Pure phase equilibrium

EQUI("Calcite") Moles of a phase in the pure-phase (equilibrium-phase) assemblage... 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

Clapeyron-Clausius equation A thermodynamic equation applying to any two-phase equilibrium for a pure substance. The equation states ... 

In the phase equilibrium between a pure solid (or a liquid) and its vapour, the addition of other gases, as long as they are insoluble in the solid or liquid, has negligible effect on the partial pressure of the vapour. 

This database provides thermophysical property data (phase equilibrium data, critical data, transport properties, surface tensions, electrolyte data) for about 21 000 pure compounds and 101 000 mixtures. DETHERM, with its 4.2 million data sets, is produced by Dechema, FIZ Chcmic (Berlin, Germany) and DDBST GmhH (Oldenburg. Germany). Definitions of the more than SOO properties available in the database can be found in NUMERIGUIDE (sec Section 5.18). 

Fig. 7. Isothermal cross section of the system H20-CH4-CsH8 on a water-free basis at —3° C. The points represent experimental results and the curves have been obtained from a theoretical analysis. The line AB represents the four-phase equilibrium HiHn ice G the gas G consists of almost pure methane, Hj contains only methane. Consequently, the composition of the latter two phases almost coincide in the figure, and the situation around point A has therefore been drawn separately on an enlarged scale.

The equilibrium between a compressed gas and a liquid is outside the scope of this review, since such a system has, in general, two mixed phases and not one mixed and one pure phase. This loss of simplicity makes the statistical interpretation of the behavior of such systems very difficult. However, it is probable that liquid mercury does not dissolve appreciable amounts of propane and butane so that these systems may be treated here as equilibria between a pure condensed phase and a gaseous mixture. Jepson, Richardson, and Rowlinson39 have measured the concentration of... 

In summary, we now have the tools for describing phase equilibrium for both pure materials and for mixtures, and for understanding chemical processes at equilibrium. We will rely upon the foundation developed in this chapter as we... 

So far, we have described the effect of pressure and temperature on the phase equilibria of a pure substance. We now want to describe phase equilibrium for mixtures. Composition, usually expressed as mole fraction x or j, now becomes a variable, and the effect of composition on phase equilibrium in mixtures becomes of interest and importance. 

The penetration theory has been used to calculate the rate of mass transfer across an interface for conditions where the concentration CAi of solute A in the interfacial layers (y = 0) remained constant throughout the process. When there is no resistance to mass transfer in the other phase, for instance when this consists of pure solute A, there will be no concentration gradient in that phase and the composition at the interface will therefore at all Limes lie the same as the bulk composition. Since the composition of the interfacial layers of the penetration phase is determined by the phase equilibrium relationship, it, too. will remain constant anil the conditions necessary for the penetration theory to apply will hold. If, however, the other phase offers a significant resistance to transfer this condition will not, in general, be fulfilled. 

Assuming the solid phases as to be pure, the equilibrium pressure of carbon dioxide is then a function only of temperature ... 

The phase equilibrium for pure components is illustrated in Figure 4.1. At low temperatures, the component forms a solid phase. At high temperatures and low pressures, the component forms a vapor phase. At high pressures and high temperatures, the component forms a liquid phase. The phase equilibrium boundaries between each of the phases are illustrated in Figure 4.1. The point where the three phase equilibrium boundaries meet is the triple point, where solid, liquid and vapor coexist. The phase equilibrium boundary between liquid and vapor terminates at the critical point. Above the critical temperature, no liquid forms, no matter how high the pressure. The phase equilibrium boundary between liquid and vapor connects the triple point and the... 

The Clausius-Clapeyron equation provides a relationship between the thermodynamic properties for the relationship psat = psat(T) for a pure substance involving two-phase equilibrium. In its derivation it incorporates the Gibbs function (G), named after the nineteenth century scientist, Willard Gibbs. The Gibbs function per unit mass is defined... 

At present there are two fundamentally different approaches available for calculating phase equilibria, one utilising activity coefficients and the other an equation of state. In the case of vapour-liquid equilibrium (VLE), the first method is an extension of Raoult s Law. For binary systems it requires typically three Antoine parameters for each component and two parameters for the activity coefficients to describe the pure-component vapour pressure and the phase equilibrium. Further parameters are needed to represent the temperature dependence of the activity coefficients, therebly allowing the heat of mixing to be calculated. 

The equation-of-state method, on the other hand, uses typically three parameters p, T andft/for each pure component and one binary interactioncparameter k,, which can often be taken as constant over a relatively wide temperature range. It represents the pure-component vapour pressure curve over a wider temperature range, includes the critical data p and T, and besides predicting the phase equilibrium also describes volume, enthalpy and entropy, thus enabling the heat of mixing, Joule-Thompson effect, adiabatic compressibility in the two-phase region etc. to be calculated. 

The pressure-temperature-composition diagram presented by Morey is shown in Fig. 8. The vapor pressure of pure water (on the P-T projection) terminates at the critical point (647 K, 220 bar). The continuous curve represents saturated solutions of NaCl in water, i.e., there is a three-phase equilibrium of gas-solution-solid NaCl. The gas-phase pressure maximizes over 400 bar at around 950 K. Olander and Liander s data for a 25 wt. % NaCl solution are shown, and T-X and P X projections given. At the pressure maximum, the solution phase contains almost 80% NaCl. 

The film pressure values for the detergency system are also listed in Table 2. These quantities represent the difference in interfacial tension between two pure phases and the interfacial tension of the same two phases which are at saturation equilibrium with the third phase. Since the PEG fiber surface was assumed insoluble in either the bath or soil, = 0. 

It must be emphasized that the choice of a particular standard state of reference has no influence on the result of equilibrium calculations and is only a matter of convenience. It is generally convenient to adopt as standard state for solid components the condition of pure component in the pure phase at the P and T of interest or, alternatively, the condition of pure component in the pure phase at P = 1 bar and T = 298.15 K. ... 

As one more example of the nonappearance of pure phases in the equilibrium equation, examine the reaction of lithium bromide with hydrogen ... 

The end product of the dehydroxylation of pure phases is, in all cases, hematite, but with lepidocrocite, maghemite occurs as an intermediate phase. The amount of water in stoichiometric FeOOH is 10.4 g kg , but adsorbed water may increase the overall amount released. Thermal dehydroxylation of the different forms of FeOOH (followed by DTA or TG) takes place at widely varying temperatures (140-500 °C) depending on the nature of the compound, its crystallinity, the extent of isomorphous substitution and any chemical impurities (see Fig. 7.18). Sometimes the conversion temperature is taken from thermal analysis data (e. g. DTA), but because of the dynamic nature of the thermoanalysis methods, the temperature of the endothermic peak is usually higher than the equilibrium temperature of conversion. 

VOCs), and to a decrease in production yields. Quantitation of these phenomena and determination of material balances and conversion yields remain the bases for process analysis and optimisation. Two kinds of parameters are required. The first is of thermodynamic nature, i.e. phase equilibrium, which requires the vapour pressure of each pure compound involved in the system, and its activity. The second is mass-transfer coefficients related to exchanges between all phases (gas and liquids) existing in the reaction process. 

Why can the equilibrium condition for the pure phase equilibria of Model 1 be written as... 

The KTTS depends upon an absolute zero and one fixed point through which a straight line is projected. Because they are not ideally linear, practicable interpolation thermometers require additional fixed points to describe their individual characteristics. Thus a suitable number of fixed points, ie, temperatures at which pure substances in nature can exist in two- or three-phase equilibrium, together with specification of an interpolation instrument and appropriate algorithms, define a temperature scale. The temperature values of the fixed points are assigned values based on adjustments of data obtained by thermodynamic measurements such as gas thermometry. 

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