Henry sorption

This picture fits very well with the tendency of the sorption isotherm curvature (and hence of the site sorption mode) to disappear at T > Tg. On a more quantitative level, the above characterization of the Henry sorption mode is supported by the smooth temperature dependence of K, found in the PET-C02 system 12), which indicates a roughly unchanged enthalpy of sorption AH, above and below Tg. Additional support is provided by the correlation between K, and the Lennard-Jones parameter s/k characteristic of the gaseous penetrant, in accordance with... 

The experimental permeation results could be consistently described using Eqs. (9.43b) and (9.47) for Langmuir and Henry sorption respectively as shown by de Lange in a full analysis of sorption, permeation and separation results of five different gases [63]. This description requires knowledge of adsorption isotherms which could be measured only on unsupported membranes. To use these data for calculation of the permeation of supported membranes requires the assumption of equal pore characteristics in both cases. As discussed by de Lange et al. this is probably not correct in the case of silica layers. Based on sorption data a microporosity of about 30% and a pore size distribution with a peak at 0.5 nm is found. Analysis of permeation data point to a pore diameter of = 0.4 nm and a considerably smaller porosity. Table 9.7 summarises the sorption data. H2 and CH4 have relatively low (isosteric) adsorption heats (cf ) while CO2 and isobutane strongly adsorb. 

To describe the module performance mass, energy and momentum balances have to be solved. The mass balance is determined for each component in the gas mixture. The balances calculated for the feed and permeate side are coupled using a mass transfer equation which depends on the operating conditions as well as on membrane characteristics. Assuming Henry sorption, non-coupling of permeate fluxes and equality of the chemical potential at the surface of the active membrane layer a simplified mass transfer equation can be used ... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Permeability P, can be expressed as the product of two terms. One, the diffusion coefficient, reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient, reflects the number of molecules dissolved in the membrane material. Thus equation 9 can also be written as equation 10. 

There is a continuing effort to extend the long-established concept of quantitative-structure-activity-relationships (QSARs) to quantitative-structure-property relationships (QSPRs) to compute all relevant environmental physical-chemical properties (such as aqueous solubility, vapor pressure, octanol-water partition coefficient, Henry s law constant, bioconcentration factor (BCF), sorption coefficient and environmental reaction rate constants from molecular structure). 

Peng, J., Wan, A. (1998) Effect of ionic strength on Henry s law constant of volatile organic compounds. Chemosphere 36, 2731-2740. Peng, J., Wan, A. (1998) Effect of ionic strength on Henry s constants of volatile organic compounds. Chemosphere 36, 2731-2740. Pennell, K.D., Rhue, R.D., Rao, P.S.C., Johnston, C.T. (1992) Vapor-phase sorption of p-xylene and water on soils and clay minerals. Environ. Sci. Technol. 26, 756-763. 

Pollutants with high VP tend to concentrate more in the vapor phase as compared to soil or water. Therefore, VP is a key physicochemical property essential for the assessment of chemical distribution in the environment. This property is also used in the design of various chemical engineering processes [49]. Additionally, VP can be used for the estimation of other important physicochemical properties. For example, one can calculate Henry s law constant, soil sorption coefficient, and partition coefficient from VP and aqueous solubility. We were therefore interested to model this important physicochemical property using quantitative structure-property relationships (QSPRs) based on calculated molecular descriptors [27]. 

Predicting sorption coefficients and hence the mobility of organic pollutants in aqueous-solid systems requires complete knowledge and analysis of various physical and chemical properties of such pollutants. This includes properties such as solubility, equilibrium vapor pressure, Henry s law constant, partition coefficient, as well as pKa and pKb values. Such properties can initially help determine the sorption-desorption behavior of organic pollutants once they are released, directly and/or indirectly, to the aqueous environment and then are in direct contact with solid phases. The following sections briefly summarize these properties. 

In water, neither volatilization nor sorption to sediments and suspended particulates is expected to be an important transport mechanism. Using the Henry s Law constant, a half-life of 88 days was calculated for evaporation from a model river 1 m deep with a current of 1 m/second, and with a wind velocity of 3 m/second (Lyman et al. 1982). The biological treatment of waste water containing phenol has shown that less than 1% of phenol is removed by stripping (Kincannon et al. 1983 Petrasek et al. 1983). 

PhC properties most investigated by scientists to date are their water solubility (s, mg/mL), volatility (correlated to the Henry constant H) (pg m atr/pg m wastewater), biodegradability (correlated to pseudo-first-order degradation constant bioi L gSS d ), acid dissociation constant K, distribution and sorption (through the sludge-water distribution coefficient K, expressed in L gSS or the octanol-water partition coefficient Kg ). The main focus has been to find any correlations between these parameters and to determine PhC removal rates during the different treatment steps. Thus, different properties have been quantified for many compounds, and software, such as EPl Suite 4.00 [54], consenting their estimation, is available. 

Isophorone has a water solubility of 12,000 ppm, a log octanol/water partition coefficient of 1.67, a Henry s Law constant of 4.55 X 10 atm m mof, a vapor pressure of 0.3 mm Hg at 20 C, a log sediment sorption coefficient of approximately 1.46, and a log bioconcentration factor (BCF) of 0.85. Isophorone is released to air and water from its manufacturing and use. Based on its water solubility, some isophorone may wash out of the atmosphere however, only limited amounts will be washed out because of the short atmospheric half-life of isophorone. Particularly during the day, when hydroxyl radical (HO) concentrations are highest, very little atmospheric transport will occur due to its fast reaction with HO. ... 

In Silicalite. A variety of papers are concerned with sorption of methane in the all-silica pentasil, silicalite. June et al. (87) used a Metropolis Monte Carlo method and MC integration of configuration integrals to determine low-occupancy sorption information for methane. The predicted heat of adsorption (18 kJ/mol) is within the range of experimental values (18-21 kJ/ mol) (145-150), as is the Henry s law coefficient as a function of temperature (141, 142). Furthermore, the center of mass distribution for methane in silicalite at 400 K shows that the molecule is delocalized over most of the total pore volume (Fig. 9). Even in the case of such a small sorbate, the channel intersections are unfavorable locations. 

June et al. investigated the sorption and spatial distribution of butane and three hexane isomers within the pores of silicalite, using a Metropolis MC method (87) and MD simulations (85). Perturbations of conformation as a result of confinement within the pore were also reported. Heats of adsorption and Henry s law coefficients were found to be in good agreement with experimental values for butane (48-51 kJ/mol) (142,148,150,163-165) and n-hexane (70-71 kJ/mol) (163, 166, 167). The heats of sorption of the other two hexane isomers, 2- and 3-methylpentane, were predicted to be 5 kJ/mol lower than that of n-hexane. 

The configuration-bias Monte Carlo (CB-MC) technique (112) has also been extensively applied to characterize the sorption of alkanes, principally in silicalite (111, 156, 168-171) but also in other zeolites (172-174). Smit and Siepmann (111, 168) presented a thorough study of the energetics, location, and conformations of alkanes from n-butane to n-dodecane in silicalite at room temperature. A loading of infinite dilution was simulated, based on a united-atom model of the alkanes and a zeolite simulation box of 16 unit cells. Potential parameters were very similar to those used in the MD study of June et al. (85). As expected, the static properties (heat of adsorption, Henry s law coefficient) determined from the CB-MC simulations are therefore in close agreement with the values of June et al. The... 

The results of experimental studies of the sorption and diffusion of light hydrocarbons and some other simple nonpolar molecules in type-A zeolites are summarized and compared with reported data for similar molecules in H-chabazite. Henry s law constants and equilibrium isotherms for both zeolites are interpreted in terms of a simple theoretical model. Zeolitic diffusivitiesy measured over small differential concentration steps, show a pronounced increase with sorbate concentration. This effect can be accounted for by the nonlinearity of the isotherms and the intrinsic mobilities are essentially independent of concentration. Activation energies for diffusion, calculated from the temperature dependence of the intrinsic mobilitieSy show a clear correlation with critical diameter. For the simpler moleculeSy transition state theory gives a quantitative prediction of the experimental diffusivity. 

For the sorption of hydrocarbons in type-A zeolites at ordinary temperatures, the region of linearity of the isotherm is limited to very low pressures, and Henry constants are usually obtained by extrapolation from measurements outside the linear region. 

In principle, the Henry constant may be predicted theoretically by evaluation of the configuration integral for an occluded molecule. Such calculations are subject to the considerable uncertainties implicit in theoretical potential calculations (17), and the utility of this approach is now limited to simple spherical molecules such as the inert gases (18, 19). A fair estimate of the standard entropy of sorption or of the value of K0 may, however, be obtained from a simple idealized model. 

Table I. Values of Kq and q0 Giving Temperature Dependence of Henry Constants for Sorption in 5A Zeolite and Chabazite according to Equation 2 ...

The virial isotherm equation, which can represent experimental isotherm contours well, gives Henry s law at low pressures and provides a basis for obtaining the fundamental constants of sorption equilibria. A further step is to employ statistical and quantum mechanical procedures to calculate equilibrium constants and standard energies and entropies for comparison with those measured. In this direction moderate success has already been achieved in other systems, such as the gas hydrates 25, 26) and several gas-zeolite systems 14, 17, 18, 27). In the present work AS6 for krypton has been interpreted in terms of statistical thermodynamic models. 

Thus, in terms of a, the sorption isotherm for osmotically ideal solutions is of Type III in Brunauer s classification (29) and reduces to Henry s law for (Mi/M2)a< 1. 

The driving force of the polymerization reaction is the monomer concentration at the surface of the polymer. In this case Langmuir s isotherm (equation 5.4-7) could be used to describe the monomer concentration quantitatively or, more simply, Henry s sorption rule (Eqn 5.4-8) holds true... 

When the solvent concentration is very small, as in the case of gas or low-activity vapor sorption, Eq. (1) becomes the limiting Henry s law and a linear sorption behavior is expected. 

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