Phase diagrams systems

and three-component systems will be considered. A one-component system is one substance that defines composition uniquely throughout a diagram. Temperature and/or pressure are usually the variables under consideration to define the state of a system. In phase transition work, variables such as density, heat capacity, optical properties, etc. may be measured to determine changes in phase state as the variables of state are changed. If there are no transitions in a one-component system in a region under consideration, there is very limited phase chemistry as such. 

The usual two-component diagram is plotted on rectangular coordinate graph paper. Temperature is usually the vertical axis while the relative percents of the components are plotted along the horizontal axis. The components may be molecules, salts, or ions, depending upon the system under study. In inorganic phosphate chemistry, a metal oxide is usually chosen as one component while P2O5 is chosen as a second component. 

Three-component diagrams can usually be plotted on a triangular graph with temperature plotted on an axis that is perpendicular to the base plane of the composition diagram. Then the diagram is usually represented as a surface. Usually, P2O5 is one component while two different metal oxides reside at the other corners of the base triangle. 

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System Type of phase diagram System Type of phase diagram... 

Phase diagram, system MgS04.-Hj0. [By permission, from J. H. Perry (ed.), Chemical Engineers Handbook, 4th ed. Copyright, 1963, McGraw-Hill Book Company. ... 

Had the system reported above not been heated to 600 °C before it was declared a Kurrol s salt, then these results could be more acceptable. As noted in K2O-P2O5 phase diagrams, systems heated to 600 °C convert to potassium Kurrol s salts irrespective of the degree of polymerization of an ammonium feed stock. Exactly the same results would have been obtained had the starting raw materials been mono- or diammonium orthophosphates. 

Figure 6-1. Calculated phase diagram for the acetone(I)-methanol(2) system.

The example of a binary mixture is used to demonstrate the increased complexity of the phase diagram through the introduction of a second component in the system. Typical reservoir fluids contain hundreds of components, which makes the laboratory measurement or mathematical prediction of the phase behaviour more complex still. However, the principles established above will be useful in understanding the differences in phase behaviour for the main types of hydrocarbon identified. 

Fig. XIV-11. Schematic phase diagram of a microemulsion-fortning system. (From Ref. 77.)...

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Figure A2.5.3. Typical liquid-gas phase diagram (temperature T versus mole fraction v at constant pressure) for a two-component system in which both the liquid and the gas are ideal mixtures. Note the extent of the two-phase liquid-gas region. The dashed vertical line is the direction x = 1/2) along which the fiinctions in figure A2.5.5 are detemiined.

Figure A2.5.5. Phase diagrams for two-eomponent systems with deviations from ideal behaviour (temperature T versus mole fraetion v at eonstant pressure). Liquid-gas phase diagrams with maximum (a) and minimum (b) boiling mixtures (azeotropes), (e) Liquid-liquid phase separation, with a eoexistenee eurve and a eritieal point.

A third kind of phase diagram in a two-eomponent system (as shown in figure A2.5.5(e) is one showing liquid-liquid phase separation below a oritieal-solution point, again at a fixed pressure. (On aT,x diagram, the eritieal point is always an extremum of tire two-phase eoexistenee eurve, but not always a maximum. 

Flalf a century later Van Konynenburg and Scott (1970, 1980) [3] used the van der Waals equation to derive detailed phase diagrams for two-component systems with various parameters. Unlike van Laar they did not restrict their treatment to the geometric mean for a g, and for the special case of b = hgg = h g (equalsized molecules), they defined two reduced variables. 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

In the absence of special syimnetry, the phase mle requires a minimum of tliree components for a tricritical point to occur. Synnnetrical tricritical points do have such syimnetry, but it is easiest to illustrate such phenomena with a tme ternary system with the necessary syimnetry. A ternary system comprised of a pair of enantiomers (optically active d- and /-isomers) together with a third optically inert substance could satisfy this condition. While liquid-liquid phase separation between enantiomers has not yet been found, ternary phase diagrams like those shown in figure A2.5.30 can be imagined in these diagrams there is a necessary syimnetry around a horizontal axis that represents equal amounts of the two enantiomers. 

Syimnetrical tricritical points are also found in the phase diagrams of some systems fomiing liquid crystals. 

Figure A2.5.31. Calculated TIT, 0 2 phase diagram in the vicmity of the tricritical point for binary mixtures of ethane n = 2) witii a higher hydrocarbon of contmuous n. The system is in a sealed tube at fixed tricritical density and composition. The tricritical point is at the confluence of the four lines. Because of the fixing of the density and the composition, the system does not pass tiirough critical end points if the critical end-point lines were shown, the three-phase region would be larger. An experiment increasing the temperature in a closed tube would be represented by a vertical line on this diagram. Reproduced from [40], figure 8, by pennission of the American Institute of Physics.

Another important reaction supporting nonlinear behaviour is the so-called FIS system, which involves a modification of the iodate-sulfite (Landolt) system by addition of ferrocyanide ion. The Landolt system alone supports bistability in a CSTR the addition of an extra feedback chaimel leads to an oscillatory system in a flow reactor. (This is a general and powerfiil technique, exploiting a feature known as the cross-shaped diagram , that has led to the design of the majority of known solution-phase oscillatory systems in flow... 

Flere we discuss the exploration of phase diagrams, and the location of phase transitions. See also [128. 129. 130. 131] and [22, chapters 8-14]. Very roughly we classify phase transitions into two types first-order and continuous. The fact that we are dealing with a finite-sized system must be borne in mind, in either case. 

Frenkel D, Mulder B M and McTague J P 1984 Phase-diagram of a system of hard ellipsoids Phys. Rev.L 52 287-90... 

Robbins M O, Kremer K and Grest G S 1988 Phase diagram and dynamics of Yukawa systems J. Chem. Phys. 88 3286-312... 

The accompanying sketch qualitatively describes the phase diagram for the system nylon-6,6, water, phenol for T > 70°C.f In this figure the broken lines are the lines whose terminals indicate the concentrations of the three components in the two equilibrium phases. Consult a physical chemistry textbook for the information as to how such concentrations are read. In the two-phase region, both phases contain nylon, but the water-rich phase contains the nylon at a lower concentration. On this phase diagram or a facsimile, draw arrows which trace the following procedure ... 

Fig. 1. Phase diagram of an amphiphile—oil—water system that forms a middle-phase microemulsion, definition of microemulsion, and illustration of the...

Fig. 2. The phase diagrams and terminology of a microemulsion system close to its two critical end points, where the middle phase and one of the binodals...

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