Ice, vapor pressure

WATER (LIQUID OR SUPERCOOLED) AND ICE VAPOR PRESSURES AND THEIR RATIO (WATER ACTIVITY BELOW FREEZING) AT 0°C AND SEVERAL SUBFREEZING TEMPERATURES... 

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

The rate of spray is deterrnined by propellant concentration, the solvent used, and valve and vapor pressure. The pressure must be high enough to dehver the product at the desired rate under the required operating conditions. For example, a windshield ice remover that is likely to be used around 0°C must be formulated to provide an adequate pressure at that temperature. Spray dryness or wetness and droplet size depend upon propellant concentration. 

Fig. 1. Vapor pressure and relative humidity over CaCl solutions and solids. The straight horizontal lines ia the right-hand portion represent two soHd phases and a gas phase for vertical line iatersections. In addition, a soHd phase, saturated solution, and a vapor phase occur ia the regions between the vertical lines. The lower left-hand corner shows the ice solution line. The region ia between, with skewed isothermal lines, represents unsaturated solutions ...

Fig. 3. Water-vapor pressure over ice and several drying agents.

Vapor Pressure of Water and Ice and Calculation of Humid Air State Values 71... 

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 ... 

The diazirines are of special interest because of their isomerism with the aliphatic diazo compounds. The diazirines show considerable differences in their properties from the aliphatic diazo compounds, except in their explosive nature. The compounds 3-methyl-3-ethyl-diazirine and 3,3-diethyldiazirine prepared by Paulsen detonated on shock and on heating. Small quantities of 3,3-pentamethylenediazirine (68) can be distilled at normal pressures (bp 109°C). On overheating, explosion followed. 3-n-Propyldiazirine exploded on attempts to distil it a little above room temperature. 3-Methyldiazirine is stable as a gas, but on attempting to condense ca. 100 mg for vapor pressure measurements, it detonated with complete destruction of the apparatus." Diazirine (67) decomposed at once when a sample which had been condensed in dry ice was taken out of the cold trap. Work with the lower molecular weight diazirines in condensed phases should therefore be avoided. 

Curve AC represents the vapor pressure curve of ice. At any point along this line, such as point A (0°C, 5 mm Hg) or point C, which might represent — 3°C and 3 mm Hg, ice and vapor are in equilibrium with each other. 

Point A on a phase diagram is the only one at which all three phases, liquid, solid, and vapor, are in equilibrium with each other. It is called the triple point. For water, the triplepoint temperature is 0.01°C. At this temperature, liquid water and ice have the same vapor pressure, 4.56 mm Hg. 

The freezing point lowering, like the boiling point elevation, is a direct result of the lowering of the solvent vapor pressure by the solute. Notice from Figure 10.8 that the freezing point of the solution is the temperature at which the solvent in solution has the same vapor pressure as the pure solid solvent. This implies that it is pure solvent (e.g., ice) that separates when the solution freezes. 

The freezing points of electrolyte solutions, like their vapor pressures, are lower than those of nonelectrolytes at the same concentration. Sodium chloride and calcium chloride are used to lower the melting point of ice on highways their aqueous solutions can have freezing points as low as —21 and — 55°C, respectively. 

NOTE The triple point is the point at which water coexists as a solid (ice), liquid, and vapor (steam). This point corresponds to 32.02 °F (0.01 °C) at a vapor pressure of0.089 psia (0.611 kPa). 

Lyophilization is a similar technique and is, in fact, evaporation at reduced temperature under vacuum. In some cases, an aqueous sample can be frozen and the vapor pressure of the ice is sufficient to produce a relatively rapid rate of evaporation. It can also be used effectively where the substances of interest have vapor pressures that are sufficiently high at room temperature, to cause substance loss under normal evaporation procedures. As the vapor pressure of a substance is exponentially related to the temperature, a relatively small reduction in temperature can reduce the vapor pressure of the sample components sufficiently to render any loss during evaporation relatively insignificant. This technique is gentler than evaporation and,... 

In confectionery manufacture aerated products such as frappe, mazetta, or ice cream are based on the use ot foams. Foams are affected by vapor pressure, surface tension, crystallization, denature-tion, and gelation. The production of foams in aerated icings and in whipped cream products is analyzed. 

There are three essentials for a stable icing foam. The first is a low vapor pressure. When a bubble rising in a liquid comes near the surface, it lifts a dome above the bubble. If the vapor pressure within the bubble is low enough (as in the case of very cold soda water), the bubble is retained in the liquid. 

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... 

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