Partition Coefficients and Distribution Ratios

Earlier we learned that the partitioning of a solute between two phases is described by a partition coefficient. If the solute is initially in an aqueous phase and is extracted into an organic phase  

A large value for Kd indicates that the extraction of the solute into the organic phase is favorable. 

In evaluating the efficiency of an extraction, however, we must consider the solute s total concentration in each phase. We define the distribution ratio, D, to be the ratio of the solute s total concentration in each phase. 

When the solute exists in only one form in each phase, then the partition coefficient and the distribution ratio are identical. If, however, the solute exists in more than one form in either phase, then Kd and D usually have different values. For example, if the solute exists in two forms in the aqueous phase, A and B, only one of which, A, partitions itself between the two phases, then 

This distinction between Kd and D is important. The partition coefficient is an equilibrium constant and has a fixed value for the solute s partitioning between the two phases. The value of the distribution ratio, however, changes with solution conditions if the relative amounts of forms A and B change. If we know the equilibrium reactions taking place within each phase and between the phases, we can derive an algebraic relationship between Kd and D. 

---

Equilibrium Partition Constants and Standard Free Energy of Transfer Effect of Temperature on Equilibrium Partitioning Using Linear Free Energy Relationships (LFERs) to Predict and/or to Evaluate Partition Constants and/or Partition Coefficients Box 3.2 Partition Constants, Partition Coefficients, and Distribution Ratios -A Few Comments on Nomenclature Concluding Remarks... 

Box. 3.2 Partition Constants, Partition Coefficients, and Distribution Ratios, A Few Comments on Nomenclature... 

DISTRIBUTION CONSTANT, PARTITION COEFFICIENT, AND DISTRIBUTION RATIO... 

It assumes that there are no significant solute-solute interactions and no strong solute-solvent interactions which would influence the distribution process. Concentrations are expressed as mass/unit volume, and usually C1 refers to an aqueous phase and C2 to a non-aqueous phase. The equilibrium constant (P or K) defining this system is referred to as the partition coefficient or distribution ratio. The thermodynamic partition coefficient (P ) is given by the ratio of the respective mole fractions as follows ... 

Colloid-water partition coefficient The distribution ratio for chemical substances between colloids and water. 

Volatility, Relative Volatility, and Distribution Ratio (DR) or Partition Coefficient... 

On the other hand, the ratio of total concentrations of ionized and nonionized species between both phases is named distribution coefficient (symbolized as D). It is often referred to as an effective or apparent partition coefficient and, in concentration terms, it is mathematically defined as ... 

The un-ionized form is assumed to be sufficiently lipophilic to traverse membranes in the pH-partition hypothesis. If it were not, no transfer could be predicted, irrespective of pH. The lipophilicity of compounds is experimentally determined as the partition coefficient (log P) or distribution coefficient (log D) [16]. The partition coefficient is the ratio of concentrations of the neutral species between aqueous and nonpolar phases, while the distribution coefficient is the ratio of all species between aqueous and nonpolar phases [17,18],... 

When two immiscible solvents are placed in contact with each other and a non-ionizable compound is dissolved in one of the solvents, the compound distributes itself between the two solvents. This distribution is referred to as partitioning. The ratio of the concentrations of the compound in each phase is a constant for a specific set of solvents, pH, buffers, buffer concentrations, ionic strength and temperature. This ratio is referred to as a partition coefficient or distribution coefficient and is equal to the ratio of the solubilities in the two solvents. When the compound is a weak acid or base, the distribution of the compound can be shown to be given by the following equation for a monoprotic compound ... 

The linear isotherm is obtained when the ratio of the concentration of substance adsorbed per unit mass and the concentration of the substance in solution remains constant. This means the partition coefficient or distribution constant, K (see Section 1.4) is a constant over all working concentration ranges. Thus, the front and rear boundaries of the band or zone will be symmetrical. 

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. 

A partition coefficient or distribution coefficient is a measure of the equilibrium between two different means, such as two different phases or two different immiscible liquids [Dearden, 1985]. It is usually denoted by K or P and defined as the ratio of the concentrations of a compound in a two-compartment system under equilibrium conditions ... 

Equation (3.75) is an important outcome of our derivation efforts. Let us proceed to interpret this equation as it relates to the cadmium-oxine system. Equation (3.75) states that the distribution ratio for the 1 2 complex between an aqueous phase and a chemically bonded silica such as a Cig sorbent depends on the magnitude of the molecular partition coefficient and the degree to which cadmium is found as the 1 2 complex. Given that Eqs. (3.70)-(3.72) enable one to calculate Sq, Si, and Sj, respectively, and that we... 

A more complex kind of partition is that of the distribution of small organic molecules between proteins and an aqueous phase. A number of such studies 41) have been correlated by an equation similar to Eq. (16) with the octanol-water partition coefficient and K2 the binding constant of the solute with protein or the ratio of the percent bound solute to the percent free solute. In other studies (47), the binding constant is expressed as 1/C, where C is the molar concentration of the solute necessary to produce a 1 1 (or higher) complex of protein and the solute molecule. The way that K2 is defined greatly affects the intercept and makes it difficult to compare with the data of ordinary solvent-... 

Liquid-liquid extraction is an equilibrium process between two immiscible phases, described by a equilibrium constant, usually called the distribution constant or partition coefficient. The distribution constant, K, is defined as the ratio of the concentration of the substance in the two phases at equilibrium K = Cu/Cl, where Cu is the concentration of analyte in the less dense (upper) phase and Cl its concentration in the more dense (lower) phase). The distribution or partition ratio, G, defined as the ratio of the solute masses in the two phases (G = mi]/mi, where ntu is the mass of analyte in the less dense phase and Wl its mass in the more dense phase), is often more useful. The distribution constant and distribution ratio are related through the phase ratio, X by G = KV. The phase ratio is the volume ratio of the liquid phases (V = volume of the less dense phase/volume of the more dense phase). 

The term partition coefficient refers to the equilibrium distribution of a solute between two phases separated by a boundary. In this case, the two phases are the solid plastic and seawater. Any compound (such as a POP) in seawater wiU readily diffuse into the hydrophobic plastic as well resulting in an equilibrium concentration of the compound in the plastic will be very much higher than that in seawater (Ogata et al., 2009). The partition coefficient is the ratio of the concentrations, and in the case of plastics in seawater can be expressed as follows ... 

Partition coefficient. Lipophilic preservatives tend to accumulate in the lipid phase of a formulation. This phenomenon is particularly important when planing preservative systems for emulsions, where the partition coefficient, as the ratio of preservative concentrations in the oil and water phases respectively, is a significant index of how they partition in emulsions. Adding alcohol to an aqueous milieu can shift the distribution coefficient in favour of the aqueous phase. In contrast, non-ionic surfactants tend to shift the partition coefficient in favour of the oil phase, resulting in a reduction of preservative efficacy in the water phase (WallhauBer, 1984). 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

In the simplest form of liquid-liquid extraction, the only reaction affecting extraction efficiency, is the partitioning of the solute between the two phases (Figure 7.20). In this case the distribution ratio and the partition coefficient are equal. 

For a simple liquid-liquid extraction, the distribution ratio, D, and the partition coefficient, Kd, are identical. 

Once the composition of each equiHbrium phase is known, infinite dilution activity coefficients for a third component ia each phase can then be calculated. The octanol—water partition coefficient is directly proportional to the ratio of the infinite dilution activity coefficients for a third component distributed between the water-rich and octanol-rich phases (5,24). The primary drawback to the activity coefficient approach to estimation is the difficulty of the calculations involved, particularly when the activity coefficient model is complex. 

---