High pressure, phase equilibria solid-liquid equilibrium

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

The Earth s core is thought to be mainly iron, and seismic data indicate that the inner core is solid and the outer core is liquid. The pressure at the center of the Earth is 3.6 x 1011 Pa, and at this pressure, iron melts at 6350 K. From this information, what can you infer about the solid-liquid equilibrium boundary in the iron high-pressure phase diagram (Pressure and temperature both increase toward the Earth s center.)... 

Foot et al. [22] have determined experimentally the high-pressure phase behavior of the binary systems (butane adamantane) and (butane -I- diamantane). The phase behavior of these binary systems is shown schematically in Figure 1.7. Because the phase diagrams of pure adamantane and diamantane show a solid-solid (si + S2) transition line the curve representing the (solid diamondoids -I- liquid + vapor) equilibrium will split into two branches. One branch corresponds to the (si -f 1 -f v) equilibrium and the other branch corresponds to the (. 2 1 ) equilibrium. Both branches intersect at the (si S2) equilibrium line of the pure diamondoids. The... 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

The phase equilibrium for pure components is illustrated in Figure 4.1. At low temperatures, the component forms a solid phase. At high temperatures and low pressures, the component forms a vapor phase. At high pressures and high temperatures, the component forms a liquid phase. The phase equilibrium boundaries between each of the phases are illustrated in Figure 4.1. The point where the three phase equilibrium boundaries meet is the triple point, where solid, liquid and vapor coexist. The phase equilibrium boundary between liquid and vapor terminates at the critical point. Above the critical temperature, no liquid forms, no matter how high the pressure. The phase equilibrium boundary between liquid and vapor connects the triple point and the... 

In applying equation 33, Cpsl (the constant-pressure molar heat capacity of the stoichiometric liquid) is usually extrapolated from high-temperature measurements or assumed to be equal to Cpij of the compound, whereas the activity product, afXTjafXT), is estimated by interjection of a solution model with the parameters estimated from phase-equilibrium data involving the liquid phase (e.g., solid-liquid or vapor-liquid equilibrium systems). To relate equation 33 to an available data base, the activity product is expressed... 

The potential of supercritical extraction, a separation process in which a gas above its critical temperature is used as a solvent, has been widely recognized in the recent years. The first proposed applications have involved mainly compounds of low volatility, and processes that utilize supercritical fluids for the separation of solids from natural matrices (such as caffeine from coffee beans) are already in industrial operation. The use of supercritical fluids for separation of liquid mixtures, although of wider applicability, has been less well studied as the minimum number of components for any such separation is three (the solvent, and a binary mixture of components to be separated). The experimental study of phase equilibrium in ternary mixtures at high pressures is complicated and theoretical methods to correlate the observed phase behavior are lacking. 

Solubilities of meso-tetraphenylporphyrin (normal melting temperature 444°C) in pentane and in toluene have been measured at elevated temperatures and pressures. Three-phase, solid-liquid-gas equilibrium temperatures and pressures were also measured for these two binary mixtures at conditions near the critical point of the supercritical-fluid solvent. The solubility of the porphyrin in supercritical toluene is three orders of magnitude greater than that in supercritical pentane or in conventional liquid solvents at ambient temperatures and pressures. An analysis of the phase diagram for toluene-porphyrin mixtures shows that supercritical toluene is the preferred solvent for this porphyrin because (1) high solubilities are obtained at moderate pressures, and (2) the porphyrin can be easily recovered from solution by small reductions in pressure. 

Dissolved pollutants can be transferred from a condensed (liquid or solid) phase into the vapor phase under the action of steam or air streams. As a mass transfer phenomenon, it is driven by a concentration gradient between the condensed and gas phases. It applies fundamentally to pollutants that show sufficiently high vapor pressures under the operating conditions. If the source phase is a liquid, Henry s law regulates the corresponding equilibrium (see Chapter 6). Steam can remove pollutants that may be difficult to remove with air. Obviously, the resulting (contaminated) gas stream or condensate must be treated before its release into the atmosphere. 

Alkene hydration to alcohols is a reaction of some industrial importance, although there have been few fundamental investigations in recent years. Beranek and Kraus have pointed out that the reaction equilibrium for the vapour phase process, though more favoured by low temperatures, still favours dehydration even at room temperature. Consequently, when high temperatures are employed to give more rapid reaction, high pressures must also be employed and even then the maximum attainable conversion may be low. Matters are improved somewhat by use of a three phase system (solid catalyst, liquid water, and gaseous alkene), for which conversion is improved by virtue of the alcohol solubility in water. 

The solubility is defined with respect to a second precipitated phase. The solubility of an impurity is the maximum concentration, which can be incorporated in the liquid or solid phase without precipitating a second phase. For most impurities in solid silicon at high-temperatures, equilibrium is achieved with the liquid phase governed by the liquidus in the phase diagram. Solid solubility is temperature-dependent as represented by the solidus or solvent curves in the phase diagram. At lower temperatures, the reference phase is usually a compound or an impurity-rich alloy. When the impurity is volatile, the saturated crystal is in equilibrium with the vapor, and the impurity solubility also depends on its vapor pressure. 

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