Phase transition solution-vapor

We have already illustrated equation 2.32 for a solution enthalpy (of liquid ethanol see section 2.5). We now apply it to another phase transition the vaporization of a pure substance. 

Solution The entropy change due to the phase transition (the vaporization of ethanol), can be calculated using the following equation. Recall that the temperature must be in nnits of Kelvin (78.3°C = 351 K). 

Solution This problem is very similar to Example 2.1 . where we calculated the enthalpy changes for the same conditions. The normal boiling point of toluene is = 383.79 K therefore, in both cases we are dealing with a phase transition. The vapor phase will be treated as an ideal gas. Both the ideal-gas heat and liquid-phase heat capacities are given by the pol)momial function... 

Solvent Injection The solvent injection technique involves the injection of solutions of lipid in solvents with high vapor pressure (ether, fluorocarbons, ethanol) into excess aqueous phase under reduced pressure. In general, the aqueous phase is maintained above the phase transition of the lipids (Te) and a reduced pressure... 

The enthalpies of phase transition, such as fusion (Aa,s/f), vaporization (AvapH), sublimation (Asut,//), and solution (As n//), are usually regarded as thermophysical properties, because they referto processes where no intramolecular bonds are cleaved or formed. As such, a detailed discussion of the experimental methods (or the estimation procedures) to determine them is outside the scope of the present book. Nevertheless, some of the techniques addressed in part II can be used for that purpose. For instance, differential scanning calorimetry is often applied to measure A us// and, less frequently, AmpH and AsubH. Many of the reported Asu, // data have been determined with Calvet microcalorimeters (see chapter 9) and from vapor pressure against temperature data obtained with Knudsen cells [35-38]. Reaction-solution calorimetry is the main source of AsinH values. All these auxiliary values are very important because they are frequently required to calculate gas-phase reaction enthalpies and to derive information on the strengths of chemical bonds (see chapter 5)—one of the main goals of molecular energetics. It is thus appropriate to make a brief review of the subject in this introduction. 

In the previous section (2.1.2) we were concerned with phase transitions between liquid and vapor and discussed the various techniques for effecting such changes. In this section we will look at transferring solute components from one liquid phase to a second liquid phase. This technique is referred to as liquid-liquid extraction (LLE). The main restriction on this separation technique is that the two phases must be immiscible. By immiscible liquids we mean two liquids which are completely insoluble in each other. A little reflection will reveal it is very difficult to have two liquids that are mutually insoluble. If such a system were achievable, then the total pressure, P, of the system would be defined by. 

Apart from liquid-liquid transitions, liquid-vapor transitions in aqueous electrolyte solutions have played a crucial role in debates on ionic criticality [142-144], The liquid-vapor transition is usually associated with a mechanical instability with diverging density fluctuations, while liquid-liquid transitions are associated with a material instability with diverging concentration fluctuations. This requires, however, that both regimes are well-separated. Their interference can lead to complex phase behavior with continuous transitions from liquid-liquid demixing to liquid-gas condensation [9, 145, 146]. It is then not trivial to define the order parameter [147-149]. 

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. 

If a reaction in a mixture of solids is accompanied by the formation of gas or fluid phases (melts, solutions), solid solutions, or by the generation of defects, then, for a more strict thermodynamic forecast, it is necessary to take into account the changes of entropy and specific heat capacity during phase transitions of the components (melting, vaporization, dissolution), changes of volume and other parameters. If these factors are not taken into account, one can come across the contradictions between experimental data and thermodynamic calculations. 

The next example shows applications of Equations 6.5-2 through 6.5-5 to the determination of a vapor pressure and phase-transition temperatures for a known solution concentration, and to the calculation of a solution composition and solute molecular weight from a measured colligative property. 

Phase equilibria of vaporization, sublimation, melting, extraction, adsorption, etc. can also be represented by the methods of this section within the accuracy of the expressions for the chemical potentials. One simply treats the phase transition as if it were an equilibrium reaction step and enlarges the list of species so that each member has a designated phase. Thus, if Ai and A2 denote liquid and gaseous species i, respectively, the vaporization of Ai can be represented stoichiometrically as —Aj + A2 = 0 then Eq. (2.3-17) provides a vapor pressure equation for species i. The same can be done for fusion and sublimation equilibria and for solubilities in ideal solutions. 

Hygroscopic behavior has been well characterized in laboratory studies for a variety of materials, for example, ammonium sulfate (Figure 14), an important atmospheric material. When an initially dry particle is exposed to increasing RH it rapidly accretes water at the deliquescence point. If the RH increases further the particle continues to accrete water, consistent with the vapor pressure of water in equilibrium with the solution. The behavior of the solution at RH above the deliquescence point is consistent with the bulk thermodynamic properties of the solution. However, when the RH is lowered below the deliquescence point, rather than crystallize as would a bulk solution, the material in the particle remains as a supersaturated solution to RH well below the deliquescence point. The particle may or may not undergo a phase transition (efflorescence) to give up some or all of the water that has been taken up. For instance, crystalline ammonium sulfate deliquesces at 79.5% RH at 298 K, but it effloresces at a much lower RH, 35% (Tang and Munkelwitz, 1977). This behavior is termed a hysteresis effect, and it can be repeated over many cycles. 

Simulations of the RPM predict a phase transition for the RPM at low reduced temperature and low reduced density. It was difficult to localize because of the low figures of the critical data. By corresponding states arguments this critical point corresponds to the liquid/vapor transition of molten salts and to some liquid/liquid transitions in electrolyte solutions in solvents of low dielectric constant [23, 24],... 

An iteration scheme is used to numerically solve this minimization condition to obtain Peq(r) at the selected temperature, pore width, and chemical potential. For simple geometric pore shapes such as slits or cylinders, the local density is a function of one spatial coordinate only (the coordinate normal to the adsorbent surface) and an efficient solution of Eq. (29) is possible. The adsorption and desorption branches of the isotherm can be constructed in a manner analogous to that used for GCMC simulation. The chemical potential is increased or decreased sequentially, and the solution for the local density profile at previous value of fx is used as the initial guess for the density profile at the next value of /z. The chemical potential at which the equilibrium phase transition occurs is identified as the value of /z for which the liquid and vapor states have the same grand potential. 

For ascertaining the process conditions of RESS and PGSS, it is essential to have knowledge of the equilibrium solubility of the solute in dense gas (SCF phase) and vice versa, and also the P-T trace for the solid-liquid-vapor (S-L-V) phase transition of the drug substance. If all three phases coexist, there is only a single degree of freedom for a binary system, and a P-T trace of the S-L-V equilibrium is sufficient to determine the phase equilibrium compositions. 

The relative stabilities of tautomers of unsubstituted thiobarbituric acid were calculated using the AMI method. The oxo-thione structure 189a was found to be the most stable in the gas phase. On transition from vapor to water, the population of the most polar tautomer, the oxo(hydroxy) form, increases. However, the order of stability remains unchanged, and only for 5-halo derivatives the possibility of coexistence of two tautomeric forms in solution has been suggested (89JHC639). 

Equation 3.28 differs from Equation 3.26 in another very fundamental way as well. While Equation 3.26 has both a low-density solution (gas phase) and a high-density solution (liquid phase) at many (T, p) combinations, Equation 3.28 has only a high-density (liquidlike) solution. In other words, the equilibrium vapor pressure of an infinite polymer chain is zero, and hence a liquid— gas phase transition is not possible for a polymer. 

See solution to Problem 5.41. If fluid is unstable, then a vapor-liquid phase transition can occur. 

If a liquid solute is being studied, the vapor-liquid phase transition is determined in a similar manner (Occhiogrosso, 1985). The piston is slowly adjusted to lower the system pressure into the two-phase region. This decompression step is performed very slowly. If the pressure of the system is within 2 bar of the phase-split pressure, the rate of decompression is usually maintained at —0.03 bar/sec. The actual phase transition for the liquid solute is in the pressure interval between this two-phase state and the previous single, fluid-phase state. The entire procedure is then performed several times to decrease the pressure interval from two phases to one phase, so it falls within an acceptable range. The system temperature is now raised and the entire procedure is repeated to obtain more VLE information without having to reload the cell. In this manner, without sampling, an isopleth (constant composition at various temperatures and pressures) is obtained. 

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