Water vapor pressure of ice

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]).

Some solid molecules can attain enough energy to change directly from solid to gas. Such a transformation is called sublimation. Because of sublimation, there is a vapor pressure of the material that is present over a solid. The water vapor pressure of ice is normally considered to be dependent only on temperature. The heat of sublimation for ice to steam is slightly greater than the sum of the heat of fusion for ice to water plus the heat of vaporization from water to steam. 

Temperature, F Vapor Pressure of Liquid Water Vapor Pressure of Ice Specific Volume of Saturated Temperature, op Vapor Pressure of Liquid Water, Spedlic Volume of Saturated Water... 

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

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). 

Figure 2.8.1 shows a typical installation for flasks and other containers in which the product is to be dried. The condenser temperature for this plant is offered either as -55 °C or as -85 °C. For this type of plant, a condenser temperature of -55 °C is sufficient as this temperature corresponds with a water vapor pressure of approx. 2.1 10 2 mbar, allowing a secondary drying down to approx. 3 10-2 mbar. This is acceptable for a laboratory plant, in which the limitations are not the condenser temperature but the variation of heat transfer to the various containers, the rubber tube connections and the end pressure of the vacuum pump (2 stage pump, approx. 2 10 2 mbar). Figure 2.8.2 shows that these units are designed for very different needs. The ice condenser in this plant can take up 7.5 kg of ice at a temperature down to -53 °C. 

In this operation some ice sublimes from the condenser to the LN2-cooled surface. However, the surfaces of the LN2 plate can be controlled between -80 °C and -100 °C, that corresponds to a water vapor pressure of approx. 5 10-4 to 2 1 () " mbar. 

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. 

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. 

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. 

The freezing point is the temperature at which water and ice are in equilibrium. Ice has a vapor pressure that is indicated by the line down to the left in Figure 25. The freezing point of water is the temperature at which the vapor pressure of pure water and ice are equal. Because the vapor pressure of the solution is lower, the vapor pressure of the solution intersects the line for the vapor pressure of ice at a lower temperature. Ice and water in the solution are in equilibrium at a lower temperature. The freezing point of the solution is therefore lower than that of pure water. 

Effect of impurities on the melting point. The student will recall that a substance in either the solid or liquid form exerts a definite vapor pressure and that this pressure increases with the temperature. It will also be recalled from the vapor-pressure diagram of water that at 0° C. the vapor pressure of ice (solid) and of water (liquid) are the same (4.5 mm of mercury). Figure 13 represents the vapor pressure of naphthalene. At 80° the vapor pressures of both liquid and solid are the same. The rate of transformation of solid naphthalene to liquid at 80° equals the rate of transformation of liquid naphthalene to solid. Below 80° the transformation of liquid naphthalene to solid proceeds faster than that from the solid to liquid, and the substance solidifies. Above 80° the vapor pressure... 

Snow and ice sublime spontaneously when the partial pressure of water vapor is below the equilibrium vapor pressure of ice. At 0°C the vapor pressure of ice is 0.0060 atm (the triple-point pressure of water). Taking the enthalpy of sublimation of ice to be 50.0 kj mol , calculate the partial pressure of water vapor below which ice will sublime spontaneously at -15°C. 

The equilibrium vapor pressure of ice at — 10 C is 1.950 mm. and that of supercooled water at the same temperature is 2.149 mm. Calculate the free energy change in cal. accompanying the change of 1 mole of supercooled water to ice at — 10 C, and the same total (atmospheric) pressure. Is the sign in agreement with expectation ... 

Consequently, we can also calculate the sublimation pressure and vapor pressure of ice and water, respectively, at other temperatures. Using these equations, we find... 

See Vapor Pressure of Ice and Vapor Pressure and other Saturation Properties of Water ... 

Vapor Pressure Deficit. The water-holding capacity of saturated wood changes when it cools below the freezing point, with lowering of the fiber-saturation point (ii). When saturated wood is frozen, the vapor pressure of ice, is lower at the same temperature than the vapor pressure of supercooled water, e, bound to internal surfaces. The resulting saturated vapor pressure diflFerence between the ice and the supercooled water is given by and may be referred to as a vapor pressure deficit (VPD). 

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