Phase diagram, for solid-liquid

TWO-COMPONENT SOLID-LIQUID PHASE DIAGRAMS FOR SOLID-LIQUID EQUILIBRIA... 

Fig. 2 Schematic phase diagrams for solid-liquid equilibria in three dimensions, pressure p, temperature T, and distribution D (a) for a macroscopic system, in which the change from solid to liquid is discontinuous at the melting point Tm(p) and D changes from — 1 to +1 (b) for a small system, for which D changes discontinuously between —1 and an intermediate value, and again between a much higher intermediate value and +1, but varies continuously between those two intermediate values...

Univariant equilibrium for which there is one degree of freedom, represents the equilibrium between two co-existing phases. Since there is only one degree of freedom, choosing a value for one external variable, e.g. temperature, determines the remaining variable in a dependent manner, and the locus of points represented on the phase diagram for univariant behavior must lie on a line or curve. Thus the curves on the unary phase diagram represent solid-liquid, solid-vapor, solid-solid, and liquid-vapor equilibrium. 

The order of a transition can be illustrated for a fixed-stoichiometry system with the familiar P-T diagram for solid, liquid, and vapor phases in Fig. 17.2. The curves in Fig. 17.2 are sets of P and T at which the molar volume, V, has two distinct equilibrium values—the discontinuous change in molar volume as the system s equilibrium environment crosses a curve indicates that the phase transition is first order. Critical points where the change in the order parameter goes to zero (e.g., at the end of the vapor-liquid coexistence curve) are second-order transitions. 

Figure 8 Pressure versus temperature phase diagram for a liquid, showing the solid/liquid/gas phase boundaries and above a 7). and a P, the supercritical domain. Abbreviations T, critical temperature P, critical pressure.

Following is a portion of a phase diagram for two liquids that are only partially miscible. Note that the phase diagram contains both the coexistence curve (solid line) and a curve indicating the stability limit for each phase (dashed line) (i.e., the... 

AC or BC, which melts at a higher temperature than either of the pure elements (except for the InSb-Sb case). The binary phase diagram consists of two simple eutectic systems on either side of the compound (e.g., the A-AC and the AC-C systems). The third binary phase diagram represents solid-liquid equilibrium between elements from the same group. In Figure 1 the A-B portion of the ternary phase diagram is depicted as being isomorphous... 

Phase diagrams for solid mixtures and their melting behavior often resemble those of liquid mixtures and their boiling behavior. In the same way that repeated boiling can purify a liquid mixture, repeated melting can purify a solid mixture. This is called zone refining it is used to purify metals. 

Suppose you know the phases of H2O in your system at equilibrium. You don t have to specify any degrees of freedom because there is only one set of conditions in which that will occur For H2O in the solid, liquid, and gas phases, those conditions are 273.16 K and 6.11 mbar. (See Figure 6.5 There is only one point on that phase diagram where solid, liquid, and gas exist in equilibrium, and that is the triple point.) There is a relationship between the number of phases occurring at equilibrium and the number of degrees of freedom necessary to specify the point in the phase diagram that describes the state of the system. 

A brief discussion of solid-liquid phase equihbrium is presented prior to discussing specific ciystaUizatiou methods. Figures 22-1 and 22-2 illustrate the phase diagrams for biuaiy solid-solution and eutec-... 

Fig. 3.1. The phase diagram for the lead-tin alloy system. There ore three phases L - a liquid solution of lead and tin (Pb) - a solid solution of tin in lead and (Sn) - o solid solution of lead in tin. The diagram is divided up into six fields - three of them are single-phase, and three ore two-phose.

Figure 8.1 Phase diagram for CCF. Point (a) is the critical point and point (b) is the triple point. Line ab gives the vapor pressure of the liquid, line be gives the vapor pressure of the solid, and line bd gives the melting temperature as a function of pressure.

Figure 8.21 gives the ideal solution prediction equation (8.36) of the effect of pressure on the (solid + liquid) phase diagram for. yiC6H6 + xj 1,4-C6H4(CH3)2. The curves for p — OA MPa are the same as those shown in Figure 8.20. As... 

Solid + Liquid Equilibria in Less Ideal Mixtures We should not be surprised to find that the near-ideal (solid + liquid) phase equilibria behavior shown in Figures 8.20 and 8.21 for (benzene + 1,4-dimethylbenzene) is unusual. Most systems show considerably larger deviations. For example, Figure 8.22 shows the phase diagram for. vin-C Hw +. The solid line is the fit of the... 

Figure 8.22 (Solid + liquid) phase diagram for. vin-CiaHut +. viCsHs. The circles are the experimental melting temperatures and the lines are the fit of the experimental results to equation (8.31). The dashed lines are the ideal solution predictions from equation (8.30).

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

P8.4 The (solid + liquid) phase diagram for (.Yin-C6Hi4 + y2c-C6Hi2) has a eutectic at T = 170.59 K and y2 = 0.3317. A solid phase transition occurs in c-CftH at T— 186.12 K, resulting in a second invariant point in the phase diagram at this temperature and. y2 — 0.6115, where liquid and the two solid forms of c-C6H12 are in equilibrium. A fit of the experimental... 

FIGURE 8-7 The phase diagram for carbon dioxide (not to scale). The liquid can exist only at pressures above 5.1 atm. Note the slope of the boundary between the solid and liquid phases it shows that the freezing point rises as pressure is applied. 

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

Self-Test 8.4A From the phase diagram for carbon dioxide (Fig. 8.7), predict which is more dense, the solid or the liquid phase. Explain your conclusion. 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

Use the phase diagram for compound X below to answer these questions (a) Is X a solid, liquid, or gas at normal room temperatures (b) What is the normal melting point ol X ... 

The phase diagram constructed in this way, with the assumption that the difference in free energy of liquid lead and solid lead, Fo(l) — Fg(c), is a linear function of the temperature, and that the other parameters remain unchanged, is shown as Fig. 8. It is seen that it is qualitatively similar to the phase diagram for the lead-thallium system in the range 0-75 atomic percent thallium. 

Although fractional crystallization has always been the most common method for the separation of diastereomers. When it can be used, binary-phase diagrams for the diastereomeric salts have been used to calculate the efficiency of optical resolution. However, its tediousness and the fact that it is limited to solids prompted a search for other methods. Fractional distillation has given only limited separation, but gas chromatography and preparative liquid chromatography have proved more useful and, in many cases, have supplanted fraetional crystallization, especially where the quantities to be resolved are small. 

Fig. 5. The essential form of the phase diagram for the mesogen GB(3.0, 5.0, 2, 1) the open circles indicate the approximate coexistence lines and the solid circles show the density of the isotropic liquid in equilibrium with the vapour phase...

The phase diagram for water, shown in Figure 11-39. illustrates these features for a familiar substance. The figure shows that liquid water and solid ice coexist at the normal freezing point, T = 273.15 K and P = 1.00 atm. Liquid water and water vapor coexist at the normal boiling point, P — 373.15 K and P — 1.00 atm. The triple point of water occurs at 7 = 273.16 K and P = 0.0060 atm. The figure shows that when P is lower than 0.0060 atm, there is no temperature at which water is stable as a liquid. At sufficiently low pressure, ice sublimes but does not melt. 

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