K for a Multiphase Reaction

Concentration expressions are never included in equilibrium constants for the following materials in the reactions being studied pure solids pure liquids and solvents in dilute solutions. 

A molecular pure solid contains a fixed number of molecules within a given volume and hence the molecular concentration within the solid is constant and does not vary. Provided there is always some solid present, the overall concentration (Frame 40) or activity (Frame 39) remains unchanged during reactions in which the solid is either reacted (and hence removed) or formed (and hence increased) or when further solid is added. A similar situation applies in the case of pure liquids. 

Similarly, the concentration (activity) of solvents in dilute solutions is (virtually) unchanged during reactions and thus their concentration (activity) can be regarded as being constant. The constant concentrations of solids, liquids or solvents are therefore, effectively absorbed (i.e. are included) within the equilibrium constant itself. 

Thus consider the reaction of the liquid drying agent thionyl chloride, SOCI2 and liquid water it seeks to dry (the two liquids are immiscible)  

Equilibrium constant, K is written in terms of activities (and partial pressure). 

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Explicit expressions for the ratio (k /k ) of a multiphase reaction product layer have been presented in the literature, see, for example, [H. Schmalzried (1981)]. If k(2) of the second kind, which depends only on the properties of phase p, is calculated or measured for every phase p individually, it is possible to derive (from all NiiP, A p, and the molar volumes Vp) the rational rate constant k p] of the first kind, and thus eventually k in Eqn. (6.41). 

A Xi is the reaction layer thickness in the case where it is formed in a reaction starting with the pure reactants. A Xj, on the other hand, is the reaction layer thickness in the case of a reaction where the reaction layer under consideration is formed from the saturated adjacent phases. These definitions hold for a one-phase reaction product as well as for a multiphase reaction product. Since the average diffusion coefficients in a certain reaction layer (phase k) cannot depend upon the starting material if local equilibrium prevails, one may return to eqs. (7-35) and (7-36) in order to obtain a relation between the reaction rate constants of the first and second kind. By taking into account the definitions, the relation between the two rate constants for a reaction product with phases of very narrow ranges of homogeneity can be shown to be ... 

Kobayashi, S. J0rgensen, K. A. (Eds.) Cycloaddition Reactions in Organic Synthesis, Wiley-VCH, Weinheim, Germany, 2002 Carmichael, A. J., Earle, M. J., Holbrey, J. D. et al. The Heck reaction in ionic liquids a multiphasic catalyst system, Org. Lett., 1999, 1, 997-1000 Forsyth, S. A., Gunaratne, H. Q. N. Hardacre, C. et al. Utilisation of ionic liquid solvents for the synthesis of Lily-of-the-Valley fragrance beta-Lilial (R), 3-(4-t-butylphenyl)- 2-methylpropanal, J. Mol. Catal. A-Chem., 2005, 231(1-2), 61-66. 

K. Bouche et al.,117 W. Mayr et a/.,118 S. Wohlert and R. Bormann119 and other researchers (see Refs 6, 11, 13, 120-125), it can be concluded that the simultaneous occurrence and the more so the simultaneous parabolic growth of more than two compound layers in reaction couples of multiphase binary systems is an exception rather than the rule. Contrary to these observations, the diffusional considerations usually start from the quite opposite point of view - the layers of all chemical compounds present on the phase diagram of a multiphase binary system must occur and grow simultaneously from the very beginning of interaction between initial substances (see, for example, Ref. 22). 

The low-temperature kinetics data of these early difficult experiments did not have the time or spectral resolution to consider these possibilities. However, there is now an excellent set of temperature-dependent kinetics data for the similar bacterium Rp. viridis [16, 17]. These data clearly show multiphasic kinetics that can be resolved into very fast, fast and slow phases, most of which slow with temperature roughly an order of magnitude before reaching a temperature-independent plateau. What does change dramatically with temperature is the contribution of each of these phases, with the fast phases falling away dramatically at a temperature around 210 K for the wild-type Rp. viridis. Thus, the overall result is a dramatic decrease in half-time of the reaction with temperature, as Devault and Chance observed. 

Operating MSR under novel process windows, the key performance parameters can be increased by a few orders of magnitude. A few examples are presented here. In the case of esterification of phthalic anhydride with methanol 53-fold higher reaction rate between 1 and 110 bar for a fixed temperature of 333 K was observed [14]. A multiphase (gas/liquid) explosive reaction of oxidation of cyclohexane under pure oxygen at elevated pressure and temperature (>200 C and 25 bar) in a transparent silicon/glass MSR increased the productivity fourfold. This reaction under conventional conditions is carried out with air [15]. Another example is for the synthesis of 3-chloro-2-hydroxypropyl pivaloate a capillary tube of 1/8 in. operated at 533 K and 35 bar, superheated pressurized processing much above the boiling point, allowedto decrease reaction time 5760-fold as compared to standard batch operation [16]. The condensation of o-phenylenediamine with acetic acid to 2-methylbenzimidazole in an MSR is an impressive example of the reduced reaction time from 9 weeks at room temperature to 30 s at 543 K and 130 bar [17]. 

N. de Mas A. Gunther, M.A. Schmidt, K.F. Jensen, Scalable microfabricated multiphase reactors for direct fluorination reactions, TRANSD UCERS, Solid-State Sensors, Actuators... 

Wiese, K.-D., Moeller, O., Protzmann, G., and Trocha, M. (2003) A new reactor design for catalytic fluid-fluid multiphase reactions. Catal. Today, 79-80,97-103. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Cull, S. G. Holbrey, J. D. Vargas-Mora, V. et al. Room-temperature ionic liquids as replacements for organic solvents in multiphase bioprocess operations, BiotechnoL Bioeng., 2000, 69(2), 227-233 Lau, R. M. van Rantwijk, F. Seddon, K. R. Sheldon, R. A. Lipase-catalyzed reactions in ionic liquids, Org. Lett., 2000, 2(26), 4189-4191. 

For multiphase reactive systems of types (a) and (b), at least one of the reactants has to reach the reaction zone from a different phase. In such systems, generally mass transfer between these two different phases (and its interaction with chemical reactions) is of primary importance and turbulent mixing is often of secondary importance. For such systems, modeling multiphase flows as discussed in Chapter 4 is directly applicable. The only additional complexity is the possibility of interaction between mass transfer and chemical reactions. The typical interphase mass transfer source for component k between phases p and q can be written (for the complete species conservation equation, refer to Chapter 4) ... 

The use of these criteria requires an experimentally measured point value for the reaction rate, the solubility of gas phase reactant and an estimation of gas to liquid mass transfer coefficient k,a. Some correlations for calculating k,a values in different multiphase reactor systems are presented in Table 3. 

The description of a dispersed multiphase flow with chemical reactions leads to a complex system of differential and algebraic equations, which can only be solved by specifying appropriate boundary and initial conditions. For the gas phase equations, the boundary conditions are imposed on the gas velocity u, the temperature T, the turbulent kinetic energy k, and its dissipation e. The spray equations require conditions at the nozzle exit and for the interactions of the droplets with the walls. 

M. W. Losey, R. (. Jackman, S. L. Firebaugh, M. A. Schmidt and K. F. Jensen, Design and fabrication of microfluidic devices for multiphase mixing and reaction. Journal of Microdectromechanical Systems, 2002,... 

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