Molar sorption

The sorption enthalpy AHm >s for fluoride, chloride, nitrite, orthophosphate, and sulfate is small or zero, respectively, since no relation between In k and the reciprocal temperature could be established. The change in the molar sorption enthalpy is therefore... 

Figure 10.85. Molar sorption of sulfur dioxide by polymeric membranes vs. their Gutman s donor number. [Data from Semenova S 1 Smirnov S I, J. Membrane Sci., 168, Nos.1-2, 13th March 2000, p.167-73.]...

The basic principle of SIM follows from a fundamental phenomenological experience that stems from basic research executed in the area of physical sorption over many decades, viz., sorption isosteres may presumptively be considered as straight lines at constant sorption-phase composition, n = const., in Clausius-Clapeyron plots, In p vs. I / T.ln accordance with [41-43], this finding allows to calculate the differential molar sorption heat, Q, as difference between the molar enthalpy of the gas phase, Hg, and the partial molar enthalpy of the sorbed substance, // ... 

Sorption-thermodynamic functions as dependences on concentration, n, e.g., the isosteric molar sorption enthalpy, Af/(n), the standard sorption entropy, AS°(n), and the standard Gibbs free sorption energy, AG°(n), can be calculated by basic formulas (21), (22) and (14), respectively,... 

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

AT is intended to include any and all of the effects of the sorption rate of monomer on the surface, steric arrangement of active species, the addition of the monomer to the live polymer chain, and any desorption needed to permit the chain to continue growing. We assume a steady state in which every mole of propylene that polymerizes is replaced by another mole entering the shell from the gas, so that all of the fluxes are equal to Ny gmol propylene reacted per second per liter of total reactor volume. The following set of equations relates the molar flux to each of the concentration driving forces. 

The binding constants of a number of compounds were measured using dialysis, solubility and sorption techniques. The solubility technique was used for compounds which were not radiolabeled. All data was collected at pH = 8.3. The binding constants were then compared to the octanol/water partition coefficients for the compounds and the molar solubilities of the compounds. The data is presented in Table II. The Kow values were taken from the literature.18 22-2 The solubility values were determined in this research with the exception of DDT and Lindane, which were taken from the literature. A plot of log Kc vs. log Kow is presented in Figure 5. The slope of this line is 0.71, the intercept is 0.75 and the value of the correlation coefficient is 0.9258. The regression is highly significant... 

Sulfate poorly prevents arsenate sorption onto metal oxides and soils (Wu et al. 2001 Inskeep et al. 2002 Violante et al. 2005b). Violante et al. (2005b) found that high concentrations of sulfate (sulfate/arsenate molar ratio (rf) 4-10) retarded but not prevented arsenate sorption onto ferrihydrite (see their Fig. 15.10) or other metal oxides. Roy et al. (1986) showed that the sorption of arsenate by two soils (an Ultisol and a Typic Apludults) was reduced in the presence of molybdate. 

Fig. 3. Sorption of arsenate (ASO4) onto ferrihydrite or Al(OH)x in the presence of phosphate (PO4) or phosphate and malate (Mai) at 50% surface coverage of arsenate and at initial ASO4/PO4 molar ratio of 1.0 or 0.5. Arsenate and phosphate were added as a mixture (As04+P04 As04+2P04) or phosphate was added 24 hrs before arsenate (P04 before As04) or arsenate was added 24 hrs before phosphate (As04 before P04). Arsenate, phosphate and malate were added as a mixture (As04+ P04/Mal molar ratio of 1). The numbers in parenthesis indicate the effectiveness of phosphate in preventing arsenate sorption. From Del Gaudio (2005).

Grafe et al. (2001) found that arsenate sorption onto goethite was reduced by humic and fulvic acid, but not by citric acid, whereas arsenite sorption was decreased by all three organic acids between pH 3.0 and 8.0 in the order of citric acid > fulvic acid > humic acid. Del Gaudio (2005) showed that the inhibition of malate (Mai) on arsenate sorption was negligible onto ferrihydrite (100% Arsenate surface coverage) even when malate was added before arsenate but not onto Al(OH)x. At an initial Mal/As molar ratio of 1, the sorption of arsenate onto Al(OH)x after 24 hrs of reaction was reduced by 40% (Fig. 5). 

Fig. 6. Kinetics of arsenate (As04) sorption onto ferrihydrite (A) or Al(OH)x (B) at pH 5.0 in the absence or presence of phosphate (P04) or phosphate and malate (Mai). Initial PO4/ASO4 molar ratio of 1 (As04 + P04) and AsO4 + PO/Mal molar ratio of 1 (As04+P04 +2Mal). Arsenate was added at 50% of surface coverage (authors unpublished data, 2007).

O Reilly et al. (2001) studied the effect of sorption residence time on arsenate desorption by phosphate (phosphate/arsenate molar ratio of 3) from goethite at different pH values. Initially, desorption was very fast (35% arsenate desorbed at pH 6.0 within 24 hrs) and then slowed down. Total desorption increased with time reaching about 65% total desorption after 5 months. These authors found no measurable effect of aging on desorption of arsenate in the presence of phosphate. Furthermore, desorption results at pH 4.0 were similar to the desorption behaviour at pH 6.0. On the contrary, Arai and Sparks (2002) demonstrated that the longer the residence time (3 days-1 year), the greater was the decrease in arsenate desorption by phosphate from a bayerite. 

The octanol-water partition coefficient, Kow, is the most widely used descriptor of hydrophobicity in quantitative structure activity relationships (QSAR), which are used to describe sorption to organic matter, soil, and sediments [15], bioaccumulation [104], and toxicity [105 107J. Octanol is an amphiphilic bulk solvent with a molar volume of 0.12 dm3 mol when saturated with water. In the octanol-water system, octanol contains 2.3 mol dm 3 of water (one molecule of water per four molecules of octanol) and water is saturated with 4.5 x 10-3 mol dm 3 octanol. Octanol is more suitable than any other solvent system (for) mimicking biological membranes and organic matter properties, because it contains an aliphatic alkyl chain for pure van der Waals interactions plus the alcohol group, which can act as a hydrogen donor and acceptor. 

Certain SEC applications solicit specific experimental conditions. The most common reason is the limited sample solubility. In this case, special solvents or increased temperature are inavoid-able. A possibility to improve sample solubility and quality of eluent offer multicomponent solvents (Sections 16.2.2 and 16.8.2). The selectivity of polymer separation by SEC drops with the deteriorating eluent quality due to decreasing differences in the hydrodynamic volume of macromolecules with different molar masses. The system peaks appear on the chromatograms obtained with mixed eluents due to preferential solvation of sample molecules (Sections 16.3.2 and 16.3.3). The multicomponent eluents may create system peaks also as a result of the (preferential) sorption of their components within column packing [144,145]. The extent of preferential sorption is often sensitive toward pressure variations [69,70,146-149]. Even if the specific detectors are used, which do not see the eluent composition changes, it is necessary to discriminate the bulk sample solvent from the SEC separated macromolecules otherwise the determined molecular characteristics can be affected. This is especially important if the analyzed polymer contains a tail of fractions possessing lower molar masses (Sections 16.4.4 and 16.4.5). 

For now, we focus on bulk DOM parameters. Using pyrene as a common sorbate, 17 different DOMs were tested for their ability to sorb this PAH at 25°C. Correlations of the resultant KlD0C values with the bulk properties of the DOMs were then sought (Chin et al., 1997 Georgi, 1998). For pyrene sorption, the molar absorptivities at 280 nm (reflecting aromaticity) and the O/C ratio (reflecting overall polarity) were found to yield a significant correlation (Fig. 9.14) ... 

The index m, representing the maximum sorption in the cavity, may he derived from considerations of the zeolitic cavity volume and molar volume of the sorhate, as m <. v/0. However Schirmer et al. (7 ) state that a maximum of 6 terms has been used in their work. 

Figure 5. Variation of integral molar energy of sorption with coverage for (x) methane and ( ) Kr on 5A zeolite (EU data of Rolniak for CHt (--------) theo-...

Both models give substantially similar integral molar entropies of sorption. 

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