Partition coefficients capacities

In all the phase diagrams presented above, mole fractions x or mass fractions w were used to characterize compositions. In separation processes, however, concentrations in mol/volume (in the unit mol m ) or mass/volume (kg m ) are more important, since partition coefficients, capacity ratios, etc. are normally defined using concentrations instead of mole fractions (see Equations (2) and (6)). The differences between the isothermal p(x) and p(c) phase diagrams are very important, especially at low pressures [10-14]. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

The nonlinear character of log has not often been discussed previously. Nevertheless, Jorgensen and Duffy [26] argued the need for a nonlinear contribution to their log S regression, which is a product of H-bond donor capacity and the square root of H-bond acceptor capacity divided by the surface area. Indeed, for the example above their QikProp method partially reflects for this nonlinearity by predichng a much smaller solubility increase for the indole to benzimidazole mutation (0.45 versus 1.82 [39, 40]). Abraham and Le [41] introduced a similar nonlinearity in the form of a product of H -bond donor and H -bond acceptor capacity while all logarithmic partition coefficients are linear regressions with respect to their solvation parameters. Nevertheless, Abraham s model fails to reflect the test case described above. It yields changes of 1.8(1.5) and 1.7(1.7) [42] for the mutations described above. 

The gas-liquid partition coefficient is relate to the capacity factor by equation (1.11). 

Razak, J. L. Cutak, B. J. Larive, C. K. Lunte, C. E., Correlation of the capacity factor in vesicular electrokinetic chromatography with the octanokwater partition coefficient for charged and neutral analytes, Pharm. Res. 18, 104—111 (2001). 

Soils and vadose zone information, including soil characteristics (type, holding capacity, temperature, biological activity, and engineering properties), soil chemical characteristics (solubility, ion specification, adsorption, leachability, cation exchange capacity, mineral partition coefficient, and chemical and sorptive properties), and vadose zone characteristics (permeability, variability, porosity, moisture content, chemical characteristics, and extent of contamination)... 

Because of their water solubility and low partition coefficients, MTBE and other oxygenates are difficult to adsorb on GAC. Other, more preferentially adsorbed, contaminants in groundwater may also reduce the capacity of GAC to remove MTBE and other oxygenates. 

Sorption. Capture of neutral organics by non-living particulates depends on the organic carbon content of the solids (9). Equilibrium sorption of such "hydrophobic" compounds can be described by a carbon-normalized partition coefficient on both a whole-sediment basis and by particle size classes. The success of the whole-sediment approach derives from the fact that most natural sediment organic matter falls in the "silt" or "fine" particle size fractions. So long as dissolved concentrations do not exceed 0.01 mM, linear isotherms (partition coefficients) can be used. At higher concentrations, the sorptive capacity of the solid can be exceeded, and a nonlinear Freundlich or Langmuir isotherm must be invoked. 

Equilibrium. Equilibrium between compartments can be expressed either as partition coefficients K.. (i.e. concentration ratio at equilibrium) or in the fugacity models as fugacity capacities and Z. such that K.. is Z./Z., the relationships being depicted in Figur 1. Z is dellned as tfte ratio of concentration C (mol/m3) to fugacity f (Pa), definitions being given in Table I. 

An advantage of the fugacity capacity approach is that for N compartments N values of Z are defined while there may be N(N-l)/2 partition coefficients. Using Z values the partitioning properties between two phases are attributed independently to each phase. It is possible to assign (accidentally) three inconsistent partition coefficients between air, soil and water but the three Z values are inherently consistent. 

Figure 1. Relationships between fugacity capacities and partition coefficients. See Table 1 for symbol definitions.

Only a subset of the parameter values in the O Flaherfy model require inputs from the user to simulate blood and tissue lead concentrations. Lead-related parameters for which values can be entered into the model include fractional absorption from the gastrointestinal tract partition coefficients for lead in nonbone tissues and in the surface region of bone maximum capacity and half-saturation concentration for capacity-limited binding in the erythrocyte elimination clearance fractional clearance of lead from plasma into forming bone and the restricted permeability coefficients for lead diffusion within bone, from plasma into bone, and from bone into plasma (O Flaherty 1991a). 

Maximum binding capacity of erythrocytes Half-saturation concentration Partition coefficients for blood/tissue kinetics Blood/liver Blood/kidney... 

Another feature of the process is that the sorption capacity of type II organoclays is inversely related to the aqueous solubility of the NOCs (Chiou 1989). For example, the affinity of HDTMA-smectite for various phenols increases in the order phenol < chlorophenol < dichlorophenol < trichlorophenol since phenol is the most water-soluble while trichlorophe-nol is the most hydrophobic (Mortland et al. 1986, Lo et al. 1998). The relationship between the distribution (partition) coefficient in a type II organoclay and water-solubility is illustrated in Fig. 5 for a range of nonionic organic pollutants. 

Solubility in water and vapor pressure are both saturation properties, i.e., they are measurements of the maximum capacity that a solvent phase has for dissolved chemical. Vapor pressure P (Pa) can be viewed as a solubility in air, the corresponding concentration C (mol/m3) being P/RT where R is the ideal gas constant (8.314 J/mol.K) and T is absolute temperature (K). Although most chemicals are present in the environment at concentrations well below saturation, these concentrations are useful for estimating air-water partition coefficients as ratios of saturation values. It is usually assumed... 

The Level I calculation proceeds by deducing the fugacity capacities or Z values for each medium (see Table 1.5.3), following the procedures described by Mackay (2001). These working equations show the necessity of having data on molecular mass, water solubility, vapor pressure, and octanol-water partition coefficient. The fugacity f (Pa) common to all media is deduced as... 

The Level I calculations for environmental pHs of 5.1 and 7 suggest that if 100,000 kg (100 tonnes) of pentachlorophenol (PCP) are introduced into the 100,000 km2 environment, most PCP will tend to be associated with soil. This is especially the case at low pH when the protonated form dominates. Very little partitions into air and only about 1% partitions into water. Soil contains most of the PCP. Sediments contain about 2%. There is evidence of bioconcentration with a rather high fish concentration. Note that only four media (air, water, soil and bottom sediment) are depicted in the pie chart therefore, the sum of the percent distribution figures is slightly less than 100%. The air-water partition coefficient is very low. As pH increases, dissociation increases and there is a tendency for partitioning to water to become more important. Essentially, the capacity of water for the chemical increases. Partitioning to air is always negligible. 

Hammers, W.E., Meurs, G.J., De Ligny, C.L. (1982) Correlations between liquid chromatographic capacity ratio data on Lichrosorb RP-18 and partition coefficients in the octanol-water system. J. Chromatogr. 247, 1-13. 

Sherblom, P.M., Eganhouse, R.P. (1988) Correlations between octanol-water partition coefficients and reversed-phase high-performance liquid chromatography capacity factors. J. Chromtogr. 454, 37-50. 

Opperhuizen, A. (1987) Relationships between octan-l-ol/water partition coefficients, aqueous activity coefficients and reversed phase HPLC capacity factors of alkylbenzenes, chlorobenzenes, chloronaphthalenes and chlorobiphenyls. Toxicol. Environ. Chem. 15, 349-364. 

El Tayar, N., Mark, A. E., Vallat, P., Bmnne, R. A., Testa, B. and van Gunsteren, W. E. Solvent-dependent conformation and hydrogen-bonding capacity of cyclosporin A evidence from partition coefficients and molecular dynamics simulations, J.Kled. Chem., 36 (1993), 3757-3764... 

Vowles and Mantoura [38] determined sediment-water partition coefficients and the high-performance liquid chromatography capacity factors for 14 alkylbenzene and polyaromatic hydrocarbons. The partition coefficients correlated well with the alkyl-cyano capacity factors, and it was concluded that this phase gave a better indication of sorption on sediment than either the octanol or octadecylsilane phases. 

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