Vapor phase transition

In Section 12.2 we learned that the vapor presstrre of a liquid increases with increasing temperature. When the vapor pressure reaches the external pressure, the liquid boils. In fact, the boiling point of a substance is defined as the temperatirre at which its vapor pressure equals the external, atmospheric pressure. As a result, the boiling point of a substance varies with the external pressure. At the top of a moimtain, for example, where the atmospheric pressme is lower than that at sea level, the vapor pressure of water (or any liqttid) reaches the external pressiue at a lower temperature. Thus, the boiling point is lower than it would be at sea level. 

Because the boiling point is defined in terms of the vapor pressure of the liquid, the boiling point is related to the molar heat of vaporization the amoimt of heat required to vaporize 

Molar Heats of Vapori/.ation for Sciccicd Liquids 

The opposite of vaporization is condensatioa In principle, a gas can be liquefied (made to condense) either by cooling or by applying pressure. Cooling a sample of gas decreases the kinetic energy of its molecules, so eventually the molecules aggre te to form small drops of liquid. Applying pressure to the gas (compression), on the other hand, reduces the distance between molecules, so they can be pulled together by intermolecular attractions. Marty liquefication processes use a combination of reduced temperature and increased pressure. 

Every substance has a critical temperature above whtcK its gas phase carmotbe lique- 

The isothermal vaporization of a pure liquid results in a phase change from saturated liquid to saturated vapor at vapor pressure P . The 

The enthalpy change and entropy change of vaporization are directly related  

This equation follows from Eq. (4-15), because vaporization at the vapor pressure P occurs at constant T. 

As shown by Smith, Van Ness, and Abbott [Introduction to Chemical Engineering Thermodynamics, 7th ed., p. 221, McGraw-Hill, New York (2005)] the heat of vaporization is directly related to the slope of the vapor-pressure curve. 

Known as the Clapeyron equation, this exact thermodynamic relation provides the coimection between the properties of the liquid and vapor phases. 

The temperature at which the vapor pressure ofaKciuidisequaltot atm is called the norma/ boiling point 

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

TABLE 12.6 ivlolar Heals of Vapun/atKin for Selected Liquids 

Tc is the highest temperature at which a substance can exist as a liquid. 

---

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

The theoretical foundation for describing critical phenomena in confined systems is the finite-size scaling approach [64], by which the dependence of physical quantities on system size is investigated. On the basis of the Ising Hamiltonian and finite-size scaling theory, Fisher and Nakanishi computed the critical temperature of a fluid confined between parallel plates of distance D [66]. The critical temperature refers to, e.g., a liquid/vapor phase transition. Alternatively, the demixing phase transition of an initially miscible Kquid/Kquid mixture could be considered. Fisher and Nakashini foimd that compared with free space, the critical temperature is shifted by an amoimt... 

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... 

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. 

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. 

The following phase diagram shows part of the liquid/vapor phase-transition boundaries for pure ether and a solution of a nonvolatile solute in ether. 

Let us first consider the liquid/vapor phase transition of NaCl. PVT data have been recorded up to about 2000 K, which is still far below the critical point. Extrapolations guided by simulations and theory predict Tc = 3300 K and the critical mass density dc = 0.18 g cm-3 [33], With a = 0.276 nm and e = 1, this maps onto Tc = 0.05 and p = 0.08. 

A very important aspect of phase behavior in a system consisting of a volatile organic solvent, such as ethanol, and a supercritical fluid, such as CO2, is that the mixture critical pressure coincides with the liquid vapor phase transition. This means that above a single phase exists for all solvent compositions, whereas the (ethanol-rich and C02-rich) two-phase region lies below this curve. This fact has important implications for the mass transfer and precipitation mechanisms. Complete miscibility of fluids above P means that there is no defined or stable vapor liquid or liquid liquid interface, and the surface tension is reduced to zero and then thermodynamically becomes... 

Another point relevant to our context deals with thermal instability of a wide class of liquids. For example, most if not all of polymeric liquids are thermally unstable ones. The line of its attainable superheat for these liquids exceeds the onset temperature of thermal decomposition of molecules. So, the liquid-vapor phase transition ceases to be point-like with respect to temperature and proves to be dependent on the heating time, or more exactly, on the heating trajectory in time-temperature plane.This determines the difference of the phenomenon of spontaneous nucleation in complex fluids, compared to that of simple ones. 

One experimental observation in phase equilibrium is that the two coexisting equilibrium phases must have the same temperature and pressure. Clearly, the arguments given in Secs. 7.1 and 7.2 establish this. Another experimental observation is that as the pressure is lowered along an isotherm on which a liquid-vapor phase transition occurs, the actual volume-pressure behavior is as shown in Fig. 7.3-3, and not as in Fig. 7.3-2. 

Widom B, Rowlinson IS (1970) New model for the study of liquid-vapor phase transitions. J Chem Phys 52 1670-1684... 

The theory of detonation is applied to the liquid-vapor phase transition in superheated fluids. It is shown that such detonations are always we detonations, characterized by supersonic flow of the shocked region. The detonation state is therefore determined by the transport properties— the viscosity and reaction rate— rather than by the boundary conditions. A numerical example is presented using the Van der Waals equation of state with parameters api opriate for water superheated approximately 100 degrees at a pressure of 5 bars. Detonation pressures of the order of 100 bars and explosion energies of the order of 10 J/Kg are predicted for this example. 

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.

Vaporization Phase transition in which liquid is converted into gas. 

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. 

There exist two phase reparation mechanisms governing liquid/vapor phase transitions ... 

---