Equilibrium, phase-partitioning

Firstly, we need to note that stating a value of (partition) is useless unless we know how the equilibrium constant (partition) was written, i.e. which of the phases T and 2 in Equation (5.8) is the air and which is the liquid ... 

The complexing ability of crown ethers in solvents of low polarity has been studied using two-phase partition experiments (Frensdorf, 1971b). The equilibrium between an aqueous solution of the salt (MX) and an organic solution containing the crown ether (Cr) is given by (2). Further dissociation of... 

Note that a. B may reflect either kinetic or equilibrium isotope partitioning between phases A and B. As discussed in the previous chapter, a -B for Fe/ Fe ratios typically varies between 0.997 and 1.003 (Chapter lOA Beard and Johnson 2004). In general, we will describe isotopic fractionations using A. b, following standard definitions ... 

If the diffusion of a minor or trace element can be treated as effective binary (not uphill diffusion profiles) with a constant effective binary diffusivity, the concentration profile may be solved as follows. The growth rate u is determined by the major component to be n D ff, and is given, not to be solved. Use i to denote the trace element. Hence, w, and Dt are the concentration and diffusivity of the trace element. Note that Di for trace element i is not necessarily the same as D for the major component. The interface-melt concentration is not fixed by an equilibrium phase diagram, but is to be determined by partitioning and diffusion. Hence, the boundary condition is the mass balance condition. If the boundary condition is written as w x=o = Wifl, the value of Wi must be found using the mass balance condition. In the interface-fixed reference frame, the diffusion problem can be written as... 

When the reaction takes place in the continuous phase this means that now Hb = 0 and that A is soluble in the continuous phase (partition coefficient is equal to H, which means that, at equilibrium and when there is no reaction, ac = cuHa). 

Once the composition of each equilibrium phase is known, infinite dilution activity coefficients for a third component in each phase can then be calculated. The octanol—water partition coefficient is direcdy 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 Kqw estimation is the difficulty of the calculations involved, particulady when the activity coefficient model is complex. 

This interface is also known as the perm-selective interface (Fig. 6.1a). It is found in ion-selective sensors, such as ion-selective electrodes and ion-selective field-effect transistors. It is the site of the Nernst potential, which we now derive from the thermodynamic point of view. Because the zero-current axis in Fig. 5.1 represents the electrochemical cell at equilibrium, the partitioning of charged species between the two phases is described by the Gibbs equation (A.20), from which it follows that the electrochemical potential of the species i in the sample phase (S) and in the electrode phase (m) must be equal. 

In the laboratory, we usually determine Kl2 from the slope of C versus C2 over a range of concentrations. Partition coefficients can be measured for essentially any two-phase system air-water, octanol-water, lipid-water, particle-water, and so on. In situ partition coefficients also can be measured where site-specific environmental conditions might influence the equilibrium phase distribution. 

Kibbey, T. C. G. Ramsburg, C. A. Pennell, K. D. Hayes, K. F. Effects of Surfactant Properties on Equilibrium and Non-equilibrium Alcohol Partitioning into Dense Nonaqueous-Phase Liquids (DNAPLs) for In Situ Density Modification Applications, presented at the Fall American Geophysical Union national meeting, San Francisco, California, December, 1998. 

There is a general belief that peptides are not thermodynamically stable [99], but the formation of an internal bond in a peptide chain actually corresponds to a process that is not far from equilibrium (Kpep 0.1 M-1) and enzymatic peptide synthesis can yield peptides in satisfactory yield provided that the product is removed from the solution by precipitation or other systems of phase partition [100,101]. 

The classical measurement of LogP is the shake flask method [17]. A known amount of drug is dissolved in a flask containing both octanol phase and aqueous buffer at controlled pH to ensure the existence of only nonionic form (at least two units from the drug pA) ). The flask is shaken to equilibrate the sample between two phases. There must be no undissolved substance present in both phases. After the system reaches its equilibrium, which is time- and temperature-dependent, the concentration of drug is analyzed by HPLC in both phases. Partitioning coefficient is calculated as... 

Adsorption from solution involves the transfer of soluble species from the liquid phase to the surface of an adsorbent, a transfer which is governed by specific system dynamics and which results in a characteristic equilibrium distribution, or phase partitioning, of a solute. In the case of microporous adsorbents such as activated carbon, the uptake of solute consists of the four basic steps illustrated schematically in Figure 4 I) advective or bulk... 

An important type of heterogeneous equilibrium involves partitioning a solute species between two immiscible solvent phases. Such equilibria are used in many separation processes in chemical research and in industry. 

All other variables being equal, a partitioned equilibrium for the analyte between the sample matrix and the extraction solvent is reached more quickly at higher temperature and pressure because the analyte solubilization kinetics are improved. Therefore, cycle time can be much shorter for ASE extractions relative to room-temperature/pressure-solvent extractions. If certain sample variables such as pore size or structure make rapid equilibrium questionable, it is simple to design a recovery versus extraction time experiment (the results of which are shown in Figure 9) so that variability and lower recovery due to a pre-equilibrium phase separation can be avoided. The desirable extraction duration is a trade-off between the recovery and the time required to achieve it and generally runs from 10 to 17 min. 

The value of PDiiuent/feed phase determines the equilibrium concentrations of the pollutant in the LM, and the treated wastewater based on its definition in Eq. (1). The higher the Ppiiuent/feed phase value, the higher the loading of the pollutant that can be dosed into the two-phase partitioning bioreactor system, based on the higher solubility of the pollutant in the LM. At the same time, however, the lower the rate of diffusion from the LM into the feed phase, thus the longer the time required for the elimination of the... 

For phase partitioning (equilibrium), the variable of interest is the solute concentration in the first phase that would be in equilibrium with the solute concentration in a second phase. For example, in the distillation example above, each component is partitioned between the vapor and liquid phases. The mathematical description of the equilibrium relationship is usually given as the concentration in one phase as a function of the concentration in the second phase as well as other parameters. Some examples are the Henry s Law relation for the mole fraction of a solute in a liquid as a function of the mole fraction of the solute in the gas phase which contacts the liquid ... 

An important factor in the use of phase partitioning for separations is the degree of change in composition between the two phases. In the limit where the composition in each phase is identical, separation by this mechanism is futile. For vapor-liquid equilibrium, the condition is called an azeotrope. Irrespective of the phases, this condition corresponds to a partition coefticient of unity. 

CMC, and the hydrophilic aqueous pseudophase, which has a monomeric surfactant concentration equal to the CMC. Dissolved CAD is present in the aqueous pseudophase, and solubilized CAD is present in the micellar pseudophase. The equilibrium CAD partitioning between the sorbed phase and the aqueous pseudophase is still characterized by Kpartition coefficient, Km, which represents the ratio of Xm, tihe mole fraction of CAD in the micellar pseudophase, to Xa, the mole fraction of CAD in the aqueous pseudophase. (Edwards D.A. et al., 1994)... 

---