Solids sublimation pressure

One complication with this description is that a species can be present in a liquid mixture, though at the temperature and pressure of the mixture the substance would be a vapor or a solid as a pure component. This is especially troublesome if the compound is below its melting point, so that it is the solid sublimation pressure rather than the vapor pressure that is known, or if the compound is above its critical temperature, so that the vapor pressure is undefined. In the first case one frequently ignores the phase change and extrapolates the liquid vapor pressure from higher temperatures down to the temperature of interest using, for example, the Antoine equation, eqn. (2.3.11). For supercritical components it is best to use an EOS and compute the fugacity of a species in a mixture, as described in Section 2.5. 

Phosphorus exists as white and red phosphorus. The former allotrope may be preserved in the dark at low temperatures but otherwise reverts to the more stable red form. The white form is a waxy, translucent, crystalline, highly-toxic solid subliming at room temperature and inflaming in air at 35°C, so it is handled under water. The red form is a reddish violet crystalline solid which vaporizes if heated at atmospheric pressure and condenses to give white phosphorus. The red form ignites in air at 260°C. Both are insoluble in water, and white phosphorus can be stored beneath it. Phosphorus forms a host of compounds such as phosphine, tri- and penta-halides, tri-, tetra- and penta-oxides, oxyacids including hypophosphorous, orthophosphorous and orthophosphoric acids. 

The reaction mixture was removed from the vessel and distilled at a pressure of 30-60 mm, and a bath temperature of 30°C to 50°C until the methanol had all been removed. The extremely viscous tarry residue remaining in the still pot was given a very crude distillation, the distillate boiling at B2°C to 1 32°C/2 mm. In an attempt to purify this distillate by a more careful distillation, 5.3 g of a liquid distilling from 53°C to 150°C/5 mm was collected. At this point, much solid sublimate was noted not only in this distillate but in the condenser of the still. 7 g of the solid sublimate was scraped out of the condenser of the still. Recrystallization of the sublimate from ethyl acetate containing a small amount of petroleum ether gave beautiful crystals melting at 175°C to 177°C (5 g). Infrared analysis confirmed that this compound was hydroquinone (9% conversion). 

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

Abbreviations s, solid sublimes d, solid decomposes. Under pressure. 

FIGURE 7.26 For some substances and at certain pressures, the molar Gibbs free energy of the liquid phase might never lie lower than those of the other two phases. For such substances, the liquid is never the stable phase and, at constant pressure, the solid sublimes when the temperature is raised to the point of intersection of the solid and vapor lines. 

Liquid carbon dioxide is usually stored under 20 bar pressure at — 18°C. Compression and cooling of the gas between the temperature limits at the triple point and the critical point will cause it to liquefy. The triple point is the pressure temperature combination at which carbon dioxide can exist simultaneously as gas, liquid and solid. Above the critical temperature point of 31°C it is impossible to liquefy the gas by increasing the pressure above the critical pressure of 73 bar. Reduction in the temperature and pressure of liquid below the triple point causes the liquid to disappear, leaving only gas and solid. (Solid carbon dioxide is also available for cryogenic work and at —78°C the solid sublimes at atmospheric pressure.)... 

To model the solubility of a solute in an SCF using an EOS, it is necessary to have critical properties and acentric factors of all components as well as molar volumes and sublimation pressures in the case of solid components. When some of these values are not available, as is often the case, estimation techniques must be employed. When neither critical properties nor acentric factors are available, it is desirable to have the normal boiling point of the compound, since some estimation techniques only require the boiling point together with the molecular structure. A customary approach to describing high-pressure phenomena like the solubility in SCFs is based on the Peng-Robinson EOS [48,49], but there are also several other EOS s [50]. 

In the phase diagram, panel (a). solid C02 (Dry Ice) is in equilibrium with gaseous C02 at a temperature of —78.7°C and a pressure of 1.00 bar." The solid sublimes without turning into liquid. At any temperature above the triple point at —56.6°C, there is a pressure at which liquid and vapor coexist as separate phases. For example, at 0°C, liquid is in equilibrium with gas at 34.9 bar. Moving up the liquid-gas boundary, we see that two phases always exist until the critical point is reached at 31.3 C... 

In this approach the standard state fugacity of a liquid or solid component is usually the fugacity of die pure solid or liquid component, and is closely related to the sublimation pressure P- b or vapour pressure P.at, respectively. I.e., on the sublimation curve of a pure component we have... 

The enhancement factor contains three terms supercritical phase, ideal behaviour of the pure component 2 in the vapour phase at the sublimation pressure, and the Poynting factor that describes the influence of the pressure on the fugacity of pure solid 2. 

Some of these ambiguities can be partially solved using a simple approach recently proposed by Gamier et al. [62], The sublimation pressure of a solid can be estimated using experimental fusion properties and the vaporization enthalpy derived from the equation of state. Using the Clapeyron equation P b can be approximated by ... 

At temperatures below the triple-point temperature, the vapor-pressure line divides the conditions for which the substance is solid from the conditions for which the substance is gas. This line also is called the sublimation-pressure line. Theoretically, this line extends to a temperature of absolute zero and a pressure of absolute zero. 

Elemental iodine, I2 (solid, sublimes at 184°C), consists of violet-black rhombic crystals with a lustrous metallic appearance. More irritating to the lungs than bromine or chlorine, its general effects are similar to the effects of these elements. Exposure to iodine is limited by its low vapor pressure, compared to liquid bromine or gaseous chlorine or fluorine. 

Thus, If the solid phase properties (densities and sublimation pressures) are known, then the solubility of the solute In the supercritical solvent at any pressure and temperature can be calculated provided an equation of state Is available for the calculation of The results for five binary systems using Patel-... 

Enhancement factors are given In Table 2. Solid densities and sublimation pressures used In the solubility calculations (Eq. 2) are given In Table 3. The densities were supplied by the manufacturers whereas the sublimation pressures were extrapolated... 

From the third law, entropies are always positive, requiring that the chemical potential of all phases decrease with temperature. However, because entropy is a measure of randomness, 5m gas > liq >, S , sol, and the chemical potential falls most rapidly with temperature for the gas phase and least rapidly for the solid phase. In Fig. la (drawn for a particular value of pressure), as the temperature is increased, pliq(7 ) crosses psol(T) at the melting point, and the liquid remains the most stable phase until pgas(T) crosses pliq(r) at the boiling point. In Fig. lb (drawn for a different substance or at a different pressure), pgas(7 ) falls so rapidly with temperature that it crosses psol( T) before pliq(7 ) does. As a result, liquid is never the most stable phase and, at the given pressure, the solid sublimates directly to gas. 

The sublimation pressure of C02 at —78°C is 780 torr. What area should be assigned to solid C02 on the Cu surface in order to obtain the same surface area as calculated in Example 4. 

Zirconium tetrachloride is a white crystalline solid with specific gravity 2.803.4 The solid sublimes under atmospheric pressure at 331° [log pBin. = — (26,000/4.57T) + 12.30] but melts at 437° under its own pressure, which is about 25 atm. at this temperature.18 The vapor density shows normal behavior up to 500°, at which point dissociation is suspected.16 Electron-diffraction results show tetrahedral symmetry with the Zr-Cl distance 2.33 A.17 Todd18 has recently determined the heat capacity of zirconium tetrachloride at low temperatures (extrapolated below —222°) and calculated the usual thermodynamic constants for the compound. The melting point of hafnium tetrachloride has been estimated as 432° under its own pressure, but the solid sublimes under atmospheric pressure at 317°.12 Both metal chlorides are extremely hygroscopic. They are easily soluble in water, although extensively hydrolyzed. All high-purity samples should be desiccated as well as possible. 

The phase diagram (Figure 1-18) indicates the existence of three phases solid, liquid, and gas. The conditions under which they exist are separated by three equilibrium lines the vapor pressure line TA, the melting pressure line TC, and the sublimation pressure line BT. The three lines meet at point T,... 

The importance of a suitable G.C. method for evaluating the pure solid properties was evidenced. The limitations of the different G.C. methods are due to the limited experimental data available in the literature for heavy multifunctional compounds. The PR EOS with classical mixing rules gives the same results than the most complex UNIFAC approach. The importance of the sublimation pressure for correlating solubility data was underlined. 

Face-centered cubic argon is the stable solid phase of pure argon, but upon the addition of as little as 1 percent of N2 to Ar, the solid phase crystallizes with the close-packed hexagonal structure. A study of the sublimation pressures of solid solutions of Ar with small amounts of N2 would give valuable information concerning the hexagonal phase, and such a study could be made with the apparatus used in this experiment. 

The partial pressure of the condensing species is a function of the tsrpe of transformation (i.e., vapor to liquid condensation or vapor to solid sublimation) and the temperature. The partial pressure of the condensing species, P , as a function of temperature, T, is given by... 

V apor pressure is an important property of liquids, and to a much lesser extent, of solids. If a liquid is allowed to evaporate in a confined space, tlie pressure of tlie vapor phase increases as tlie amount of vapor increases. If tliere is sufficient liquid present, tlie pressure in tlie vapor space eventually comes to equal exactly tlie pressure exerted by the liquid at its own surface. At tliis point, a dynamic equilibrium exists in wliich vaporization and condensation take place at equal rates and tlie pressure in tlie vapor space remains constant. The pressure exerted at equilibrium is called tlie vapor pressure of the liquid. Solids, like liquids, also exert a vapor pressure. Evaporation of solids (sublimation) is noticeable only for tlie few solids characterized by appreciable vapor pressures. 

The pure solid sublimes before melting at ordinary pressures. From studies on CaFg-AlFg and NaCl-AlFg binary systems, Millet et al. (4) estimated a triple point temperature for AlPg of 2523 K at 30000 atm. Our adopted values lead to a pressure for AIFg(t) AlFg(g) of -2200 atm. The calculated dimer pressure at this temperature is also -2200 atm. 

One of the most useful and convenient techniques for the purification of solids is sublimation. In this process, the solid is warmed (often under reduced pressure) until its vapor pressure becomes high enough for it to collect on a cooled surface placed above the solid. Sublimation is limited to compounds which have reasonably high vapor pressures and which pass directly from the solid state to the vapor. However, the process involving initial melting followed by vaporization and deposition on the condenser may be carried out in the same apparatus and is often loosely called sublimation. 

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