Water vapor adsorption equation

Water vapor adsorption isotherms have been obtained on cotton from room temperature up to 150°C [303,304]. Theoretical models for explaining the water vapor sorption isotherms of cellulose have been reviewed [303]. Only adsorption theories will be discussed here at ambient temperatures. The shape of the isotherm indicates that multilayer adsorption occurs and thus the Brunauer, Emmett and Teller (BET) or the Guggenheim, Anderson and deBoer (GAB) theory can be applied. In fact, the BET equation can only be applied at relative vapor pressures (RVPs) below 0.5 and after modification up to a RVP of 0.8 [305]. The GAB equation, which was not discussed in the chapter in the book Cellulose Chemistry and Its Applications [303], can be applied up to RVPs above 0.9 [306]. Initially as the RVP... 

The BET equation is useful in describing water vapor adsorption by soils and clays, as shown in Figure 10.7, and may also be applicable to the adsorption of organic vapors (including volatile pesticides) on dry soils and clays. 

Surface fractal dimensions of a number of Cambisols and Luvisols were determined using the FHH equation from data obtained from N2 and water vapor adsorption isotherms. Values were compared with those obtained from the mercury intmsion method and with mass fractal dimensions that were evaluated from particle-size distributions using a modified number-based method [108] (Figure 6.3). This method was proposed by Kozak et al. [116] in order to correct some inconsistencies of previous approaches... 

Slawiiiski et al. [106] applied the so-called pore-solid-fractal (PSF) model to describe water retention curves that were measured for six peat soils in order to obtain their Du values. Furthermore, A values were determined by applying the FHH equation to water vapor adsorption and desorption and N2 adsorption isotherms. The PSF model gave Du values ranging from 2.88 to 2.94. In contrast to the results described above for Cambisols and Luvisols [108], A values obtained from N2 adsorption isotherms (2.25 < A < 2.575) were lower than those evaluated from water adsorption (2.58 < A < 2.70) and desorption (2.63 < A < 2.75) isotherms. 

Tables 2 and 3 give the main results obtained from CO2 and water vapor adsorption respectively. The folding of the structure under different outgassing condition (0.1 Pa) is associated with a decrease of the micropore volume accessible to CO2 observed between 70 and 130°C. The volume of gas, which once adsorbed is able to completely fdl the micropores, was calculated using Dubinin s equation (ref. 12) and conveitied into liquid volume using 1.08 and l.OS g/cm for liquid CO2 at 273K and 293K respectively. The values obtained for temperature lower than that...

Table 16-4 shows the IUPAC classification of pores by size. Micropores are small enough that a molecule is attracted to both of the opposing walls forming the pore. The potential energy functions for these walls superimpose to create a deep well, and strong adsorption results. Hysteresis is generally not observed. (However, water vapor adsorbed in the micropores of activated carbon shows a large hysteresis loop, and the desorption branch is sometimes used with the Kelvin equation to determine the pore size distribution.) Capillary condensation occurs in mesopores and a hysteresis loop is typically found. Macropores form important paths for molecules to diffuse into a par-... 

Equation 10.27 is generally known as Freundlich equation. Equation 10.27 with concentration replaced by pressure was also used to describe the adsorption isotherms of gases on solids, suggesting the incorrect idea that adsorption from solution by a solid could be paralleled with gas or vapor adsorption on the same adsorbents. Whereas in some cases the restriction to dilute solutions was imposed by the solubility of solids (e.g., benzoic acid in water or stearic acid in benzene) it was not imposed on the investigation of mixtures of completely miscible liquids, e.g., acetic acid in water. 

Satisfactory integration cannot be performed unless adsorption data are obtained at very low pressures (II). The lowest pressure that could be measured reliably in this series of experiments was 8.5 microns of Hg. An empirical equation fitted to the experimental points at low pressure was used to extrapolate the isotherm to zero pressures. calculated from each of the isotherms is plotted in Figure 4. Values of the decrease in surface energy, 7r, range upward to 200 ergs cm.-2 at room temperature, a value about the same as is found in other solid-vapor adsorption systems and less than ten times as high as is obtained by the spreading of insoluble monolayers on water (7). 

Although water vapor is absorbed into amorphous solids and not simply adsorbed on the surface, it still has been found that such sorption isotherms can be fit to the BET equation up to a. P/F of about 0.40 as with vapor adsorption, and over the entire range... 

A solvent dissolution, a vapor adsorption, any kind of surface-active substance exchange between the surface and the adjacent subphase, or heating makes the surface tension locally vary, thus generating Marangoni stresses and convection. Then, gravitocapillary waves (wavelength X and amplitude q) excited and sustained by the Marangoni effect in the shallow water waves approximation can be described by the equation ... 

Consider the following adsorption isotherm data for water vapor on silica gel at 25°C. Fit the data to the Langmnir, Freundlich, Redlich-Peterson, and B.D.D.T. equations. 

FIGURE 14.14 Adsorption data of water vapor on silica gel at 25°C. Isotherm fits Brunauer-Deming-Dem-ing-Teller Freundlich, Langmuir, and Redhch-Peterson equations. 

If the adsorbate is in the gas phase and tends to form many layers on the surfaces of soil clay particles, as do water vapor and the inert gases listed in Table 1.6, then can be calculated as the reciprocal of the sum of slope and y intercept of the line obtained by fitting adsorption data to a linear form of the Brunauer-Emmett-Teller equation- ... 

H. D. Orchiston, Adsorption of water vapor. I Soils at 25 C, Soil Sci. 76 453 (1953). J. P. Quirk, Significance of surface areas calculated from water vapor sorption isotherms by use of the BET equation. Soil Sci. 80 423 (1955). 

Chung, D.S. and Pfost, H.B., Adsorption and desorption of water vapor by cereal grains and their products. Part II Development of the general isotherm equation, Trans. ASAE, 10(4) 552-555 (1967). 

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