Vapor pressure of ice

TABLE 5.4 Vapor Pressure of Ice in Millimeters of Mercury For temperatures from —99 to 0°C. 

When the temperature is under 0 °C, the saturation pressure is calculated using the vapor pressure of ice (ice turns into vapor directly, i.e., sublimates) and we can use the following empirical formula ... 

For the vapor pressure of ice, the equation of Clapeyron can be obtained in the same way as for water ... 

In freeze-drying, a solution is filled into vials, a special slotted stopper is partially inserted into the neck of the vial (Fig. 3), and trays of filled vials are transferred to the freeze-dryer. The solution is frozen by circulation of a fluid, such as silicone oil, at a temperature in the range of — 35 to about — 45°C through internal channels in the shelf assembly. When the product has solidified sufficiently, the pressure in the freeze-dry chamber is reduced to a pressure less that the vapor pressure of ice at the temperature of the product, and heat is applied to the... 

Equation (5) is equivalent to stating that sublimation and subsequent transport of 1 g of water vapor into the chamber demands a heat input of 650 cal (2720 J) from the shelves. The vial heat transfer coefficient, Kv, depends upon the chamber pressure, Pc and the vapor pressure of ice, P0, depends in exponential fashion upon the product temperature, Tp. With a knowledge of the mass transfer coefficients, Rp and Rs, and the vial heat transfer coefficient, Kv, specification of the process control parameters, Pc and 7 , allows Eq. (5) to be solved for the product temperature, Tp. The product temperature, and therefore P0, are obviously determined by a number of factors, including the nature of the product and the extent of prior drying (i.e., the cake thickness) through Rp, the nature of the container through Kv, and the process control variables Pc and Ts. With the product temperature calculated, the sublimation rate is determined by Eq. (4). 

The product temperatures were -21.2°C for KC1 and -31.0°C for povidone. The arrows mark the values of the vapor pressure of ice at the operating temperatures. The normalized dried product resistances increase smoothly with pressure as the vapor pressure of ice is approached and exceeded. Thus, the sublimation rate decreases smoothly throughout this pressure range and does not drop to zero at a total system pressure which exceeds the vapor pressure of ice. This observation is completely consistent with the theoretical concepts developed... 

Fig. 1.77. Schema of the barometric temperature measurement (BTM) and plot of the water vapor pressure of ice (Fig. 4 from [1.108]).

Table 1.11 Equilibrium water vapor pressure of ice and the related specific density of the vapor (from [1.109]).

Most recently, Gallagher et al.21 measured the water uptake of Nafion membrane under subfreezing temperatures, which showed a significant reduction in the maximum water content corresponding to membrane full hydration. The Nafion membrane with 1,100 equivalent weight, for example, uptakes A 8 of water at -25°C when it equilibrates with vapor over ice because of the low vapor pressure of ice compared to supercooled liquid water. They also found the electro-osmotic drag coefficient to be 1 for Nafion membrane under sub freezing temperatures. 

Since the driving force for freeze drying is the vapor pressure of ice, it is important from the standpoint of process efficiency to keep the product temperature as high as practical during primary drying. However, the... 

Fig. 2.88. T n as a function of pc. The plot tion vapor pressure of ice. (Measurements by...

The vacuum drying methods take advantage of the greater vapor pressure of water in the liquid phase in contrast to the lower vapor pressure of ice or water at its melting point (4) vapor pressure of H20 at 0°C = 4.6 mm vapor pressure of H20 at 4.4°C = 6.3 mm (potential efficiency increase of 37%) vapor pressure of H20 at 10°C = 9.2 mm (potential efficiency increase of 100% ). 

The melting and boiling points for a substance are determined by the vapor pressures of the solid and liquid states. Figure 16.51 shows the vapor pressures of solid and liquid water as functions of temperature near 0°C. Note that below 0°C the vapor pressure of ice is less than the vapor pressure of liquid water. Also note that the vapor pressure of ice has a larger temperature dependence than that of the liquid. That is, the vapor pressure of ice increases more rapidly for a given rise in temperature than does the vapor pressure of water. Thus, as the temperature of the solid is increased, a point is eventually reached where the liquid and solid have identical vapor pressures. This is the melting point. 

Experiment 2 pressure is 2.0 torn Again we start with ice as the only component in the cylinder at — 20°C. The pressure exerted by the piston in this case is only 2.0 torr. As heating proceeds the temperature rises to — 10°C, where the ice changes directly to vapor through the process of sublimation. Sublimation occurs when the vapor pressure of ice is equal to the external... 

When a solute is dissolved in a solvent, the freezing point of the solution is lower than that of the pure solvent. Why Recall that the vapor pressures of ice and liquid water are the same at 0°C. Suppose a solute is dissolved in water. The resulting solution does not freeze at 0°C because the water in the solution has a lower vapor pressure than that of pure ice. No ice forms under these conditions. However, the vapor pressure of ice decreases more rapidly than that of liquid water as the temperature decreases. Therefore, as the solution is cooled, the vapor pressure of the ice and that of the liquid water in the solution will eventually become equal. The temperature at which this occurs is the new freezing point of the solution and is below 0°C. The freezing point has been depressed. 

However, a slowing down of ice sublimation will be observed if the total pressure in the chamber becomes too close to the pressure above the sublimation interface [9,10,12], Indeed, for an efficient removal of water vapor from the containers, a sufficient pressure differential must exist between the ice-vapor interface and the chamber. The total pressure above the ice-vapor interface is approximately equal to the saturated vapor pressure of ice at the temperature of the, sublimation front, as the head space contains mostly water vapor [10-12], Therefore, the pressure gradient that promotes water removal will no longer exist if the pressure level of the calibrated leak exceeds the saturated vapor pressure of ice at the target product temperature. 

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