Phase distribution equilibria

An obvious correlation between polar and alpine environments is the decrease in temperature with increasing latitude or elevation. This temperature change leads to a shift in environmental phase distribution equilibria - i.e. a chemical moves from the atmosphere to terrestrial surfaces, including direct deposition to surface waters, but also to snowpack and soils from which movement into surface and groundwater is possible. This process has been termed cold condensation but should more correctly be called cold-trapping because the contaminants are not actually condensing. 

The external factors comprise the nature of the membrane, the substrate concentration in the aqueous phase and any other external species that may participate in the process. They may strongly influence the transport rates via the phase distribution equilibria and diffusion rates. When a neutral ligand is employed to carry an ion pair by complexing either the cation or the anion, the coextracted uncomplexed counterion will affect the rate by modifying the phase distribution of the substrate. The case of a cationic complex and a counteranion is illustrated schematically in Figure 10 (centre). 

C represents the equipotent concentration, k and m are constants for a particular system, and A is a physicochemical constant representative of phase distribution equilibria such as aqueous solubility, oil/water partition coefficient, and vapor pressure. In examining a large and diverse number of biological systems, Hansch and coworkers defined a relationship (Equation 1.62) that expressed biological activity as a function of physicochemical parameters (e.g., partition coefficients of organic molecules) (19). 

Radioactive tracers are ideal tools for studying problems of diffusion, phase distribution equilibria, and processing contamination. Kane and Larrabee state "without reservation, that all reliable values for segregation coefficients for impurities in semiconductors have been determined by using radiotracer methods"... 

One of the most powerful approaches to separations involves pairs of phases in which the component of interest transfers from one phase to the other more readily than do interfering substances. For all phase-distribution equilibria, the classical phase rule of Gibbs is applicable and useful. The phase rule... 

This exercise affords the student an opportunity to further utilize gas chromatography in combination with two different sample preparation methods. Whenever a sample preparation method is used, there is most always loss of analyte due to sample handling, and if the method involves phase distribution equilibria, some analyte is lost between phases. This is particularly important when conducting VOCs analyses due to volatility losses of the analytes. It thus becomes imperative that, prior to actual sample analysis, a recovery study be undertaken to evaluate these losses. An analyst cannot assume that every method yields a 100% recovery of every organic compound Recovery studies thus become a major part of a good quality assurance program for the trace environmental analysis laboratory. 

FIGURE 6 Phase distribution equilibria involving pure phases with importance for describing environmental phase partitioning. Kaw, air-water partition coefficient Kow, octanol-water partition coefficient Kqa, octanol-air partition coefficient Pl, (supercooled) liquid vapor pressure Cw and Co, saturation solubility in water and octanol, respectively yw and yo, activity coefficient in water and octanol, respectively. 

The pKa of a molecule, a charge-state-related parameter, is a descriptor of an acid-base equilibrium reaction [34,35]. Lipophilicity, often represented by the octanol-water partition coefficient Kp is a descriptor of a two-phase distribution equilibrium reaction [36]. So is solubility [37-39]. These three parameters are thermodynamic constants. On the other hand, permeability Pe is a rate coefficient, a kinetics parameter, most often posed in a first-order distribution reaction [40-42]. 

Hansch and coworkers have amply demonstrated that Equation 1.69 applies not only to systems at or near phase distribution equilibrium but also to systems removed from equilibrium (184,185). 

This equation suggests that for spontaneous physical and/or chemical change to occur, the process proceeds with a decrease in free energy. As applied to phase distribution, equilibrium is reached when the infinitesimal increase in G per infinitesimal increase in the number of moles of solute i added to each phase becomes equal. Hence, the chemical potential of solute i is defined as... 

The phase-distribution restrictions reflect the requirement that ff =ff at equilibrium where/is the fugacity. This may be expressed by Eq. (13-1). In vapor-hquid systems, it should always be recognized that all components appear in both phases to some extent and there will be such a restriction for each component in the system. In vapor-liquid-hquid systems, each component will have three such restrictions, but only two are independent. In general, when all components exist in all phases, the uumDer of restricting relationships due to the distribution phenomenon will be C(Np — 1), where Np is the number of phases present. 

Vapor and liqmd streams and respectively are in equilibrium with each other by definition and therefore are at the same T and P. These two inherent identities when added to C-component balances, one energy balance, and the C phase-distribution relationships give... 

Now to complete the solution of the problem one would need to know the solution laws for iron, and a small amount of nickel, in each of these carbide phases, since equilibrium requires that and a , in the segregated carbide must be 0-74 and 0-08 respectively as well as a., being 0-18. At present nothing is known about these laws except that the metal atoms might well be randomly distributed in the carbide phase, in which case, as an example. 

The distribution coefficient can be determined by batch experiments in which a small known quantity of resin is shaken with a solution containing a known concentration of the solute, followed by analysis of the two phases after equilibrium has been attained. The separation factor, a, is used as a measure of the chromatographic separation possible and is given by the equation,... 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

Suppose that an ionic component i is in a distribution equilibrium between an oil phase O and an aqueous phase W and also adsorbs at the interface between O and W. At equilibrium, the condition of distribution equilibrium is... 

Lipophilicity is a molecular property expressing the relative affinity of solutes for an aqueous phase and an organic, water-immiscible solvent. As such, lipophilicity encodes most of the intermolecular forces that can take place between a solute and a solvent, and represents the affinity of a molecule for a lipophilic environment. This parameter is commonly measured by its distribution behavior in a biphasic system, described by the partition coefficient of the species X, P. Thermodynamically, is defined as a constant relating the activity of a solute in two immiscible phases at equilibrium [111,112]. By convention, P is given with the organic phase as numerator, so that a positive value for log P reflects a preference for the lipid phase ... 

The effect of the medium (solvent) on the dissolved substance can best be expressed thermodynamically. Consider a solution of a given substance (subscript i) in solvent s and in another solvent r taken as a reference. Water (w) is usually used as a reference solvent. The two solutions are brought to equilibrium (saturated solutions are in equilibrium when each is in equilibrium with the same solid phase—the crystals of the dissolved substance solutions in completely immiscible solvents are simply brought into contact and distribution equilibrium is established). The thermodynamic equilibrium condition is expressed in terms of equality of the chemical potentials of the dissolved substance in both solutions, jU,(w) = jU/(j), whence... 

The distribution equilibrium for uncharged species distributed between two phases is determined by the equality of the chemical potentials of the... 

Consider a system of two solvents in contact in which a single electrolyte BA is dissolved, consisting of univalent ions. A distribution equilibrium is established between the two solutions. Because, in general, the solvation energies of the anion and cation in the two phases are different so that the ion with a certain charge has a greater tendency to pass into the second phase than the ion of opposite charge, an electrical double layer appears at... 

Basic Equations and Required Data for Calculating the Phase Distribution of Contaminants under Equilibrium Conditions... 

When the SVE technology is applied in a contaminated site, the NAPL is gradually removed. Towards the end of the remediation and when NAPL is no longer present, a three-phase model should be considered to calculate the phase distribution of contaminants (see Table 14.3). In this case, the vapor concentration in pore air (Ca) is calculating using the Henry s Law equation (Equation 14.5), which describes the equilibrium established between gas and aqueous phases ... 

Step 4 Estimate the effectiveness factor i) for the removal and the cleanup time required to obtain a residual toluene concentration of 150 mg/L. The phase distribution calculations carried out in Step 2 indicate that the equilibrium concentration of toluene in the gas phase is Ca equil = 109 mg/L (see Table 14.4). The concentration measured in the extracted air during the field tests is lower, at Q,flew = 78 mg/L, indicating that the removal effectiveness is limited either as a result of mass transfer phenomena or the existence of uncontaminated zones in the airflow pattern. The corresponding effectiveness factor is T = 78/109 = 0.716. 

The distribution of solute between the two phases at equilibrium can be quantified by the K-value or distribution coefficient ... 

The phase distribution observed in the alloys deposited from AlCb-NaCl is very similar to that of Mn-Al alloys electrodeposited from the same chloroaluminate melt [126 129], Such similarity may also be found between the phase structure of Cr-Al and Mn-Al alloys produced by rapid solidification from the liquid [7, 124], These observations are coincident with the resemblance of the phase diagrams for Cr-Al and Mn-Al, which contain several intermetallic compounds with narrow compositional ranges [20], inhibition of the nucleation and growth of ordered, often low symmetry, intermetallic structures is commonly observed in non-equilibrium processing. Phase evolution is the result of a balance between the interface velocity and... 

In many practical situations solute A may dissociate, polymerize or form complexes with some other component of the sample or interact with one of the solvents. In these circumstances the value of KD does not reflect the overall distribution of the solute between the two phases as it refers only to the distributing species. Analytically, the total amount of solute present in each phase at equilibrium is of prime importance, and the extraction process is therefore better discussed in terms of the distribution ratio D where... 

The only potential that varies significantly is the phase boundary potential at the membrane/sample interface EPB-. This potential arises from an unequal equilibrium distribution of ions between the aqueous sample and organic membrane phases. The phase transfer equilibrium reaction at the interface is very rapid relative to the diffusion of ions across the aqueous sample and organic membrane phases. A separation of charge occurs at the interface where the ions partition between the two phases, which results in a buildup of potential at the sample/mem-brane interface that can be described thermodynamically in terms of the electrochemical potential. At interfacial equilibrium, the electrochemical potentials in the two phases are equal. The phase boundary potential is a result of an equilibrium distribution of ions between phases. The phase boundary potentials can be described by the following equation ... 

After Cmax and distribution equilibrium have been reached, the subsequent drug elimination phase can generally be described by first-order kinetics. The time-dependent decrease in drug-plasma concentration is paralleled by a corresponding decrease in elimination rate. Under these conditions, the plasma concentration of the drug at time t is given by Eq. (3.1). 

The solute distribution between the two liquid phases (eluent and adsorbed phase in equilibrium) can be expressed by... 

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 ... 

In this system the basicity constant K - is given by equation (8). As regards the distribution equilibrium of the free aromatic substances between the acid and organic phases, one again finds, from (13) ... 

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