Estimation from partition constants

Physiological parameters for volumes and blood flow of the compartments are listed in Table 2-4. Physiologic constants (compartment volume, blood flows, etc) were taken from published values. Values for the solubility of n-hexanc in blood and tissues (partition coefficients) are taken from human tissue (Perbellini et al. 1985). Rate constants (Table 2-4, Figure 2-5) were estimated from animal and human data and are all assumed to be first-order. 

The partitioning exhibited through the Henry s Law constant can be used to estimate the vaporization of various PCB contaminants from solid surfaces. In the presence of water, organic compounds volatilize more rapidly than would be expected based upon vaporization of the pure compound. This tendency accounts for the presence of low vapor pressure contaminants, such as the PCBs, in the atmosphere at higher concentrations than one would estimate from the chemistry of the pure compounds [403,408,409]... 

The rate constants, k+ and k of the forward and backward reactions are finally derived from (12) and (13) according to the transition-state theory, i.e. assuming that the transition and the initial states, on the one hand, and the transition and final states, on the other, are in equilibrium (Glasstone et al., 1941). Thus, estimating the partition function of these three states in the classical way gives (18) and (19), where p is the reduced mass of the two reactants in the homogeneous case and m the mass of the reactant in the electrochemical case. 

Nicotine aa> values in tobacco smoke particulate matter can be estimated based on nicotine volatility from the smoke particulate matter phase, as controlled by the gas/partitioning constant Kp (Pankow et al. 1997) ... 

Physical and Chemical Properties. The physical and chemical property data available for 2-hexanone are sufficient to allow a limited estimation of the potential environmental fate of this chemical. The estimated Henry s law constant (Mabey et al. 1982) and K°c (Hassett et al. 1983) need to be verified experimentally to help confirm the estimates of partitioning in environmental media. Since there does not seem to be a consensus on the solubility of 2-hexanone in water (reported values range from about 20-35 g/L) (Morrison and Boyd 1974 Verschueren 1983), additional measurements would be useful to more accurately predict the environmental fate of this compound. 

We conclude this section by a few general remarks about extrathermodynamic approaches. These quantitative methods involve empirical approaches that cannot be derived strictly from thermodynamic theory. They are widely used to predict and/ or to evaluate partition constants and/or partition coefficients (see Box 3.2 for nomenclature) of organic compounds. There are many situations in which some of the data required to assess the partitioning behavior of a compound in the environment are not available, and, therefore, have to be estimated. For example, we may need to know the water solubility of a given compound, its partition coefficient between natural organic matter and water, or its adsorption constant from air to a natural surface. In all these, and in many more cases, we have to find means to predict these unknown entities from one or several known quantities. 

For estimating the air-olive oil partition coefficient, calculate first the air-octanol partition constant from the air-water (Kisw) and octanol-water (Ki0Vi) partition constants given in Appendix C (Eq. 6-11) ... 

Illustrative Example 7.2 Estimating Octanol-Water Partition Constants from Structure Using the Atom/Fragment Contribution Method Illustrative Example 7.3 Estimating Octanol-Water Partition Constants Based on Experimental KI0W s of Structurally Related Compounds... 

Estimating Octanol-Water Partition Constants from Structure Using the Atom/Fragment Contribution Method... 

What are the major difficulties of any atom/fragment contribution method for estimation of solvent-water partition constants from structure ... 

Apply Eq. 11-12 to estimate the Kiastaf value of an apolar compound with p L = 1 Pa at 15°C by using an apparent vdWsurf value that you can calculate from the slope of the LFER Eq. 2 (slope = 0.135 vdWsurf note that the slope is independent of the units in which the partition constant is expressed) ... 

Estimate Koc from the octanol-water partition constant, Kow, using the linear free energy relationship (Eq. 9-26f), with log Kov/ = 2.88 (Appendix C) ... 

The partition function provides the bridge to calculating thermodynamic quantities of interest. Using the molecular partition function and formulas derived in this section, we will be able to calculate the internal energy E, the heat capacity Cp, and the entropy S of a gas from fundamental properties of the molecule, such as its mass, moments of inertia, and vibrational frequencies. Thus, if thermodynamic data are lacking for a species of interest, we usually know, or can estimate, these molecular constants, and we can calculate reasonably accurate thermodynamic quantities. In Section 8.6 we illustrate the practical application of the formulas derived here with a numerical example of the thermodynamic properties for the species CH3. 

In the cases above, a two-parameter model well represents the data. A model with more parameters would be more flexible, but by using a partition constant, K, or a desorption rate constant ka and k, , for the mass-transfer coefficients, the data are well described (see Figs. 3.4-15 and 3.4-13). While K would be a value experimentally determined, kp can be estimated from eqn. (3.4-97) with the external mass-transfer coefficient, km, estimated from the correlation of Stiiber et al. [25] or from that of Tan et al. [27], and the effective diffusivity from the Wakao Smith model [36], Typical values of kp obtained by fitting the data of Tan and Liou are shown in Fig. 3.4-16. As expected, they are below the usual mass-transfer correlations, because internal resistance diminishes the global mass transfer coefficient. These data correspond to the regeneration of spent activated carbon loaded with ethyl acetate, using high-pressure carbon dioxide, published by Tan and Liou [45]. 

The rate of H2Oz consumption and the OH production were directly related to total iron concentration. The concentrations of hydroxyl radical produced were controlled by the rate of reaction with dissolved constituents. Rate constants for adsorption (ka) and desorption (kd) of PCBs from particles were calculated by regression of data from 1.5 to 5 hr. Adsorption rate constants were estimated from Equation (6.130) assuming that the partitioning rate constants between 2 and 5 hr without OH could be used for calculation of equilibrium partition coefficients Ky)... 

The vapor pressure of a chemical is the pressure its vapor exerts in equilibrium with its liquid or solid phase. The vapor pressure s importance in environmental work results from its effects on the transport and partitioning of chemicals among the environmental compartments (air, water, and soil). The vapor pressure expresses and controls the chemical s volatility. The volatilization of a chemical from the water surface is determined by its Henry s law constant (see Chapter 4), which can be estimated from the ratio of a chemical s vapor pressure to its water solubility. The volatilization of a chemical from the soil surface is determined largely by its vapor pressure, although this is tempered by its sorption to soil solids and its Henry s law constant between soil, water, and air. A substance s vapor pres-... 

Particle-gas partitioning can be described by a variation of the Pankow absorption model, in which liquid-phase vapor pressure is replaced by the octanol-air partition coefficient as a fitting parameter (equations (22)-(25)). Section 10.3.4 states the advantages of doing so. Koa has been reported as a function of temperature for several PCB congeners, chlorobenzenes, PAHs, polychloronaphthalenes (PCNs), and p,p -DDT (Harner and Bidleman, 1996, 1998b Harner and Mackay, 1995 Komp and McLachlan, 1997). For others, Koa can be estimated from the ratio of the octanol-water partition coefficient to the Henry s law constant (H = Pa m3/ mol) (Finizio et al., 1997 Harner and Mackay, 1995 Simonich and Hites, 1995). 

Consider the equilibrium between reactants A, B,.. . and products M, N,.. . in the gas phase as well as in solution in a given solvent S (Figure 2.2). The equilibrium constant in the gas phase, K%, depends on the properties of the reactants and the products. In very favourable cases it can be estimated from statistical thermodynamics via the relevant partition functions, but for the present purposes it is regarded as given. The problem is to estimate the magnitude of the equilibrium constant in the solution, A , and how it changes to KP-, when solvent Su is substituted for solvent St. 

Calculations of 180 EIEs upon reactions of natural abundance O2 require the normal mode stretching frequencies for the 160—160 and 180—160 isotopologues (16 16j/ and 18 16, ). These values can often be obtained directly from the literature or estimated from known force constants. DFT calculations can be used to obtain full sets of vibrational frequencies for complex molecules. Such calculations are actually needed to satisfy the requirements of the Redlich-Teller product rule. In the event that the full set of frequencies is not employed, the oxygen isotope effects upon the partition functions change and are redistributed in a manner that does not produce a physically reasonable result. 

The various approaches to estimating diffusion coefficients and solubilities of drugs in polymers have been reviewed. The polymers typically used for drug delivery have diffusion coefficients that are characteristic of the polymer and relatively constant for drugs of a similar molecular size. Drug solubilities in a polymer can be estimated from the solubility parameters and melting points (steroids), from the melting point alone, or from the correlation of partition coefficients. 

An additional factor that complicates interpretation of SPR data occurs when the partitioning species is multivalent. In solution the two sites on a bivalent antibody bind in an equivalent and independent manner. Upon binding to immobilised antigen the two sites can interact simultaneously and hence bind with greatly increased apparent affinity to what is expected from their solution behaviour. The reliance upon pseudo first order kinetic expressions based upon 1 1 stoichiometry for multivalent species such as antibodies can lead to quite erroneous estimates of equilibrium constants when using this approach [3]. 

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