investigations (cf., 10). The irreversible second-order reaction system, in particular, has been treated extensively in several theoretical studies (10-15). These studies are however based on neglecting energy and material losses which result from evaporation of the liquid. 

Now just what is the importance of micromixing in chemical reaction systems The question is perhaps best answered using a famous example from the paper of Danckwerts cited above. Consider the isothermal, second-order irreversible reaction A + B C, carried out homogeneously and at constant volume. The initial concentrations of A and B, Cao and Cbo, are set in the ratio... 

Observe that this set of reactions is similar to the BTX system presented in Chapter 1, if ethylene and hydrogen are omitted. The kinetics of both reactions in Equation 5.1a is first-order irreversible, whereas Equation 5.1b is second-order irreversible. Thus, for component A,... 

Hie second-order reversible system will be described next and the simpler irreversible system will be developed later as a special case of the reversible one. This reversible system can be described by... 

Pyrolysis of more complex molecules proceeds via production of free radicals. Then formula (4.5) fails, because reactions of creation and recombination of radicals in these systems are irreversible. Therefore, the steady-state concentration of active particles in these systems depends on conditions of pyrolysis, determining the first or the second order of recombination of active particles, and is governed by the following equations [8]... 

The schemes considered are only a few of the variety of combinations of consecutive first-order and second-order reactions possible including reversible and irreversible steps. Exact integrated rate expressions for systems of linked equilibria may be solved with computer programs. Examples other than those we have considered are rarely encountered however except in specific areas such as oscillating reactions or enzyme chemistry, and such complexity is to be avoided if at all possible. 

It should be reminded here that the most interesting feature of the original ZGB-model is the existence of kinetic phase transitions. Denoting the mole fraction of CO in the gas phase by Yco (and therefore Yqo2 = 1 - Yco), one finds a reactive interval 0.395 = y < Yco < Vi = 0.525 [2] in which both particle types are coexisting on the surface. For Yco < V and for Yco > 2/2 the surface is completely covered by O2 or CO, respectively. The phase transitions are found to be of the second order at y and of the first order at 2/2 Because of the irreversible character the model describes a poisoned state from which the system cannot escape and reaction comes to a stop. 

These products can be viewed most simply and. in most cases, with sufficient as two-phase systems in which the dispersed panicles are steadily and irreversibly aggregating according to a second-order rale law. Thus, where C is the number of particles per cubic centimeter Ian aggregate of many primary particles being counted as one panicle) at time I. and where Co is the number of particles per cubic centimeter al zero time, and A is a constant. C depends on t according to... 

This is the most common mode of addition. For safety or selectivity critical reactions, it is important to guarantee the feed rate by a control system. Here instruments such as orifice, volumetric pumps, control valves, and more sophisticated systems based on weight (of the reactor and/or of the feed tank) are commonly used. The feed rate is an essential parameter in the design of a semi-batch reactor. It may affect the chemical selectivity, and certainly affects the temperature control, the safety, and of course the economy of the process. The effect of feed rate on heat release rate and accumulation is shown in the example of an irreversible second-order reaction in Figure 7.8. The measurements made in a reaction calorimeter show the effect of three different feed rates on the heat release rate and on the accumulation of non-converted reactant computed on the basis of the thermal conversion. For such a case, the feed rate may be adapted to both safety constraints the maximum heat release rate must be lower than the cooling capacity of the industrial reactor and the maximum accumulation should remain below the maximum allowed accumulation with respect to MTSR. Thus, reaction calorimetry is a powerful tool for optimizing the feed rate for scale-up purposes [3, 11]. 

Nernstian boundary conditions, or those for quasireversible or irreversible systems. All of these cases have been analytically solved. As well, there are two systems involving homogeneous chemical reactions, from flash photolysis experiments, for which there exist solutions to the potential step experiment, and these are also given they are valuable tests of any simulation method, especially the second-order kinetics case. 

Inasmuch as T+ continously disappears from the system, being consumed in an acid-irreversible hydrolysis, as shown in Section IV, G, it is not possible to derive K from S+ concentration measurements. Therefore, the comparison was restricted to the rate constants of semiquinone decay. This reaction has second-order kinetics and the rate constants may be correlated with the influence of the substituents (see also Section IV,D). 

The type of chemical system that has received the most attention is the one in which the dissolved gas (component A) undergoes an irreversible second-order reaction with a reactant (component B) dissolved in the liquid. For the present, the gas will be taken as consisting of pure A, so that complications arising from gas film resistance can be avoided. The stoichiometry of the reaction is represented by... 

The only problem in the above is that many reactions involved in gas/liquid systems are second order, where there is reaction of a dissolved component with a second species in solution (normally at low concentration). In such cases, the reaction can not even be approximated as pseudo-first-order, and if the reaction and diffusion rates are of the same order of magnitude a zone of reaction will exist as shown in Figure 7.28. In most cases these reactions are irreversible, or nearly so, and a suitable reaction is... 

As a function of the molar flows in an open system, for an irreversible reaction of second order, we start from the same Equation 3.23 ... 

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