Phase diagrams for pure substances

Figure 2-78. Typical phase diagram for a pure substance showing P-V-T surface and its projections [60],...

The conditions that apply for the saturated liquid-vapor states can be illustrated with a typical p-v, or (1 /p), diagram for the liquid-vapor phase of a pure substance, as shown in Figure 6.5. The saturated liquid states and vapor states are given by the locus of the f and g curves respectively, with the critical point at the peak. A line of constant temperature T is sketched, and shows that the saturation temperature is a function of pressure only, Tsm (p) or psat(T). In the vapor regime, at near normal atmospheric pressures the perfect gas laws can be used as an acceptable approximation, pv = (R/M)T, where R/M is the specific gas constant for the gas of molecular weight M. Furthermore, for a mixture of perfect gases in equilibrium with the liquid fuel, the following holds for the partial pressure of the fuel vapor in the mixture ... 

Fig. 3.2. A stylized phase diagram for a simple pure substance. The dashed line represents 1 atm pressure and the intersection with the solid-liquid equilibrium line represents the normal boiling point and the intersection with the liquid-vapor equilibrium line represents the normal boiling point.

Phase Diagram for a Pure Substance — Use of Phase Diagrams — Vapor Pressure of a Pure Substance Pressure-Volume Diagram for a Pure Substance -Density-Temperature Diagram for a Pure Substance Two-Component Mixtures 61... 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

A typical phase diagram for a pure substance (Figure 1) shows the temperature and pressure regions where the substance occurs as a single phase, such as solid, liquid, or gas. 

QUESTION 39 REFERS TO THE FOLLOWING PHASE DIAGRAM FOR A PURE SUBSTANCE ... 

A phase diagram is a convenient way of representing the phases of a substance as a function of temperature and pressure. For example, the phase diagram for water (Fig. 16.55) shows which state exists at a given temperature and pressure. It is important to recognize that a phase diagram describes conditions and events for a pure substance in a closed system of the type represented in Fig. 16.53, where no material can escape into the surroundings and no air is present. 

Figure 1.14.4. Phase diagram for the solubility ot sugar in water. Note that when we were drawing a phase diagram for a pure substance, water or dry ice, the parameters that were varied were temperature and pressure. In this diagram, however, the phase diagram for a mixture, temperature and composition are the parameters being varied. Pressure is assumed to be constant.

In Figure 2.2, we show the temperature-density phase diagram for a general pure substance. As witli the pressure-temperature diagram, the temperature-density phase diagram is divided by various curves into vapor, liquid, and solid phases. Outside these curves, the system exists as a single phase. 

Figure 7.8 Phase diagram for a pure substance. From Dean, J. R., Extraction Methods for Environmental Analysis, Copyright 1998. John Wiley Sons Limited. Reproduced with permission.

The transformation of a pure compound from a liquid to a gaseous state and vice versa corresponds to a phase change that can be induced over a limited domain by pressure or temperature. For example, a pure substance in the gaseous state cannot be liquefied above a given temperature, called the critical temperature Tq, irrespective of the pressure applied to it. The minimum pressure required to liquefy a gas at its critical temperature is called the critical pressure Pq (Figure 6.1). These points are the defining boundaries on a phase diagram for a pure substance. The curve, which limits the gas and liquid domains, stops at the critical point... 

We can represent the regions of stability of gases, liquids and solids under various temperature and pressure conditions using a phase diagram showing at which phase each substance is the most stable. As we know from thermodynamics, the most stable phase of a pure substance at a particular temperature and pressure is the one with the lowest chemical potential. A phase transition is the spontaneous conversion of one phase into another phase, which occurs at a characteristic temperature at a given pressure. For example, as seen in Figure 4.1, under latm external pressure, above 0°C, the chemical potential of... 

For every substance there is a temperature above which it can no longer exist as a liquid, no matter how much pressure is applied. Likewise, there is a pressure above which the substance can no longer exist as a gas no matter how high the temperature is raised. These points are called the supercritical temperature (T ) and supercritical pressure (Pe) respectively and are the defining boundaries on a phase diagram for a pure substance. Beyond these boundaries, the substance has properties that are intermediate between a liquid and a gas and is called a supercritical fluid. 

Figure 33 General p-T phase diagram for a non-defined pure substance.

Figure 4.8 Phase diagram for a pure substance composed of hard spheres. The fluid-phase Z was computed from the Carnahan-Starling equation (4.5.4) the solid-phase Z was taken from the computer simulation data of Alder et al. [14]. The broken horizontal line at Zt = 6.124 connects fluid (T = 0.494) and solid (t = 0.545) phases that can coexist in equilibrium, as computed by Hoover and Ree [12].

Figure 9.1 Schematic phase diagrams for a pure substance, (left) An iF-diagram, which cannot show the relative amounts in each phase when two phases are present, (right) An IF -diagram, which can show relative amounts, cp = critical point and tp = triple point.

---