Liquid solutions sublimation equilibrium

Figure 2.31. Schematic representation of the P/T equilibria in a simple two-component system (forming continuous solid and liquid solutions). In (a) a perspective view of the P-T-X diagram is shown in (b) its projection on the P/T plane. Notice the two single-component systems represented, for instance, for the component B by the three lines SB/G (sublimation line of B representing the gas/so lid equilibrium), SB/LB (melting equilibrium of B) and the boiling line LB/G. The solid solution is indicated by a. Notice in (a) the isobaric and isothermal sections of the diagrams (compare with Fig. 2.1).

Crystalline solid solutions can be formed either by sublimation or from a liquid phase and in the latter case the solid solution can be deposited either from solution in a common solvent or from a mixture of the fused components. In this method of formation, which alone will be discussed in the present chapter, we are dealing with the fusion curves of two substances, where, however, the liquid solution is in equilibrium not with one of the pure components, but with a crystalline solid solution. The simple scheme (Fig. 33, p. 103) which was obtained... 

Corresponding to the point Q/the melting-point of pure iodine, there is the point C, which represents the vapour pressure of iodine at its melting-point. At this point three curves cut i, the sublimation curve of iodine 2, the vaporisation curve of fused iodine 3, CiB, the vapour-pressure curve of the saturated solutions in equilibrium with solid iodine. Starting, therefore, with the system solid iodine— liquid iodine, addition of chlorine will cause the temperature of equilibrium to fall continuously, while the vapour pressure will first increase, pass through a maximum and then fall continuously until the eutectic point, B (Bjl), is reached. At this point the system is invariant, and the pressure will therefore remain constant until all the iodine has disappeared. As the concentration of the chlorine increases in the manner represented by the curve B/H, the pressure of the vapour also increases as represented by the curve Bj/iHi. At the eutectic point for iodine monochloride and iodine trichloride, the pressure again remains constant until all the monochloridc has disappeared. As the concentration of the solution passes along the curve HF, the pressure... 

When a solution freezes, the solid is usually pure solvent. Thus the solid-vapor equilibrium (sublimation) P-T curve is unaffected by the presence of solute. The intersection of this curve and the liquid-vapor curve is the triple point (nearly the same temperature as the freezing point, which is measured at atmospheric pressure). Since a solute lowers the solvent vapor pressure, the triple point is shifted to lower temperature, as shown in Figure 11-2. Detailed calculations show that the decrease in freezing point for a dilute solution is proportional to the total molal concentration of solutes... 

In the following equilibrium systems for a pure substance (not a solution) solid liquid (s l) fusion liquid vapour (/ g) evaporation solid vapour (s g) sublimation... 

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. 

Finally, if a process involves the sublimation of a pure solid (such as ice or solid CO2) or the evaporation of a pure liquid (such as water) in a different medium such as air. the mole (or mass) fraction of the substance in the liquid or solid phase is simply taken to be 1.0, and the partial pressure and thus the mole fraction of the substance in the gas phase can readily be determined from the saturation data of the substance at the specified temperature. Also, the assumption of thermodynamic equilibrium at the interface is very rca.sonablc for pure solids, pure liquids, and solutions, except when chemical reactions are occurring at the interface. 

Another consequence of lowering of vapour pressure is that the freezing point of the solution is lower than that of the pure solvent. The freezing point of a solution is the temperature at which the solution exists in equilibrium with solid solvent. In such an equilibrium, the solvent must have the same vapour pressure in both solid and liquid states. Consequently, the freezing point is the temperature at which the vapour pressure curves of the solvent and solution intersect the sublimation curve of the solid solvent that is, points C and D, respectively, in Fig. 2.8. The freezing point depression is T-To = ATf. An expression for freezing... 

Lyophilization (Freeze Drying) Lyophilization is most frequently used for heat-labile dosage forms that are unstable in aqueous formulation. The principle of lyophilization can be seen by reference to the phase equilibrium diagram for water (Fig. 15). Water at atmospheric pressure and ambient temperatures is stable in its liquid phase at lOO C the liquid phase attains an equilibrium with its vapor phase. Above 100 C water is stable in its vapor phase. At atmospheric pressures and 0 C the solid (ice) and liquid phases of water are in equilibrium with each other. At vacuum pressures a temperature (the eutectic point) can be reached where the three phases, solid, liquid, and vapor are all in equilibrium with each other. At even lower temperatures and pressures the solid phase comes into equilibrium with the liquid phase. The significance of this is that an aqueous solution can be concentrated by evaporation (sublimation) at low pressures without any necessity for significant heat input. 

At a temperature below its freezing point of 2.0 °C, the hydrazine will be present as a solid in equilibrium with its vapor. We are seeking the sublimation pressure of N2H4(s) at the melting point of ice, 0 °C. At its freezing point of 2.0 "C, the hydrazine coexists in three phases—liquid, solid, and vapor. We must first determine the vapor pressure of hydrazine at 2.0 °C. Then we can then use the Clausius-Clapeyron equation (12.2) to calculate the vapor (sublimation) pressure at 0 "C. Our principal task will be to identify the data needed to apply the Clausius-Clapeyron equation, three times in all, as detailed in the stepwise solution to the problem. 

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