Pressure temperature-composition phase

Fig. 12. Pressure-swing distillation of a minimum boiling binary azeotrope, (a) Temperature—composition phase diagram showing the effect of pressure on...

Fig. 1. The pressure-temperature-composition surfaces for the equilibrium between two pure solid phases, a liquid phase, and a vapor phase.

It is difficult to measure partial molar volumes, and, unfortunately, many experimental studies of high-pressure vapor-liquid equilibria report no volumetric data at all more often than not, experimental measurements are confined to total pressure, temperature, and phase compositions. Even in those cases where liquid densities are measured along the saturation curve, there is a fundamental difficulty in calculating partial molar volumes as indicated by... 

The second major component of the education of a modern materials chemist in materials synthesis is, of course, in phase equilibria, possibly through the treatment of quaternary systems and P—T—X (pressure—temperature—composition) equilibria. This subject was essentially eliminated from chemistry departments and is taught in the materials and geological science departments. Every student (and professor) aspiring to be a materials chemist will have to master this subject. 

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. 

Because there is an added term, the composition, binary systems are inherently more complex than unary systems. In order to completely represent the phase diagram of a binary system a three dimensional pressure-temperature-composition (P-T-x) diagram can be constructed. However, it is a more common... 

Equilibrium measurements of the solid hydrate phase have been previously avoided due to experimental difficulties such as water occlusion, solid phase inhomogeneity, and measurements of solid phase concentrations. Instead, researchers have traditionally measured fluid phase properties (i.e., pressure, temperature, gas phase composition, and aqueous inhibitor concentrations) and predicted hydrate formation conditions of the solid phase using a modified van der Waals and Platteeuw (1959) theory, specified in Chapter 5. 

With the evolution of these new structures, the possibility of forming metastable hydrate phases (Section 3.2), and the fact that different structures form at different thermodynamic conditions (pressure, temperature, composition), it is clear that macroscopic methods cannot adequately predict the hydrate structure(s) present. 

Figure 7.7 Phase relationships in the system Al2Si05-Mn2Si05 in pressure-temperature-composition space projected onto the P,Tplane (from Abs-Wurmbach et al., 1983 Langer, 1988). Note the large increase of the andalusite stability field (And) with increasing Mn3+ contents plotted as mole per cent theoretical MnjSiO end-member. Insets (a) and (b) show how the triple point at 500 °C and 3.8 kb for pure Al2Si05 increases with rising Mn3 content of andalusite. [Legend to Mn-Al solid-solutions (ss) Ky = kyanite Sill = sillimanite Bm=braunite Cor=corundum Vir=viridine Qu=quartz.]...

The nitrogen pressure determines the composition of the nitride if equilibrinm is attained. Thermochemical models have been established that correctly predict pressure-temperature-composition (p-T-x) relationships for nitride phases. ... 

Answers to such difficult questions can be found in applied thermodynamics - in terms of measured, macroscopic values of pressures, temperatures, compositions, volumes, enthalpies, etc. This chapter provides an overview of natural gas clathrate hydrates - structures, phase diagrams, and thermodynamic predictions/measurements that guide our understanding in dealing with such questions. The hydrate historical perspective provides an example of how knowledge advances in a technical field. At the conclusion of the chapter, future thermodynamic challenges are presented. 

Fig. 2 Pressure-temperature phase projection and examples of pressure-composition and temperature-composition phase diagrams for a Type I binary mixture.

Palladium.60 One of the unique characteristics of metallic palladium and Pd-Ag or Pd-Au alloys is the high rate of diffusion of hydrogen gas through a metal membrane compared to the rates for other metals such as nickel or iridium. There is no doubt that pressure-temperature-composition curves indicate the presence of palladium hydride phases. 

Figure 4.5 (a) A three-axis pressure-temperature-composition frame, required to display the phase relations in a... 

On a phase boundary, two phases are present (P = 2) and, from equation (S1.4), F = 2. The variance is seen to be equal to two. Thus, phase boundaries form two-dimensional surfaces in the -pressure-temperature-composition representation. A two-component system containing two phases is called a bivariant system. In a bivariant system, it is possible to change any two of the three variables temperature, pressure and composition independently but the third will be fixed by the values selected for the other two. On a phase diagram drawn for a system at atmospheric pressure, phase boundaries are drawn as lines. 

A simple pressure-temperature projection of the pressure-temperature-composition diagram for a mixture is given in Figure 2. It is necessary to define the terms bubble point, dew point, maxcondentherm, and maxcondenbar. A bubble point is a state of liquid mixture at which, if the pressure is decreased slightly, a second phase, a vapour, appears. Similarly, a dew point is a state of a vapour at which, if the pressure is increased slightly, a liquid phase appears. The dew point locus and the bubble point locus are continuous curves meeting at the critical point. The maxcondentherm and maxcondenbar are the maximum temperature and maximum pressure respectively on the bubble point-dew point... 

Determine the conditions of equilibrium (pressure, temperature, composition) in phase transformations and chemical reactions. 

For the design of distillation and absorption apparatus, it is necessary to know the equilibrium relationship yfxi) either as an analytical, homogenous equation, or at least as an equilibrium curve. According to Eq. (1-77), the fugacity or the fugacity coefficients can be calculated or found experimentally to be a function of pressure, temperature and phase composition. An expression for the fugacity is... 

The separation factor is therefore a direct measure of the separation efficiency of a separation unit or the whole process, and is thus of practical importance. It is usually dependent on pressure, temperature, and phase composition. Large values for the separation factor characterize a process whith a low separation effort. The more a approaches unity, the more difficult the separation. When a = 1 separation is impossible. 

Figure 6.6 Room-temperature pressure versus composition phase diagram of Bai Sr,fRu03 [34].

As objective function for fitting the required g -model parameters different types of objective functions and experimental or derived properties X, for example, vapor phase mole fraction, pressure, temperature, K-factor K , separation factor au, and so on, can be selected, where either the relative or the absolute deviation of the experimental and correlated values (pressure, temperature, vapor phase composition, etc.) can be minimized. 

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