Chemically reactive systems

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

CET89, Chemical equilibrium thermodynamics code for evaluating shock parameters in explosive, chemically-reactive systems, NASA 1989. 

We have covered a body of material in this chapter that deals with movement of mass along gradients and between phases. We have examined the commonalities and differences between linear driving forces, net rates of adsorption, and permeation. Each has the common feature that reaction is not involved but does involve transport between apparently well-defined regions. We move now to chemically reactive systems in anticipation of eventually analyzing problems that involve mass transfer and reaction. 

This chapter is restricted to homogeneous, single-phase reactions, but the restriction can sometimes be relaxed. The formation of a second phase as a consequence of an irreversible reaction will not affect the kinetics, except for a possible density change. If the second phase is solid or liquid, the density change will be moderate. If the new phase is a gas, its formation can have a major effect. Specialized models are needed. Two-phase ffows of air-water and steam-water have been extensively studied, but few data are available for chemically reactive systems. 

Modeling of Chemically Reactive Systems, Eds. K. H. Ebert, P. Deulfhard, W. Jager, Springer, Berlin 1981. 

Elastic Scattering in Chemically Reactive Systems (Greene, Moursund,... 

If a chemically reactive system is isolated from the rest of lhe universe at a constant temperature and pressure, a definite end-point is often attained short of the complete transmutation of reactants into resultants. In order to be certain that this end-point (short or complete transmutation) is whal is known as the equilibrium point, the equilibrium must he approached... 

Deans, H. A. and Lapidus, L. A.I.Ch.E.JI. 6 (1960) 656, 663. A computational model for predicting and correlating the behavior of fixed-bed reactors I. Derivation of model for nonreactive systems, II. Extension to chemically reactive systems. 

The multiplicity phenomenon in chemically reactive systems was first observed in 1918 by Liljenroth [1] for ammonia oxidation and it later appeared in the Russian literature of the 1940s [2]. However, it was not until the 1950s that major investigations of this phenomenon began. This development was inspired by the Minnesota school of Amundson and Aris and their students [3-5]. The Prague school also had a notable contribution in expanding the field [13-16]. 

Later development in singularity theory, especially the pioneering work of Golubitsky and Schaeffer [19], has provided a powerful tool for analyzing the bifurcation behavior of chemically reactive systems. These techniques have been used extensively, elegantly and successfully by Luss and his co-workers [6-11] to uncover a large number of possible types of bifurcation. They were also able to apply the technique successfully to complex reaction networks as well as to distributed parameter systems. 

Many laboratory experiments have been successfully designed to confirm the existence of bifurcation behavior in chemically reactive systems [25-29], as well as in enzyme systems [18]-... 

The development and application of a rigorous model for a chemically reactive system typically involves four steps (1) development of a thermodynamic model to describe the physical and chemical equilibrium (2) adoption and use of a modeling framework to describe the mass transfer and chemical reactions (3) parameterization of the mass-transfer and kinetic models based upon laboratory, pilot-plant, or commercial-plant data and (4) use of the integrated model to optimize the process and perform equipment design. 

In this section, we have used the example of C02 removal from flue gases using aqueous MEA to demonstrate the development and application of a rigorous model for a chemically reactive system. Modem software enables rigorous description of complex chemically reactive systems, but it is very important to carefully evaluate the models and to tune them using experimental data. 

This reaction is catalyzed by a platinum catalyst such as Speier s catalyst, chloroplatinic acid. Because the catalyst also isomerizes the terminal double bond, the reaction maybe run with an excess of vinyl to make sure all the reactive sites on the silicone are reacted. SiH also reacts with ROH and, for this reason, alkoxy end-capped polyethers maybe preferred. Alkoxy end-capped polyethers are also useful when the surfactant will be used in a chemically reactive system such as polyurethane foam manufacture. 

A chemically reactive system contains the following spedes in the gas phase NH3, NO, N02, 02, and H20. Determine a complete set of independent reactions for this system. How many degrees of freedom does the system have ... 

The heterogeneous reactors with supported porous catalysts are one of the driving forces of experimental research and simulations of chemically reactive systems in porous media. It is believed that the combination of theoretical methods and surface science approaches can shorten the time required for the development of a new catalyst and optimization of reaction conditions (Keil, 1996). The multiscale picture of heterogeneous catalytic processes has to be considered, with hydrodynamics and heat transfer playing an important role on the reactor (macro-)scale, significant mass transport resistances on the catalyst particle (meso-)scale and with reaction events restricted within the (micro-)scale on nanometer and sub-nanometer level (Lakatos, 2001 Mann, 1993 Tian et al., 2004). 

While studying stationary (see following) states of chemically reactive systems, we shall presume, as is done in traditional courses of chemical kinetics, that the relaxation of the concentrations of intermediates of chemical transformations to some quasi stationary state is much faster than the change of the concentrations of initial reactants (see Section 2.1). Therefore, for example, the concentration of reactive intermediates may be considered as an internal parameter in contrast to the external para meters that are the concentrations of initial reactants and final products that change considerably more slowly. 

In an open system, the entropy may change due to either increases caused by spontaneous thermodynamically irreversible internal processes in the system, djS, or exchanges between the system and the surrounding, dgS. In chemically reactive systems, djS may change as a result, for example, of spontaneous reactions inside the system, while dgS may change as a result of supply or extraction of heat and/or some reactants. 

FLUXES AND THERMODYNAMIC FORCES IN SPATIALLY HOMOGENEOUS CHEMICALLY REACTIVE SYSTEMS... 

A typical example of nonequilibrium spatially homogeneous systems is an isotropic system where a chemical reaction occurs. The apphcation of nonequibbrium thermodynamics for the consideration of chemically reactive systems has a few peculiarities. Indeed, heat and mass transfer pro cesses are characterized usually by continuous variations in temperature and concentration (see Section 1.5). On the other hand, the chemical transformations imply transitions between the discrete states that pertain to the individual reaction groups. 

It was just shown that fluxes of thermodynamic parameters that describe transformations in chemically reactive systems are in direct relationships with the rate of chemical reactions. The relationship between the rate of a chemical reaction and physicochemical parameters (reactant concentra tions, temperature, etc.) of the system is the subject of a special branch of physical chemistry called chemical kinetics. 

It is essential that the relations that are similar to the phenomenological Onsager reciprocal equations are also valid for many types of chemically reactive systems that are far from thermodynamic equilibrium (see Section 2.3.4). 

The presence of conjugation in chemically reactive systems can be reflected using the Onsager reciprocal equations, too. However, when writing this kind of reciprocal equation, some specific features are required. In reactive... 

An example is the stationary state of an open chemically reactive system, where the intermediate concentrations, which are setded in the course of the internal processes, are time constant. The rate of changing these interme diate concentrations (fluxes of these parameters) equals zero. Evidendy, the stationary state is setded at a certain ratio of the rates of elementary reactions responsible for the formation and vanishing of the reactive intermediates. 

Section 3.4 shows that the speculations can be expanded to chemically reactive systems far from thermodynamic equilibrium at least for a rather simple (linear in respect to the intermediates) set of chemical transformations. 

Let us prove the GlansdorGPrigogine theorem with an example of an arbitrary spatially homogeneous chemical reactive system. The internal parameters for such a system are the concentrations of intermediates of the stepwise chemical transformations. Any spontaneous changes of the system (and, as a result, changes in internal driving forces) relate namely to changes in the intermediate concentrations. Therefore, the partial force differential dxP may be substituted for by its full analogue related thermodynamic rushes (concentrations) of intermediates (a 1,. .., k) of the stepwise transformations ... 

To find a typical form of the functional of our interest, consider an arbi trary chemically reactive system close to its thermodynamic equilibrium. The energy dissipation rate in such a system is described by the equation... 

So, in accordance with the principle of the minimal rate of entropy pro duction in chemically reactive systems close to thermodynamic equilib rium, the stationary state must be coupled with the minimum of the positively defined functional... 

In conditions of a stable thermodynamic equilibrium, thermodynamic rushes of all of the involved interacting reaction groups are equal to one another and, therefore, O equals zero for any chemically reactive system. 

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