Phase equilibrium 652 INDEX

The partition coefficient is a very useful concept for understanding phase equilibrium theory and for developing analytical methods however, partition coefficients are prone to so many contemporaneous variables, they cannot be cataloged and indexed. This becomes clear when we look at the derivation of the partition coefficient equation. For the partitioning process, the free-energy change is described as... 

Abart R (1995) Phase equilibrium and stable isotope constraints on the formation of metasomatic gamet-vesuvianite veins (SW Adamello, N Italy). Contrib Mineral Petrol 122 116-133 Agne JJ (1997) Crustal mass transfer and index mineral growth in Barrow s garnet zone, Northeast Scotland. Geology 25 73-76... 

American Ceramic Society, Phase Equilibrium Diagrams - Cumulative Index 1998. 

In the concentration tetrahedron, the ternary azeotrope gives rise not only to three a-surfaces, but also to one specific a-line in the points of which not two but three components of the phase equilibrium coefficients are equal to each other. We will call the line a three-index a-line. For example, in Fig. 1.10b, the ternary azeotrope 123 gives rise to the o i23-line, which crosses the face 1-3-4 in the i23-point (it isn t shown). 

The stable phase equilibrium experimental results of solubilities of the quaternary system (NaCl - KCl - Na2B407 - K2B4O7 - H2O) at 298.15 K were determined, and are listed in Table 3, respectively. On the basis of the Janecke index (/b, /b/ [mol/100 mol(2Na+ + 2K+)]) in Table 3, the stable equilibrium phase diagram of the system at 298.15 K was plotted and shown in Figure 5. 

The model being proper yields a structurally solvable index 1 DAE model. Though what if we do not know it all for example a flow is not known, kinetics are not all known or some properties are missing Some of it can be handled, but for a price information must be added in the form of assumptions. There are simple assumptions, such as property is constant, thus not a function of the state. Those are easy to handle and do only remove algebraic complexity and reduce the fidelity of the model at obvious places. The more complex ones are if the lack of information makes it impossible to compute flows or reactions. At this point it is necessary to resort to more restrictive measure and make timescale assumptions. There are three commonly made assumptions, which are (i) Steady state assuming a system to exhibit a very fast dynamic relative to the modelled dynamic window, thus shifting this system out at the top end, the short time scale and assume event-dynamics. (ii) (Phase) equilibrium in which one assumes very fast communication of extensive quantity such that the two coupled systems are in equilibrium with respect to the affected extensive quantity. The most common case is thermal equilibrium and phase equilibria, (iii) (Reaction) equilibrium in which one assumes very fast reactions, such that the reactions are viewed as instantaneous. 

All such indices therefore describe separation by indicating how different the exit stream 1 composition is from the feed stream with respect to the soiute species. A somewhat similar index is the equiiibrium ratio of species i (obtained under phase-equilibrium conditions),... 

B bulk property d deactivation e effective property G gas phase i component index i reaction index L liquid phase p catalyst particle property equilibrium conditions... 

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

Measurement yields both the differences between the outer potentials and the work functions (real potentials). If two phases oc an / with a common species (index i) come into contact, at equilibrium /, (< ) = (/ ), that is at(a) - <, (/ ) = ZiFApty. These quantities are mostly measured using the vibrating condenser, thermoionic, calorimetric, and photoelectric methods. 

Generally, when two phases are in electronic equilibrium, eoifa — fa) = Hi — ji 2- In our case, the wire I is in equilibrium with the metal M, the latter is in equilibrium with the redox couple, and the platinum electrode II is in equilibrium with the reference couple (index ref ). 

The partitioning of ions is not so simple, since each solution must be electrically neutral (with the exception of a thin boundary layer at the interface). As an example we consider the case where a single salt is partitioned between the two phases for simplicity we assume that the cation and the anion have the same charge number . We denote the cation by the index +, and the anion by -. Applying the equilibrium condition Eq. (12.1) to both ions gives for the difference in inner potentials ... 

Since members of a homologous series have incremental boiling point differences and if the amount of any homolog in the moving gas phase is related to vapor pressure at the temperature of the experiment, plots of log k vs. carbon number should also be a straight line. (The enthalpy of vaporization increases monotonically with carbon number.) This in fact is observed in gas-liquid equilibrium separation systems. It is the basis of retention index systems pioneered by Kovats for qualitative identification. 

MINTEQA2 http //www.epa.gov/ceampubl/mmedia/minteq/index.htm MINTEQA2 is an equilibrium speciation model that can be used to calculate the equilibrium composition of dilute aqueous solutions in the laboratory or in natural aqueous systems. The model is useful for calculating the equilibrium mass distribution among dissolved species, adsorbed species, and multiple solid phases under a variety of conditions including a gas phase with constant partial pressures. 

Distribution ratio is the total analytical concentration of a substance in the organic phase to its total analytical concentration in the aqueous phase, usually measured at equilibrium. Symbol D. D shall be defined and, preferably, specified by an index if the distribution of mercury is measured, the distribution ratio is written D(Hg) or The term partition ratio is not used for the distribution ratio. 

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