Pure components phase diagrams, schematics

Figure 1.13 Schematic of a pure component phase diagram. (Reprinted by permission of Prentice Hall, Englewood Cliffs, New Jersey, from J.M. Prausnitz, R.N. Lichenthaler, and E. Gomes de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed., 1986, p. 417.)...

Figure 3.1 shows a schematic representation of a two-component phase diagram characterized by a UCT. The left axis corresponds to pure component A and the right axis to pure component B. The abscissa corresponds to different A-B compositions. It is very common to express the compositions in weight fraction. Mole fraction or volume fraction can also be used. The central, shaded area corresponds to the two-phase domain, also referred to as the miscibility gap. The clear zone surrounding it represents a single phase. 

The schematic phase behaviour of C02 depicted in Figure 8.1 is only valid for the pure compound. The phase behaviour of mixtures is much more complex [6], being a function of composition, and the actual phase diagram can vary considerably even for seemingly similar components. Reaction systems contain at least three substances (substrate, product and catalyst), but in most cases more components are present and a... 

Figure 15.1 Effect of /3-phase particle size on the concentration, Xeq, of component B in the a phase in equilibrium with a /3-phase particle in a binary system at the temperature T. assuming that, 6 is pure B. (a) Schematic free-energy curves for a phase and three /3-phase particles of different radii, R > R2 > Rs. The free energies (per mole) of the particles increase with decreasing radius due to the contributions of the interfacial energy, which increase as the ratio of interfacial area to volume increases, (b) Corresponding phase diagram. The concentration of B in the a phase in equilibrium with the /0-phase particles, as determined by the common-tangent construction in (a), increases as R decreases, as shown in an exaggerated fashion for clarity, (c) Schematic concentration profiles in the a matrix between the three /3-phase particles.

The constant pressure diagram for this system is shown schematically in fig. 21.14. The boiling point of the mixture is independent of composition as shown by the horizontal dotted line at except when the second component disappears when, of course, the boiling point rises abruptly to that of the pure component T or T ), The line T E gives the composition of the vapour in equilibrium with pure liquid 1 as a function of temperature. The equilibrium temperature is lower than the boiling point of 1 as its partial pressure in the vapour phase is lower than total pressure. Similarly T E gives the composition of T mixed vapour in equilibrium with p liquid 2. At the eutectic point we have co-existence of the two liquid phases and vapour. The lines T E and T E are given by equations like (18.23) and (18.23 ). 

A schematic of a pressure-temperature diagram for a fixed composition mixture is shown in Figure 2.1. The phase representation of a mixture on a P P diagram is bivariant rather than univariant as in the case of a pure-component vapor pressure curve. At temperature Tj and pressure Pj, represented by point A, the mixture is... 

In this diagram, applicable mainly to binary systems, the temperature, pressure, and overall composition are the independent variables, with the pressure held constant. The diagram, shown schematically in Figure 2.2, consists of an upper curve representing dew points and a lower curve representing bubble points. The Z coordinate represents overall mole fraction of component 1, usually chosen as the more volatile component. A vertical line at Z = 0 corresponds to pure component 2, and point A represents its boiling point at the fixed system pressure. Similarly, pure component 1 is represented by a vertical line at Z = 1, and its boiling point by point B. Points above the dew point curve are in the vapor phase, and those below the bubble point curve are in the liquid phase, while the area between the two curves corresponds to the mixed phase. 

The phase behavior for the polymer-solvent systems can be described using two classes of binary P-T diagrams, which originate from P—T diagrams for small molecule systems. Figure 3.24A shows the schematic P-T diagram for a type-III system where the vapor-liquid equilibrium curves for two pure components end in their respective critical points, Ci and C2. The steep dashed line in figure 3.24A at the lower temperatures is the P-T trace of the UCST... 

Figure 9.2 3 A section of a schematic phase diagram starting from the left at the pure flexible polymer with its melting temperature flexible- Mole fraction of the liquid crystalline component X. increases towards the right. An LC phase or phases exist to the right of flicUmif (According to [58] with permission of The American Chemical Society.)...

Figure 1 shows the schematic p,T-projections for different types of fluid phase behavior. The vapor pressure curves of the two pure components, marked g(A) and g(BX with their critical points are shown. As can be seen in these figures, the diagrams differ with respect to the number and the nature of the critical en( )oints (CEP s) occurring and also with respect to the critical lines and three-phase loci gy which are connected directly to these CEP s. A CEP is a critical phase in equilibrium with an additional phase. 

This applies to the sodium chloride-water system which is an exemplary case. Fig. 2 gives a schematic p-T-diagram of a two component system with very different critical temperatures. One observes a critical curve which is a projection from the three-dimensional pressure-temperature-composition diagram on the p-T-plane. The curve extends uninterrupted between the critical points of the two pure components. The projection of a three-phase-surface, S2LG, between a quadruple point and the triple point T2 can also be seen. It does not intersect the critical curve in this example. In the right part of Fig. 2 we have a P-x-section taken between M and B in the previous diagram. At CP the critical curve penetrates the P-x-plane. 

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