Relative vapor pressures

The relative vapor pressure of air or the relative humidity is defined by the equation... 

Relative Vapor Pressure of Solid and Liquid. If the dissolved solids in a liquid have a low vapor pressure relative to the liquid in which they are dissolved, provided the solid is not affected by the liquid boiling point, it is an easy matter to vaporize the liquid, leaving a dry residue. 

Use of the condition of constant meniscus volume is most appropriate when growth and dissolntion of the meniscus is comparatively slow. An alternative is to consider the Kelvin eqnilibrium condition. The Kelvin eqnation relates the eqnilibrinm meniscus curvature (also known as the Kelvin radius) to the relative vapor pressure and if Kelvin eqnilibrinm is maintained during the separation process, then the adhesive force becomes [19] ... 

Fig.3.1.9 (a) The adsorption-desorption isotherm (circles, right axis) and the self-diffusion coefficients D (triangles, left axis) for cyclohexane in porous silicon with 3.6-nm pore diameter as a function of the relative vapor pressure z = P/PS1 where Ps is the saturated vapor pressure, (b) The self-diffusion coefficients D for acetone (squares) and cyclohexane (triangles) as a function of the concentration 0 of molecules in pores measured on the adsorption (open symbols) and the desorption (filled symbols) branches. 

Evaporation from an alloy source largely avoids the problems of source geometry which may be encountered in simultaneous evaporation from separate pure metal sources. The success of the method depends on the relative vapor pressures of the component metals in the alloy source because one component metal with a substantially higher vapor pressure will evaporate preferentially. The alloy film will then be rich in the more volatile component compared with the composition of the source and may also be stratified into layers of different composition. Evaporation from alloy sources is discussed in detail by Dushman (43) and Holland (44) on the basis of Raoult s law, and it is possible to predict which metal pairs... 

Thus, the water activity of a food is equal to the relative vapor pressurepv/p°. The relative vapor pressure is also related to percentage relative humidity (%RH) divided by 100. It is critical to bear in mind the assumptions underlying the development and thus the use of Eq. (5) for determining the aw of a food. These assumptions are examined in detail in the next section. 

Strictly speaking, given the violations of the assumptions underlying Eq. (5) discussed earlier, the concept of aw should not be applied to food systems. However, the concept of aw has proven to be an extremely useful and practical tool in both the food industry and in food science research (Franks, 1991). Rather than discarding the use of aw in foods, perhaps it would be more prudent at this point for one to stress the time-dependent nature (i.e., kinetics) of aw measurements and perhaps, as suggested by Slade and Levine (1991) and Fennema (1996), to use the term relative vapor pressure (RVP, the measured term) in place of aw (the theoretical term). To avoid confusion, the term aw will continue to be used in this review, with the understanding that what is most often being measured is RVP. 

Typically, sorption isotherms are constructed for a single food ingredient or food system. An alternative approach is to plot the moisture content versus water activity (or relative vapor pressure) values for a variety of as is food ingredients and food systems. The result is a composite food isotherm (Figure 17). The composite isotherm fits the typical shape observed for a sorption isotherm for an individual food system, with a few products falling above or below the isotherm curve (chewing gum, honey, raisins, bread, and colby and cheddar cheeses). Slade and Levine (1991) were the first to construct such a plot using moisture content and aw values from van den... 

FIG. 17 Water activity (or relative vapor pressure) and moisture content (%, wb) values plotted for a variety of food materials ( as is ), resulting in a composite (or universal) food isotherm. Potato chip and nonfat dry milk (NFDM) data are from van den Berg (1986). All other data are from the author s laboratory (at 20 or 25 1 °C). Water activity and moisture content values for the breakfast cereal and fruit and vegetable categories had the largest ranges (expressed here as standard deviation) 0.311 0.073 aw and 2.94 1.55% me (wb) and 0.995 0.004 aw and 89.8 3.90% me (wb), respectively. The curve is to guide the eye—it is not a fitted line. 

The mobile phase for partition chromatography can also be a gas (GLC). In this case, however, the mixture components solubility in the mobile phase is not an issue—rather, their relative vapor pressures are important. This idea will be expanded in Chapter 12. 

SORPTION EXPERIMENTS. The extracts were exposed to benzene vapor at several relative vapor pressures (p/p )- Two types of sorption experiments were conducted. Experiments in which the benzene vapor pressure is raised from zero to a higher value are termed integral sorptions. Sorption experiments starting with the extract and vapor in equilibrium at a finite, nonzero pressure, and proceeding to a higher pressure, are termed incremental sorptions. 

SORPnON-DESORPTION ISOTHERMS. Sorption-desorption isotherms for the untreated, O-methylated, and O-octylated extracts are presented in Figures 6-8, where the relative vapor pressure of benzene (p/Po) is plotted against the... 

An edible film should have good water vapor barrier properties (low or no water permeation and diffusion through film), which should not increase or increase very little with increasing relative vapor pressure (Lawton, 1996). Films should withstand mechanical stress and strain to such an extent that they do not break easily under a decent mechanical force (Talja et al, 2008). Thus, composition of starch-based films is an important factor influencing its barrier and mechanical properties. Also, starch-based edible films may have an impact on the sensory and textural characteristics of the food. 

A chart giving a detailed relation between relative vapor pressures, %H2SC>4 and density of solutions is given on p 328 of Ref 1... 

While all samples showed a type IV isotherms, a sign of a significant mesopore volume, t-plots analysis indicated either a null or a minute microporosity, Vmj (cf. Table 1). Apparently this bears on the abilities to adsorb water vapor in general and in particular on the characteristics of the adsorption process against relative vapor pressures, p/p . 

PTFE polytetrafluoroethylene PUFA polyunsaturated fatty acid PV peroxide value PVDF polyvinylidene difluoride PVP polyvinylpyrrolidone PVPP polyvinylpolypyrolidone RAS retronasal aroma stimulator RDA recommended dietary allowance RF radio frequency RFI relative fluorescence intensity RI retention index RNU relative nitrogen utilization ROESY rotational nuclear Overhauser enhancement spectroscopy RP-HPLC reversed-phase HPLC RPER relative protein efficiency ratio RS resistant starch RT retention time RVP relative vapor pressure S sieman (unit of conductance)... 

EXAMPLE 8.1 Predicting the relative vapor pressures of substances... 

The abscissa of an adsorption isotherm plot is usually the pressure. For gases it is given in Pa. If we are studying the adsorption of a vapor in equilibrium with its liquid the relative vapor pressure P/Po is plotted. 

Figure 9.10 Adsorbed amount of water on a silicon oxide surfaces versus relative vapor pressure at 20°C. The continuous line was calculated with the theory of Polanyi and assuming van der Waals forces only (Eq. 9.57). Experimental results as measured on Aerosil 200 were adapted from Ref. [379] (see also Fig. 9.9). The deviation at high pressure is partially due to the porosity of the adsorbent. The equilibrium vapor pressure is P0 = 3.17 kPa.

In our experiments, the quench from a swollen to a glassy state has been achieved within tens of seconds, and has been shown not to alter the phase separation in a swollen state[49]. Figure 17 compares surface structures in SB41 films that have been exposed to a relative vapor pressure p/po of 72% and of 80%. With an increase of the solvent concentration, the in-plane order of the microdomains... 

Volatilization rates of chemicals from surface deposits are directly proportional to their relative vapor pressures. The actual rates of loss, or the proportionality constant relating vapor pressure to volatilization rates, are dependent upon external conditions that affect movement away from the evaporating surface, such as wind speed and air turbulence. Initial volatilization of pesticide deposits from leaf surfaces and grass or litter on the forest floor are examples of this type of volatilization. Factors controlling volatilization rates from plants was discussed by Taylor (1). 

Recently Deryagin and Zorin (251), by optical means, investigated the adsorption of alcohols, water, benzene, nitrobenzene, and other gases on an optically polished glass surface. Multimolecular adsorption did not occur until the relative vapor pressure was higher than 0.95. 

Figure 2. External volumetric shrinkage vs. relative vapor pressure for thin Sitka spruce cross sections containing originally different quarter-saturated salt solutions (29)...

Figure 4. External volumetric shrinkage vs. relative vapor pressure for thin white pine cross sections presoaked in different concentrations of sucrose or invert sugar (31). O, water only C, 6.25% sucrose 0, 12.5% sucrose , 25.0% sucrose , 80.0% sucrose 3, 12.5 invert sugar A, 25.0% invert sugar 60.0% invert sugar.

Often the most prominent effect is the increase in specific gravity. It should be emphasized that maximum effects are observed on extended treatment times at high relative vapor pressures. 

In studies of the substantivity of nine aroma chemicals in a fabric softener application, head-space gas chromatography showed that benzyl salicylate, aldehyde C12 MNA, lilial, musk ketone, and the synthetic musk Fixolide were lost to a far lesser extent upon drying than were alpha ionone, eugenol, or linalool (Muller, Neuner-Jehle, and Etzweiler, 1992) (Figure 13.2). This result corresponds to the relative vapor pressures of these materials, except for aldehyde C12 MNA which is a special case. 

---