Solid-liquid-gas equilibrium

The location of the UCEP is quite important in these mixtures this critical point gives the maximum temperature at which solid-gas equilibrium exists at all pressures. In order to obtain its location, we first used our NMR method to determine the S-L-G line. The results of our experimental determination of the pressure-temperature trace for the solid-liquid-gas equilibrium line that terminates at the UCEP for the naphthalene-carbon dioxide system is shown in Figure 7. 

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. 

However, for mixtures of TPP and toluene, a third (liquid) phase forms in the presence of the gas and the solid, at pressures well below the critical pressure of toluene. At higher pressures, gas-liquid and solid-liquid equilibria were observed, rather than gas-solid equilibrium. Thus, phase compositions for gas-liquid equilibrium were measured for this binary mixture to give TPP solubilities in each of the fluid phases. Pressures and temperatures for three-phase, solid-liquid-gas equilibrium were also measured for both binary mixtures. 

The following experimental techniques were used to measure the pressures and temperatures for solid-liquid-gas equilibrium, phase compositions (bubble and dew points) for gas-liquid equilibrium, and solid solubilities in supercritical pentane. Experimental procedures and the apparatus are described in detail elsewhere (13). 

Figure 1. Pressure -Temperature Projection of Vapor Pressure Curve for Pentane and Solid-Liquid-Gas Equilibrium Curve for Pentane-TPP Mixtures.

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

We call each solid line in this graph a phase boundary. If the values of p and T lie on a phase boundary, then equilibrium between two phases is guaranteed. There are three common phase boundaries liquid-solid, liquid-gas and solid-gas. The line separating the regions labelled solid and liquid , for example, represents values of pressure and temperature at which these two phases coexist - a line sometimes called the melting-point phase boundary . 

Now, consider particle motion in a phase (solid, liquid, gas). If the phase is initially inhomogeneous, random motion of atoms tends to homogenize the phase. If several phases are present and there are exchanges between the phases, the interphase reaction or exchange tends to make the chemical potential of all exchangeable components the same in all phases and diffusion again works to homogenize each phase. Hence, at equilibrium, the chemical potential of a component is constant. 

Potential energy surfaces or profiles are descriptions of reactions at the molecular level. In practice, experimental observations are usually of the behaviour of very large numbers of molecules in solid, liquid, gas or solution phases. The link between molecular descriptions and macroscopic measurements is provided by transition state theory, whose premise is that activated complexes which form from reactants are in equilibrium with the reactants, both in quantity and in distribution of internal energies, so that the conventional relationships of thermodynamics can be applied to the hypothetical assembly of transition structures. 

Weidner E, Wiesmet V, Knez Z et al (1997) Phase equilibrium (solid-liquid-gas) in polyethylene glycol-carbon dioxide systems. J Supercrit Fluids 10(3) 139-147... 

The technique was implemented as follows. With solid naphthalene in our solubility cell we brought the system to a desired temperature and C02 pressure such that solid-supercritical gas equilibrium existed. The temperature was then slowly increased (heating rate approximately 1°C/hour) at constant pressure, while the NMR signal was monitored. When the S-L-G line was intersected, the solid naphthalene in the cell would melt with the formation of the naphthalene-rich liquid phase, and this resulted in a large and rapid increase in our NMR signal. The temperature at which we saw this discontinuous jump in our NMR signal gave the location of the phase line at that pressure. 

Figure 1 Phase diagram for pure water. Solid line liquid-gas equilibrium. 

Projecting the new phase transition points (Tm, Pi) and (7b, Pi) onto the phase (P versus T) diagram leads to points D and C and hence the line AD represents the variation of melting point (i.e. solid-liquid equilibria) with pressure for the substance whilst the line CB represents the variation in the boiling point with pressure for the liquid/gas equilibrium. 

Equilibrium concentrations which tend to develop at solid-liquid, gas-liquid, or liquid-liquid interfaces are displaced or changed by molecular and turbulent diffusion between bulk fluid and fluid adjacent to the interface. Bulk motion (Taylor diffusion) aids in this mass-transfer mechanism also. 

For each polymorph (single compound), there is a solid-liquid equilibrium curve and a solid-gas equilibrium curve. The solid-gas curves meet at a point. If the liquid-gas equilibrium curve meets the two solid-gas curves after this point of intersection, there will be a solid 1, solid 2 equilibrium curve and a reversible transition point 1 2 at a specific pressure. This is known as enantiotropy. At the transition point, the free energy of the two forms is the same. 

You know that a substance s state depends on temperature and that pressure affects state changes. To get a complete picture of how temperature, pressure, and states are related for a particular substance, you can look at a phase diagram. A phase diagram has three lines. One line is a vapor pressure curve for the liquid-gas equilibrium. A second line is for the liquid-solid equilibrium, and a third line is for the solid-gas equilibrium. All three lines meet at the triple point. The triple point is the only temperature and pressure at which three states of a substance can be in equilibrium. 

Fig. 4.28 Generalized phase diagram. Only a supercritical fluid exists above the critical temperature (T ) and critical pressure (p ), which has properties intermediate between liquid and gas. (Note water is unusual in having a negative slope for the solid-liquid phase equilibrium line.)...

Here 7ig is the interfacial tension at the liquid-gas interface, and and are the interfacial tensions between the solid-gas and solid-liquid interfaces, respectively. Thus, when the solid-liquid-gas interface is at equilibrium, by using the knowledge of 7ig and the contact angle, we can determine the difference 7,.g — 7 1 but not their absolute values. 

In the contrary to the critical point in the case of the liquid - gas equilibrium, in the case of the solid - liquid equilibrium a critical point has never been observed at all. It is suspected, however, that there should be a critical point also for the solid - liquid equilibrium. At very high pressures, it is believed that the matter will be converted into a metallic state. 

With many million pure substances now known, an essentially infinite number of mixtures can be formed, resulting in a diversity of phase behavior that is overwhelming. Consider just two components not only can binary mixtures exhibit solid-gas, liquid-solid, and liquid-gas equilibria, but they might also exist in liquid-liquid, solid-solid, gas-gas, gas-liquid-liquid, solid-liquid-gas, solid-solid-gas, solid-liquid-liquid, solid-solid-liquid, and solid-solid-solid equilibria. That s a dozen different kinds of phase equilibrium situations— just for binary mixtures. For multicomponent mixtures the possibilities seem endless. 

WEI Weidner, E., Wiesmet, V., Knez, Z., and Skerget, M., Phase equilibrium (solid-liquid-gas) in polyethyleneglycol-caibon dioxide systems, J. Supercrit. Fluids, 10, 139, 1997. 

Sorption isotherms of the wet solid are, from the point of view of model structure, equilibrium relationships, and are a property of the solid-liquid-gas system. For the most common air-water system, sorption isotherms are, however, traditionally considered as a solid property. Two forms of sorption isotherm equations exist—explicit and implicit ... 

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