Phase multicomponent

In the case of a siagle-phase, multicomponent system undergoiag just a single reaction, the total Gibbs energy is as foUows ... 

Steam Distillation—Continuous Flash, Two Liquid Phases, Multicomponent and Binary... 

Orru, R.V.A. St de Greef, M. (2003) Recent Advances in Solution-Phase Multicomponent Methodology for the Synthesis of Heterocyclic Compounds. Synthesis, 1471-1499. 

Kee, R. J., Dixon-Lewis, G., Warnatz, J., Coltrin, M. E., and Miller, J. A., A Fortran Computer Code Package for the Evaluation of Gas-Phase Multicomponent Transport, Sandia Report, SAND86-8246 (1986). 

Divisek et al. presented a similar two-phase, two-dimensional model of DMFC. Two-phase flow and capillary effects in backing layers were considered using a quantitatively different but qualitatively similar function of capillary pressure vs liquid saturation. In practice, this capillary pressure function must be experimentally obtained for realistic DMFC backing materials in a methanol solution. Note that methanol in the anode solution significantly alters the interfacial tension characteristics. In addition, Divisek et al. developed detailed, multistep reaction models for both ORR and methanol oxidation as well as used the Stefan—Maxwell formulation for gas diffusion. Murgia et al. described a one-dimensional, two-phase, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymer membrane for a liquid-feed DMFC. 

Recent advances in solution-phase multicomponent methodology for the synthesis ofheterocyclic compounds. Synthesis 200i, 10, 1471-1499. 

Rather exotic methods like vapor phase, multicomponent, and template syntheses are considered to be important in cases where the other ways failed. Generally, the main purpose of their application was to prove fundamental principles. 

Orru RVA, de Greef M (2003) Recent advances in solution-phase multicomponent methodology for the synthesis of heterocyclic compounds. Synthesis 10 1471-1499 Ramon DJ, Yus M (2005) Asymmetric multicomponent reactions (AMCRs) the new frontier. Angew Chem Int Ed 44 1602-1634... 

The equations developed in Section 8.1 for single-phase, one-component systems are all applicable to single-phase, multicomponent systems with the condition that the composition of the system is constant. The dependence of the thermodynamic functions on concentration are introduced through the chemical potentials because, for such a system,... 

When the state of a system is defined by assigning values to the necessary independent variables, the values of all of the thermodynamic functions are fixed. For a single-phase, multicomponent system the independent variables are usually the temperature, pressure, and mole numbers of the components. The Gibbs energy of such a system at a given temperature and pressure is additive in the chemical potentials of the components by Equation (5.62),... 

The equations are derived from the differential of the Gibbs energy for a one-phase, multicomponent system Equation (2.33). The differential is exact, and therefore the condition of exactness must be satisfied. Two equations... 

We consider a two-phase, multicomponent system in which there is one planar surface. The state of the system is defined by assigning values to the entropy and volume of the system, the area of the surface, and the mole numbers of the components. The differential of the energy of the system is... 

We choose the total system to be the condenser and the entire dielectric medium. The condenser is immersed in the medium which, for purposes of this discussion, is taken to be a single-phase, multicomponent system. The pressure on the system is the pressure exerted by the surroundings on a surface of the dielectric. In setting up the thermodynamic equations we omit the properties of the metal plates, because these remain constant except for a change of temperature. The differential change of energy of the system is expressed as a function of the entropy, volume, and mole numbers, but with the addition of the new work term. Thus,... 

E. Y. Kenig, Mass transfer-reaction coupling in two-phase multicomponent fluid systems, Chem. Eng. J., 1995, 57, 189-204. 

These two equations are equivalent and either one can be used to calculate the compositions of a two-phase multicomponent system. These equations are most readily solved by trial and error. To simplify Ihe calculation, one mole of starting material is taken as a basis. In this case Ti. = 1 and ni + = 1. A reasonable valne of ni or ti is chosen... 

In chap 1 a survey of the elements of transport phenomena for single phase multicomponent mixtures is given. This theory serves as basis for the development of most chemical engineering models as well as the multiphase flow concepts to be presented in the following chapters. The first part of the chapter considers laminar single phase flows for multicomponent mixtures. In the second part of the chapter the governing equations are applied to turbulent flows. 

Several formalisms have been developed leading to what may be called practical thermodynamics. These treatments include the analog of solution thermodynamics, where the adsorbent and the adsorbate are considered as components in a two-phase equilibrium [6]. Another way to study the system is to use the surface excess approach, whereby the properties of the adsorbed phase are determined in terms of the properties of the real two-phase multicomponent... 

These examples with carbon illustrate how difficult it is to predict the reaction path that a multicomponent hydrogen storage system will follow. A number of ternary phase multicomponent hydrogen storage systems have been proposed (Alapati et al, 2007b), but these will not be discussed as there will be even greater uncertainty that the proposed reaction will occur and the kinetics are likely to be even worse as such systems will require mass transport between three phases rather than two. 

Kee, R. J., G. Dixon-Lewis, J. Warnatz, M.E. Coltrin, and J.A. Miller. 1986. A FORTRAN computer code package for the evaluation of gas-phase, multicomponent transport properties. Livermore. CA Sandia NationM Lab. 

Consider the single-phase, multicomponent system depicted in Figure 3.1. It is convenient for our purposes to describe the state of this system by the variables temperature, T, pressure, P., and the number of moles, of each component, ti j. Specifying the temperature, pressure,... 

Applications of solution-phase multicomponent and multigeneration reactions... 

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

Sinaiski E. G., Separation of two-phase multicomponent mixtures in oil-gas field equipment, Nedra, Moscow, 1990. 

Figure 3.7 Schematic of a single-phase multicomponent system open to exchange of mass and energy with its surroundings...

Consider a container filled with a one-phase multicomponent mixture of composition x the container is immersed in a reservoir that imposes its temperature T and pressure P on the mixture. The container is fitted with a single inlet by which more material can be reversibly injected, as shown schematically in Figure 3.9. The process considered here is addition to the container of a small amount of pure component 1. The reversible work associated with this process is given by (3.7.14) for an isobaric injection of material through one inlet with no outlets, (3.7.14) reduces to... 

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