Vapor partial pressure

TABLE 2-144 Partial Vapor Pressure of Sulfur Dioxide over Water, mm Hg... 

The upper and lower flammabihty limits are the boundary-line mixtures of vapor or gas with air, which, if ignited, will just propagate flame and are given in terms of percent by volume of gas or vapor in the air. Each of these limits also has a temperature at ch the flammabihty limits are reached. The temperature corresponding to the lower-hmit partial vapor pressure should equal the flash point. The... 

Both factors depend on the respective partial vapor pressures of water and carbon dioxide and upon the distance to the radiation source. The partial vapor pressure of carbon dioxide in the atmosphere is fairly constant (30 Pa), but the partial vapor pressure of water varies with atmospheric relative humidity. Duiser (1989) published graphs plotting absorption factors (a) against the product of partial vapor pressure and distance to flame (Px) for flame temperatures ranging from 800 to 1800 K. 

Thus the two main processes are evaporation of water and convective cooling. The first is based on the difference in partial vapor pressure and the second upon the temperature difference. 

Relative humidity is usually considered only in connection with atmospheric air, but since it is unconcerned with the nature of any other components or the total mixture pressure, the term is applicable to vapor content in any problem. The saturated water vapor pressure at a given temperature is always known from steam tables or charts. It is the existing partial vapor pressure which is desired and therefore calculable when the relative humidity is stated. 

FIGURE 8.35 The vapor pressures of the two components of an ideal binary mixture obey Raoult s law. The total vapor pressure is the sum of the two partial vapor pressures (Dalton s law). The insets below the graph represent the mole fraction of A. 

The vapor pressure of a polymer is, of course, far too small to measure We may, nevertheless, insist that such a vapor pressure exists, however small it may be. Or we may resort to the use of the escaping tendency, or fugacity, in place of the partial vapor pressure in the development given above, in accordance with usual thermodynamic procedures applied to the treatment of solutions. The treatment given here is in no way restricted to volatile solutes. 

Dalton s law states that the total vapor pressure (.Pt) over a solution is equal to the sum of partial vapor pressures attributable to each component (a,b,... ). 

Smyth, C.P., Engel, E.W. (1929) Molecular orientation and the partial vapor pressures of binary mixtures. I. Systems compounds of normal liquids. J. Am. Chem. Soc. 51, 2646-2660. 

With the help of these data Ktot and b/p can be calculated, if the water pressure at the sublimation front (pj and the partial vapor pressure in the chamber, measured by a hygrometer, is taken from the respective curves. 

Because the chemical potentials of water distributed in two phases (i.e., solution and vapor) must be equal, the water activity of a food can be measured by bringing the food into equilibrium with the air above it. At equilibrium, under conditions of constant temperature and pressure, the aw values of the aqueous phase of a food (aw l) and of the air (aw v) are equal and can be estimated from the ratio of the partial vapor pressure of water above the food (pv) to the vapor pressure of pure water (p") at the same temperature (Walstra, 2003) ... 

Permea process, 25 838-839 Permeate condensation, 18 508 Permeate side partial vapor pressure, reducing, 25 508 Permeation, in barrier polymers,... 

The power and beauty of jet techniques is the ability to produce a beam of molecules that are vibrationally and rotationally cold but are still vapors. These advantages of supersonic expansions, however, rely on the possibility of producing sufficient partial vapor pressure of the molecules of interest, typically a few millibars. By regulating the temperature of the beam, it is possible to vary the vapor pressure of the sample to the required values. As an example, hquid molecules, such as aromatic alcohols, have to be heated at about 80 °C to obtain the right vapor concentration in the beam, while other largely volatile molecules, such as aliphatic amines, must be kept in a cold bath around 0 °C to avoid saturation. 

Two solutions contain only sodium chloride, acetic acid, and water. In the first solution, the concentration of acetate ion is 0.0004 molar in the second, it is 0.0001 molar. The total ionic strength of each solution is 0.01. Compute the ratio of the activities of acetic acid in the two solutions. What can be said about the relative partial vapor pressures of the monomeric form of acetic acid above the solutions Of acetic acid dimer ... 

Pervaporation (PV) partial vapor pressure difference separation of isomers dehydration of organic liquids... 

Fig. 13.3 Reduction of permeate-side partial vapor pressure [31].

The mutual solubility of two liquids A and B depends, in general, on how much the molecules of each liquid tend to attract those of its own kind, relative to their tendency to attract those of the other. This tendency is measured by the excess Gibbs energy of mixing of the two liquids (see section 2.4), Am gL, which is related to the partial vapor pressures p/ and of the two liquids A and B in the mixture. If the composition of the system is given by and Wb moles of the respective components in a given phase, their mole fractions in this phase are... 

For most of the situations encountered in solvent extraction the gas phase above the two liquid phases is mainly air and the partial (vapor) pressures of the liquids present are low, so that the system is at atmospheric pressure. Under such conditions, the gas phase is practically ideal, and the vapor pressures represent the activities of the corresponding substances in the gas phase (also called their fugacities). Equilibrium between two or more phases means that there is no net transfer of material between them, although there still is a dynamic exchange (cf. Chapter 3). This state is achieved when the chemical potential x as... 

As the temperature of a liquid increases, the partial pressure of the vapor above the liquid increases hence, the percentage vapor composition above the pool increases. Liquid boils when its partial vapor pressure reaches the external pressure and the percentage of vapor reaches 100%. Flash point is when the vapor pressure of a substance is such that the concentration of vapor in air above the substance corresponds to the lower flammable limit. For flammable liquids, the term flammable is typically used for liquids with a flash point below 100°F (37.8°C), and the term combustible is used for liquids with a flash point above 100°F (37.8°C) (NFPA, 1997), but this in no way reflects the intensity of an ensuing fire. 

Climatic Zone Definition Criteria [Mean Annual Temperatures Measured in Open Air (°C) and Mean Annual Partial Vapor Pressure (hPa)] Long-Term Testing Condition [Temperature (°C) and RH]... 

A plot of 2 vs. -t2 for symmetrical systems (i.e., ii vo) is shown in Fig. 1 for a series of values of the heat lerm, It shows how the partial vapor pressure of a component of a binary solution deviates positively from Raoult s law more and mure as the components become more unlike in their molecular attractive forces. Second, the place of T in die equation shows that tlic deviation is less die higher the temperature. Third, when the heat term becomes sufficiently large, there are three values of U2 for the same value of ay. This is like the three roots of the van der Waals equation, and corresponds to two liquid phases in equilibrium with each other. The criterion is diat at the critical point the first and second partial differentials of a-i and a are all zero. 

For a measure of amount of water relevant to stability concerns, vapor pressure, or its related thermodynamic parameters, is more relevant. Determination of vapor pressure uses methods developed from thermodynamic roots, though if the product is not at true equilibrium, the measured quantity is not a thermodynamic descriptor of the product, although it is still a measure of a product characteristic. Water mobilities are often inferred from spectroscopic measurements of relaxational phenomena. Many workers attempt to identify different classes of water characteristic of different ranges of water content and water partial vapor pressure. Spectroscopic measurements, too, are often interpreted in terms of populations of water molecules with similar characteristics. 

Under equilibrium conditions, the partial vapor pressure of water above an aqueous sample is defined by thermodynamic parameters. The measurement of vapor pressure, therefore, is linked to thermodynamic principles, though in a real system, which may or may not be at equilibrium, the vapor pressure is not necessarily that which is to be expected at equilibrium. In order to select a methodology for determining vapor pressure or related properties, the limitations imposed by any requirement for equilibrium and the consequences of a departure from equilibrium must be understood. The purpose of this commentary is to clarify the generic constraints that exist when one attempts to determine the water vapor pressure of a sample. 

As indicated above, the equilibrium partial vapor pressure of water defines its thermodynamic state. The thermodynamic state is usually described by use of the water activity concept, which defines water activity as aw — [pjpw Ir... 

Water activity (aw) is the ratio of the partial vapor pressure of water above a solution to that of pure water at the same specific temperature. It plays an important role in evaluating the microbial, chemical, and physical stability of foods during storage and processing. The vapor pressure in the headspace of a food sample can be measured directly by a manometer. A manometer has one or two transparent tubes and two liquid surfaces where pressure applied to the surface of one tube causes an elevation of the liquid surface in the other tube. The amount of elevation is read from a scale that is usually calibrated to read directly in pressure units. Makower and Myers (1943) were the first to use this method to measure vapor pressure exerted by food. Later, the method was improved, in terms of design features of the apparatus, by various scientists (Taylor, 1961 Labuza et al., 1972 Lewicki, 1987). Trailer (1983), Lewicki (1989), and Zanoni et al. (1999) used a capacitance manometer instead of a U-tube manometer for the measurement of vapor pressure. Lewicki et al. (1978) showed that the precision and reproducibility of the method can be improved by the simultaneous measurement of the water vapor pressure and temperature of the food sample. The method is reviewed in detail by Rizvi (1995) and Rahman (1995). 

The water activity of food samples can be estimated by direct measurement of the partial vapor pressure of water using a manometer. A simple schematic diagram is shown in Figure A2.4.1. A sample of unknown water activity is placed in the sample flask and sealed onto the apparatus. The air space in the apparatus is evacuated with the sample flask excluded from the system. The sample flask is connected with the evacuated air space and the space in the sample flask is evacuated. The stopcock across the manometer is closed and temperatures are read. The equilibrium manometer reading is recorded (/, ). The stopcock over the sample is closed and the air space is connected with the desiccant flask. The manometer reading in the legs is read to give h2. The water activity of the sample is then calculated (Labuza et al., 1976) as ... 

H2o,ch = partial vapor pressure in the chamber during MD 0.245 mbar... 

---