Equilibrium characteristics

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

The initial set of experiments and the first few textbook chapters lay down a foundation for the course. The elements of scientific activity are immediately displayed, including the role of uncertainty. The atomic theory, the nature of matter in its various phases, and the mole concept are developed. Then an extended section of the course is devoted to the extraction of important chemical principles from relevant laboratory experience. The principles considered include energy, rate and equilibrium characteristics of chemical reactions, chemical periodicity, and chemical bonding in gases, liquids, and solids. The course concludes with several chapters of descriptive chemistry in which the applicability and worth of the chemical principles developed earlier are seen again and again. 

Figure 3.6 shows the equilibrium characteristics for the C-02-H20 reaction system. To favor production of CO and H2 from coal, reactions 3.9 and 3.10 should be carried out at a comparatively low pressure and low temperature. However, during actual production, synthesis of chemicals usually occur at high pressures of CO and H2, and therefore, the gasifier should be operated at high pressure and high temperature to obtain high process efficiency. 

Thermodynamic and equilibrium characteristics of gasification systems, if available, could help to determine conditions under which certain desired products may be... 

TABLE 4.1. Boiling Points and Gas-Liquid Equilibrium Characteristics (Henry s Law Constants) for Both Odorous and Nonodorous Compounds in Water at 25°C (Thibodeaux, 1996 Sander, 2000). 

V. S. Ezhov, S. N. Golovko, and E. M. Guseinov, Determination of the Equilibrium Characteristics of Vapor-Liquid and the Liquid-Liquid Systems Applicable to Products of the Oxidative Ammonolysis of Toluene and Picolines , Khim.-Farm. Zh., 10, 77-79 (1976). 

Thus, for solutes with comparable rate and equilibrium characteristics, the model predictions are in excellent agreement with the experimental data. The effect of assuming... 

The importance of considering the correlation effects is a principal for the adsorption and desorption rates in the case of dissociating molecules [126]. If the correlation effects are absent this violates the self-consistent describing of the system s kinetic and equilibrium characteristics. 

The equilibrium and non-equilibrium characteristics of the macromolecular coil are calculated conveniently in terms of new co-ordinates, so-called normal co-ordinates, defined by... 

Because of the wide variation in equilibrium, the variation in the values of m from one system to another can have an important effect on the overall coefficient and on the selection of the type of equipment to use. For example, ifm is large, the liquid-phase part of the overall resistance might be extremely large where kL might be relatively small. This kind of reasoning must be applied with caution, however, since species with different equilibrium characteristics are separated under different... 

Gibbs free energy Gibbs free energy at equilibrium Characteristic directions of the matrix G Characteristic vectors of the matrix G The constant... 

The performance of an equilibrium stage may be examined in terms of components concentration and recovery in a given product and the dependence of these quantities on the independent variables and the phase equilibrium characteristics of the system. 

The manner in which reflux influences an extractor performance and the extent of its effect depend on the equilibrium characteristics of the particular system. Also, the ranges of reflux and other operating conditions must be restricted to the two-phase region where separation is feasible, both thermodynamically and physically. 

The general pattern of microemulsion phase behavior described above is seen when the amounts of water and hydrocarbon present are comparable. However, a hydrocarbon-free mixture of surfactant and water (or brine) near optimal conditions is typically not a simple micellar solution but either the lamellar liquid crystalline phase or a dispersion of this phase in water. Starting with such a mixture and adding hydrocarbon, we sometimes find that the system passes through several multiphase regions before reaching the microemulsion/oil/water equilibrium characteristic of optimal conditions. 

Adsorbent selection criteria for any application generally include the following main attributes capacity, selectivity, regenerability, kinetics, durability, and cost. These attributes represent combinations of properties that are strongly affected by the pertinent conditions. For example, the first four govern how much adsorbent is necessary for a particular application, and the last two affect the annual cost. Furthermore, the first three are tied to the equilibrium characteristics, about which much can be said (see Section 14.3). Likewise, kinetics is covered in more detail in Section 14.4. Both will be discussed briefly here, however. Finally, adsorbent cost obviously depends on both its price and lifetime, which can depend on its resistance to attrition, degradation, fouling, and so on. 

There are a variety of boundary and initial conditions which are useful for different situations. Some examples of these boundary conditions and their applications are given in Table I. A relationship between n (adsorbed species) and c (mobile species) must be found. These relationships may either be equilibrium or kinetic relationships (mass transfer rates). Some examples of equilibrium and mass transfer relationships may be found in Tables II and III, respectively. As pointed out by Lapidus and Amundson (25), equilibrium relationships in themselves are useful in cases where mass transfer rates are not limiting. In any case, the equilibrium characteristics of the support and solute have a direct bearing on column performance. 

The technique employed to generate supersaturation in a solution is referred to as the mode of operation. The mode chosen by the designer is strongly influenced by the phase-equilibrium characteristics of the system, and it dictates the material and energy balance requirements of the system. The common techniques for producing solids (or generating supematuration) from a solution include ... 

As in all mass-transfer problems, it is necessary for a complete understanding of the process to be familiar with the equilibrium characteristics of the systems. Moreover, since the mass transfer in these cases will invariably be accompanied by simultaneous transfer of energy as well, consideration must also be given to the enthalpy characteristics of the systems. 

Equilibrium characteristics You might have noticed certain characteristics of all chemical reactions that reach equilibrium. First, the reaction must take place in a closed system—no reactant or product can enter or leave the system. Second, the temperature must remain constant. Third, all reactants and products are present, and they are in constant dynamic motion. This means that equilibrium is dynamic, not static. 

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