Partition constant, general

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. 

A second, very different general approach to predict the partition constant of a compound in a given two-phase system assumes that the free energy of transfer term for... 

Our final task in this chapter is to demonstrate how partition constants/coefficients can be used to calculate the equilibrium distribution of a compound i in a given multiphase system. As already pointed out earlier, for simplicity, we consider only neutral species. As we will see in Chapter 8, the equilibrium partitioning of ionogenic compounds (i.e., compounds that are or may also be present as charged species, as, for example, acids or bases) is somewhat more complicated to describe. However, the general approach discussed here is the same. 

There are two general experimental approaches commonly used for determining air-water partition constants, the static and the dynamic equilibration approach. A detailed description of the different existing variations of the two methods can be found in the review by Staudinger and Roberts (1996) and in the literature cited therein. Here we will confine ourselves to a few remarks on the general concepts of these experimental approaches. 

We start, however, with some general thermodynamic considerations (Section 7.2). Then, using our insights gained in Chapter 6, we compare solvent-water partition constants of a series of model compounds for different organic solvents of different polarity (Section 7.3). Finally, because n-octanol is such a widely used organic solvent in environmental chemistry, we will discuss the octanol-water partition constant in somewhat more detail (Section 7.4). 

When considering the air-water equilibrium partitioning of an organic acid or base, we may, in general, assume that the ionized species will not be present in the gas phase. The air-water distribution ratio of an organic acid, >,aw (note that we speak of a ratio and not of a partition constant since we are dealing with more than one species), is then given by ... 

Now that solubility and vapor pressure have been defined, consider how a volatile chemical partitions, or distributes itself, between water and air phases at equilibrium. In general, a partition coefficient is the ratio of the concentrations of a chemical in two different phases, such as water and air, under equilibrium conditions. The Henry s law constant, H (or KH), is a partition coefficient usually defined as the ratio of a chemical s concentration in air to its concentration in water at equilibrium. [Occasionally, a Henry s law constant is interpreted in an inverse fashion, as the ratio of a chemical s concentration in water to its concentration in air see, e.g., Stumm and Morgan (1981, p. 179). Note that in that table, KH is equivalent to 1/H as H is defined above ] Values of Henry s law constants are tabulated in a variety of sources (Lyman et al, 1990 Howard, 1989, 1991 Mackay and Shiu, 1981 Hine and Mookerjee, 1975) Table 1-3 lists constants for some common environmental chemicals. When H is not tabulated directly, it can be estimated by dividing the vapor pressure of a chemical at a particular temperature by its aqueous solubility at that temperature. (Think about the simultaneous equilibrium among phases that would occur for a pure chemical in contact with both aqueous and gas phases.) Henry s law constants generally increase with increased temperature, primarily due to the significant temperature dependency of chemical vapor pressures as previously mentioned, solubility is much less affected by the changes in temperature normally found in the environment. 

Empirical methods are based on fits of partitioning data (generally chamber observations) to identify a set of pseudo-compounds with different abundances, which can then be used to simulate the gas-particle partitioning of OA. A major challenge with this approach is whether the properties of these pseudo-compounds are constant as one extrapolates away from the conditions under which the experiment was conducted. To help minimize these errors, it is critical to condition the partitioning experiments over as much atmospherically relevant space as possible. 

This quantity q[r, W, i) may be defined in general as the probability that a molecule having a given configuration does not intersect a pore wall. If we define a local equilibrium partition constant such that... 

These equations lead to fomis for the thermal rate constants that are perfectly similar to transition state theory, although the computations of the partition functions are different in detail. As described in figrne A3.4.7 various levels of the theory can be derived by successive approximations in this general state-selected fomr of the transition state theory in the framework of the statistical adiabatic chaimel model. We refer to the literature cited in the diagram for details. 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

The equihbrium partitioning of a chemical solute between a Hquid and vapor phase is governed by Henry s law when the Hquid mixture is very dilute in the solute. Henry s law generally is vaHd at concentrations below 0.01 mol/L of solution, although the upper limit can sometimes extend to 0.1 mol/L or higher (10). Over this concentration range, a direct proportionaHty, ie, Henry s constant, is observed between the partial pressure of the chemical in the gas phase and its mole fraction in the Hquid phase. Henry s constant, when expressed in this way, has units of pressure (3). 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

Notice that the associated spin model has the following three properties (1) it is, in general, anisotropic (i.e. a-2 / CI3), (2) its set of coupling constants hi, hij, /1123) are interdependent (this should be obvious from equation 7.63, which provides a parameterization of each of these seven constants in terms of our original four independent conditional probabilities, aj (equation 7.58)), and (3) its partition function, Z, can be calculated exactly. 

If both addition and fragmentation arc irreversible the kinetics differ little from conventional chain transfer. In the more general case, the rate constant for chain transfer is defined in terms of the rate constant for addition and a partition coefficient which defines how the adduct is partitioned between products and starting materials (eq. 19). 

Despite the work of Overton and Meyer, it was to be many years before structure-activity relationships were explored further. In 1939 Ferguson [10] postulated that the toxic dose of a chemical is a constant fraction of its aqueous solubility hence toxicity should increase as aqueous solubility decreases. Because aqueous solubility and oil-water partition coefficient are inversely related, it follows that toxicity should increase with partition coefficient. Although this has been found to be true up to a point, it does not continue ad infinitum. Toxicity (and indeed, any biological response) generally increases initially with partition coefficient, but then tends to fall again. This can be explained simply as a reluctance of very hydrophobic chemicals to leave a lipid phase and enter the next aqueous biophase [11]. An example of this is shown by a QSAR that models toxicity of barbiturates to the mouse [12] ... 

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