Solid-Vapor Phase Transition

Solids can be vaporized, so solids, too, have a vapor pressure. Sublimation is the process by which molecules go directly from the solid phase to the vapor phase. The reverse process, in which molecules go directly from the vapor phase to the solid phase, is called deposition. Naphthalene, which is the substance used to make mothballs, has a fairly high vapor pressure for a solid (1 mmHg at 53°C) thus, its pungent vapor quickly permeates an enclosed space. Iodine also sublimes. At room temperature, the violet color of iodine vapor is easily visible in a closed container. 

Because molecules are more tightly held in a solid, the vapor pressure of a solid is generally much less than that of the corresponding liquid. The molar heat of sublimation (A// ,h) of a substance is the energy, usually expressed in kilojoules, required to sublime 1 mole of a solid. It is equal to the sum of the molar heats of fusion and vaporization  

Equation 12.6 is an illustration of Hess s law [M Section 5.5]. The enthalpy, or heat change, for the overall process is the same whether the substance changes directly from the solid to the vapor phase or if it changes from the solid to the liquid and then to the vapor phase. 

A heating curve can also be used to explain why hikers stranded by blizzards are warned not to consume snow in an effort to stay hydrated. When you drink cold water, your body expends energy to warm the water you consume to body temperature. If you consume snow, your body must first expend the energy necessary to melt the snow, and then to warm it. Because a phase change is involved, the amount of energy required to assimilate snow is much greater than the amount necessary to assimilate an equal mass of water—even if the water is ice-cold. This can contribute to hypothermia, a potentially dangerous drop in body temperature. 

You may want to review the calculation of the heat exchanged between the system and surroundings for temperature changes and phase changes [H4 Sections 5.3 and 5.4]. 

Because molecules are more tightly held in a sohd, the vapor pressure of a sohd is generally much less than that of the corresponding liquid. The molar enthalpy of sublimation of a 

CHAPTER 12 Intermolecular Forces and the Physical Properties of Liquids and Solids 

Heat required Heat required Heat deposited to melt and warm to warm water by boiling ice from 0°C from 0°C water 

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Vapor Pressure Equations of Adamantane and Diamantane for Eiquid-Vapor and Solid-Vapor Phase Transitions... 

In pharmaceutical systems, both heat and mass transfer are involved whenever a phase change occurs. Lyophilization (freeze-drying) depends on the solid-vapor phase transition of water induced by the addition of thermal energy to a frozen sample in a controlled manner. Lyophilization is described in detail in Chapter 16. Similarly, the adsorption of water vapor by pharmaceutical solids liberates the heat of condensation, as discussed in Chapter 17. 

It is also possible to construct schematic graphs like those of Figures 5.5 and 5.6 for solid-liquid, solid-solid, and solid-vapor phase transitions. 

Solid-Vapor Phase Transition Phase Diagrams... 

With the critical exponent being positive, it follows that large shifts of the critical temperature are expected when the fluid is confined in a narrow space. Evans et al. computed the shift of the critical temperature for a liquid/vapor phase transition in a parallel-plates geometry [67]. They considered a maximum width of the slit of 20 times the range of the interaction potential between the fluid and the solid wall. For this case, a shift in critical temperature of 5% compared with the free-space phase transition was found. From theoretical considerations of critical phenomena... 

We saw in Section 10.5 that the vapor pressure of a liquid rises with increasing temperature and that the liquid boils when its vapor pressure equals atmospheric pressure. Because a solution of a nonvolatile solute has a lower vapor pressure than a pure solvent has at a given temperature, the solution must be heated to a higher temperature to cause it to boil. Furthermore, the lower vapor pressure of the solution means that the liquid /vapor phase transition line on a phase diagram is always lower for the solution than for the pure solvent. As a result, the triplepoint temperature Tt is lower for the solution, the solid/liquid phase transition line is shifted to a lower temperature for the solution, and the solution must be cooled to a lower temperature to freeze. Figure 11.12 shows the situation. 

Vadas, E.B., Toma, P, and Zogra, G. (1991). Solid-state phase transitions initiated by water vapor sorption of crystalline L-660,711, a leukotriene PeceptorantagonislJharm. Res., 8 148-155. 

F2N.C( NF).NF.CFg.NF2 mw 232.04, N 24.14%, FB 0.0% (See preceding entry) colorless Uq, bp 55°, mp below —130°, vap pres 124mm at 10° Prepd by fluorinating cy a noguanidine with nitrogen diluted fluorine and a sodium-magnesium fluoride mixt at 0° Proposed as an oxidizer for proplnts. Extremely expl and especially sensitive when undergoing solid-liquid phase transition. Best handled with a CF Cl slush bath at —130 to —145°. Do not let vapors contact mercuty... 

Figure 8.7 The increase in the entropy of a substance at constant pressure from absolute zero to its gaseous state at some temperature. The vertical jumps at the melting and boiling points represent the contributions to S due to the solid-liquid and hquid-vapor phase transitions.

Figure 7.3 depicts the energy F e) of a wetted solid for a wide range of liquid thicknesses, ranging from the microscopic to the macroscopic. We may deduce from the figure that, just as in the case of phase separation (segregation of binary mixtures, liquid-vapor phase transition), there are two mechanisms for the drop to recede. 

Solid-gas phase transition (heat of sublimation of dry ice) absorbent type... Lithium bromide-water, water-ammonium etc. adsorbent type... Zeolite-water vapor, silica gel-water vapor etc. 

Confinement in pores affects all phase transitions of fluids, including the liquid-solid phase transitions (see Ref. [276, 277] for review) and liquid-vapor phase transitions (see Refs. [28, 278] for review). Below we consider the main theoretical expectations and experimental results concerning the effect of confinement on the liquid-vapor transition. Two typical situations for confined fluids may be distinguished fluids in open pores and fluids in closed pores. In an open pore, a confined fluid is in equilibrium with a bulk fluid, so it has the same temperature and chemical potential. Being in equilibrium with a bulk fluid, fluid in open pore may exist in a vapor or in a liquid one-phase state, depending on the fluid-wall interaction and pore size. For example, it may be a liquid when the bulk fluid is a vapor (capillary condensation) or it may be a vapor when the bulk fluid is a liquid (capillary evaporation). Only one particular value of the chemical potential of bulk fluid provides a two-phase state of confined fluid. We consider phase transions of water in open pores in Section 4.3. 

For the bound water, the liquid-sohd phase transition is smeared in the temperature interval of about 180 to 220 K, which does not depend on the pore size [281,338,350]. When the radius is less than approximately 10 to 12 A, only bound water remains, and there is no sharp solid-liquid phase transition in such small pores [281, 338, 350,352]. In simulations, freezing of water confined in narrow hydrophobic pores was obtained at very high pressures and/or by adjusting the pore size to fit some particular form of monolayer or bilayer ice [353-358]. Interestingly, studies of the liquid-vapor transition in hydrophilic pores (see Section 2.2) indicate the formation of about two water layers at the pore wall, which are in... 

Figure 63 Left panel liquid-vapor phase transitions of bulk fluid (horizontal hnes) shown mT - p coordinates together with the bulk coexistence curve (dashed line). Right panel the same transitions shown as isotherms at Ti < 72 < 73 in /j - P coordinates (solid hnes).

F i g u re 64 Liquid-vapor phase transition of bulk fluid (right panel, thin solid line) and in hydrophilic pore (dashed lines) and hydrophobic pore (dotted lines). Condensation in pore with a neutral wall, which happens at the same pressure as the bulk transition, is shown by solid line in left panel. 

Phase stability of nanostructures has been one of the central issues in nanoscience and technology. For a given specimen of a fixed size, phase transition takes place when the temperature is raised to a certain degree. The value of the critical temperature (Tc) varies with the actual process of phase transition. The Tq values are different for the magnetic-paramagnetic, ferroelectric-non-ferroelectric, solid-solid, solid-liquid, and liquid-vapor phase transitions of the same specimen. Generally, solid-size reduction depresses the Tc of a nanosolid because atomic undercoordination lowers cohesive energy of atomics in the skin. 

The porous materials are known to be of importance in many different industrial processes e.g., catalysis, oil recovery, soil pollution, chromatography and separation. In all these systems, the pore structure is known to determine the physico-chemical characteristics. The pore shape and form is not easily determined. Microsporous material is not easily analyzed using electron microscope or diffraction methods, when the mean pore-radius is 2 -50 fjm. One generally uses mercury porosimetry for larger pores, which is based on a capillary phenomena. Other methods have also been used, which are based upon the effect of the curvature of a liquid on its solid - liquid phase transition equilibria, i.e. freezing point depression, vapor pressure or heat of evaporation. 

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