Irreversible reactions, multicomponent

Multicomponent reactions (MCRs) are processes that involve sequential reactions among three or more reactant components that co-exist in the same reaction mixture. In order to be efficient, MCRs rely on components that are compatible with each other and do not undergo alternative irreversible reactions to form other products or by-products. 

Finally, Delancey and Chiang5 3,54 reported a general mathematical evaluation of multicomponent non isothermal mass transfer in the presence as well as absence of a chemical reaction. These studies followed the matrix approach to the problem. The chemical reaction considered was a simple first-order irreversible reaction. The problem was solved assuming time dependence of the rate constant and an exponential relationship between the temperature and the distance. 

E. V. Albano. On the universality classes of the discontinuous irreversible phase transitions of a multicomponent reaction system. J Phys A (Math Gen) 27 3751-3758, 1994. 

E. V. Albano. Irreversible phase transitions into non-unique absorbing states in a multicomponent reaction system. Physica A 274 426-434, 1995. 

Practically irreversible multicomponent reactions (MCRs), like the Ugi 4-component reaction (U-4CR), can usually fulfill aU essential aspects of green chemistry. Their products can be formed directly, requiring minimal work by just mixing three to nine educts. Often minimal amounts of solvents are needed, and almost quantitative yields of pure products are frequently formed. 

In particular, it is useful to define the critical point through F(nc) = 0 (the stationary state). Since multicomponent chemical systems often reveal quite complicated types of motion, we restrict ourselves in this preliminary treatment to the stable stationary states, which are approached by the system without oscillations in time. To illustrate this point, we mention the simplest reversible and irreversible bimolecular reactions like A+A —> B, A+B -y B, A + B —> C. The difference of densities rj t) = n(t) — nc can be used as the redefined order parameter 77 (Fig. 1.6). For the bimolecular processes the... 

RFRs for VOC oxidation (also referred to as regenerative catalytic oxidizers, or RCOs) are often designed assuming single irreversible exothermic reaction. Mechanisms of complete oxidation of organics are complex, particularly for oxidation of multicomponent mixtures... 

Type I MCRs are only rarely successful, because the yield of final product P strongly depends on favorable thermodynamics. However, type II and III MCRs are of foremost interest in preparative organic chemistry because thermodynamics at least favors the final reaction step and high yields can be achieved. Most successful multicomponent reactions are type II reactions. Irreversibility of the last reaction step does not exclude formation of side products because all preceding reactions are equilibrium reactions and more than one reactive species may be present at the same time. Usually, however, possible side reactions are also reversible and the irreversibly formed reaction product P predominates [15]. 

The thermodynamics of irreversible processes begins with three basic microscopic transport equations for overall mass (i.e., the equation of continuity), species mass, and linear momentum, and develops a microscopic equation of change for specific entropy. The most important aspects of this development are the terms that represent the rate of generation of entropy and the linear transport laws that result from the fact that entropy generation conforms to a positive-definite quadratic form. The multicomponent mixture contains N components that participate in R independent chemical reactions. Without invoking any approximations, the three basic transport equations are summarized below. 

In this problem we explore classical irreversible thermodynamics for a multicomponent system, entropy generation, linear laws, and the molecnlar flux of thermal energy for a ternary system. Consider an N-component system (1 < j < Af) in the presence of external force fields and mnltiple chemical reactions (1 < y < / ). g, is the external force per unit mass that acts specifically on component i in the mixture, and r, is the overall rate of production of the mass of component i per unit volume, which is defined by... 

As many of the classical multicomponent reactions, the Strecker synthesis also takes advantage of the versatile chemistry of the initially formed imine. The formation of the amino nitrile, however, is reversible under the reaction conditions which usually results in lower yields. This problem was elegantly solved in the Bucherer-Bergs variation,3 4-376 where the initially formed aminonitrile is irreversibly trapped by formation of a hydantoin as depicted in Scheme 1.8 (entry b). 

Phase diagrams of ternary systems usually contain two-phase regions in the solid state (see e.g., [2] and Figure 10.1). The diffusion mass transfer in ternary and multicomponent systems is essentially different from the case of a binary system in quasiequilibrium as there exists the possibility of two-phase zone formation in the diffusion process. Though two-phase formation is connected with the thermodynamic disadvantage of interphase boundaries formation, there are cases when any other diffusion mode is impossible. Formation of two-phase regions may also proceed at high reaction rates at interfaces, that is, the assumption of quasiequilibrium of the interdiffusion process is imposed. Subsequently, we can apply the apparatus of hnear thermodynamics for irreversible processes [3-5]. 

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