Equilibrium concepts, zone

Zone refining is a dynamic nonequilibrium separation process. However, to understand its essential features it is important to understand the equilibrium concepts on which it is based. Of central importance is the notion of the equilibrium distribution coefficient, k0 Cg/, where Cg and Cl are the concentrations of solute at equilibrium in the solid and liquid phases respectively. Since the value of ko may be dramatically different from unity, it is clear that at equilibrium a solute may distribute itself between solid and liquid phases with a great preference for one or the other at a given temperature. On this basis the relative amount of solute in each phase can be controlled, and a separation can be carried out. 

The intermediate values correspond to the approximation of the quasiequilibrium conditions of sharpening of zone boundaries. At the same time, selective displacement in equilibrium sorption dynamics conception is carried out with the... 

Prompt NO mechanisms In dealing with the presentation of prompt NO mechanisms, much can be learned by considering the historical development of the concept of prompt NO. With the development of the Zeldovich mechanism, many investigators followed the concept that in premixed flame systems, NO would form only in the post-flame or burned gas zone. Thus, it was thought possible to experimentally determine thermal NO formation rates and, from these rates, to find the rate constant of Eq. (8.49) by measurement of the NO concentration profiles in the post-flame zone. Such measurements can be performed readily on flat flame burners. Of course, in order to make these determinations, it is necessary to know the O atom concentrations. Since hydrocarbon-air flames were always considered, the nitrogen concentration was always in large excess. As discussed in the preceding subsection, the O atom concentration was taken as the equilibrium concentration at the flame temperature and all other reactions were assumed very fast compared to the Zeldovich mechanism. 

The concept of plate theory was originally proposed for the performance of distillation columns (12). However, Martin and Synge (13) first applied the plate theory to partition chromatography. The theory assumes that the column is divided into a number of zones called theoretical plates. One determines the zone thickness or height equivalent to a theoretical plate (HETP) by assuming that there is perfect equilibrium between the gas and liquid phases within each plate. The resulting behavior of the plate column is calculated on the assumption that the distribution coefficient remains unaffected by the presence of other... 

In terms of organization, the text has two main parts. The first six chapters constitute generic background material applicable to a wide range of separation methods. This part includes the theoretical foundations of separations, which are rooted in transport, flow, and equilibrium phenomena. It incorporates concepts that are broadly relevant to separations diffusion, capillary and packed bed flow, viscous phenomena, Gaussian zone formation, random walk processes, criteria of band broadening and resolution, steady-state zones, the statistics of overlapping peaks, two-dimensional separations, and so on. 

Opposiny-reactants mode. When immobilized with a catalyst or enzyme, the interconnected tortuous pores or the nearly straight pores of a symmetric inorganic membrane provides a relatively well controlled catalytic zone or path for the reactants in comparison with the pellets or beads in a fixed or fluidized bed of catalyst particles. This unique characteristic of a symmetric membrane, in principle, allows a novel reactor to be realized provided the reaction is sufficiently fast. The concept applies to both equilibrium and irreversible reactions and does not utilize the membrane as a separator. Consider a reaction involving two reactants, A and B ... 

The core to the concept of an inorganic membrane reactor is to steer a membrane-selective species of a reaction mixture in or out of the membrane, which also serves as part of the reactor boundaries, to improve either the reaction conversion or product distribution. This is accomplished primarily by equilibrium displacement due to the permselective removal of a product or by avoiding or reducing undesirable side reactions (between certain chemical species including intermediate products) via controlled addition of some key reactant to the reaction zone through the membrane. 

The concept of combining membranes and reactors is being explored in various configurations, which can be classified into three groups, related to the role of the membrane in the process. As shown in Figure 25.12, the membrane can act as (a) an extractor, where the removal of the product(s) increases the reaction conversion by shifting the reaction equilibrium (b) a distributor, where the controlled addition of reactant(s) limits side reactions and (c) an active contactor, where the controlled diffusion of reactants to the catalyst can lead to an engineered catalytic reaction zone. In the first two cases, the membrane is usually catalytically inert and is coupled with a conventional fixed bed of catalyst placed on one of the membrane sides. 

A similar model for the case of thallium cuprate is complicated by the large number of parameters that affect the state of the system, and also by the necessity to introduce two experimentally unknown quantities simultaneously into the model. However, taking into account the character of the pH dependences of all the processes that occur with the participation of thallium and copper, one can suppose that the shape of the thallium cuprate stability region would be close to that for the mixed oxide. That is, its width would increase with increasing concentration of copper ions (hydroxo complexes) within the crystallization zone. Although the crystallization process took place under a fortiori non equilibrium conditions, the results of the preparative analysis agree qualitatively with the concept of stability of the products. The interval over which formation of thallium cuprate on copper substrates occurs and the formation of the mixed oxide on platinum and carbon substrates can be observed is wider for higher values of the pH [352-354]. 

The concept that the removal of an undesired reaction product by selective adsorption from the reaction zone of an equilibrium-controlled reaction increases the conversion and the rate of formation of the desired component (based on Le Chatelier s principle) was used to develop a novel PSA process concept called SERP for direct production of fuel cell-grade hydrogen by steam reforming of methane (CH4 + 2H20 44 C02 + 4H2).57 61 The concept uses a physical admixture of a reforming (noble metal on alumina) catalyst and a chemisorbent (K2C03 promoted hydrotalcite), which selectively and reversibly chemisorbs C02 from a gas at a temperature of -450 °C in the presence of steam. The cyclic SERP steps consisted of the following ... 

As mentioned earher, the plate theory has played a role in the development of chromatography. The concept of "plate" was originally proposed as a measmement of the performance of distillation processes. It is based upon the assumption that the column is divided into a number of zones called theoretical plates, that are treated as if there exists a perfect equilibrium between the gas and the Hquid phases within each plate. This assumption imphes that the distribution coefficient remains the same fi-om one plate to another plate, and is not affected by other sample components, and that the distribution isotherm is hnear. However, experimental evidences show that this is not true. Plate theory disregards that chromatography is a dynamic process of mass transfer, and it reveals httle about the factors affecting the values of the theoretical plate number. In principle, once a sample has been introduced, it enters the GC column as a narrow-width "band" or "zone" of its composite molecules. On the column, the band is further broadened by interaction of components with the stationary phase which retains some components more than others. Increasing... 

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