Phase transfer equilibria

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 ... 

Cryptands of type 7-9 and derivatives thereof carry alkali cations [6.4], even under conditions where natural or synthetic macrocycles are inefficient. The selec-tivities observed depend on the structure of the ligand, the nature of the cation and the type of cotransported counteranion. Designed structural changes allow the transformation of a cation receptor into a cation carrier [6.1, 6.4]. The results obtained with cryptands indicated that there was an optimal complex stability and phase-transfer equilibrium for highest transport rates. Combined with data for various other carriers and cations, they give a bell-shaped dependence of transport rates on extraction equilibrium (Fig. 11), with low rates for too small or too large... 

The most efficient separations will be achieved when the lanthanide R is more strongly transported to the counterphase (RX3) and more weakly complexed by the aqueous complexant (L ) (or vice versa) If we simplify this relation by eliminating some fractions and substitute the complexation equilibrium constants, including that for the phase transfer equilibrium (Xgx), this expression becomes a relatively simple function of the extraction equilibrium constants for the metal ions (Kgx), the complex stability constants, and the free ligand concentration (recognizing that the free ligand concentration carries a pH dependence as well) ... 

Consider the system shown in Fig. 9.6, in which a liquid mixture is equilibrated with a gas phase. Transfer equilibrium exists for substance i, a constituent of both phases. Substance i is assumed to have the same molecular form in both phases, and is not, for instance, an electrol5d e. We can vary the mole fraction x,- in the liquid and evaluate the fugacity fi in the gas phase. 

The exchange of anion is of little import, however, if nothing further than that which is formulated occurs. Not only must the anion which will function as nucleophile be paired with Q", but it must find its way into the organic solution. A second equilibrium is therefore a requirement for phase transfer catalysis to be successful namely the phase transfer equilibrium. This is formulated in equation 1.6. 

The catalytic cycle accounting for the essential features of the cyanide displacement reaction is illustrated in equation 7.2. Note that this is the cycle shown in Sect. 1.4, except that the anions are identified. In essence, the process involves an equilibrium between sodium cyanide and quaternary ammonium cyanide in the aqueous phase, followed by a phase transfer equilibrium occurring across the phase boundary. Once the quaternary ammonium cyanide is present in the organic phase, nucleophilic dis-... 

He = height of a gas-phase transfer unit, m Hi = height of a Rqiiid-phase transfer unit, m X = rii/ LmlGm) = slope of equilibrium hne/slope of operating hne... 

Combined Pore and Solid Diffusion In porous adsorbents and ion-exchange resins, intraparticle transport can occur with pore and solid diffusion in parallel. The dominant transport process is the faster one, and this depends on the relative diffusivities and concentrations in the pore fluid and in the adsorbed phase. Often, equilibrium between the pore fluid and the solid phase can be assumed to exist locally at each point within a particle. In this case, the mass-transfer flux is expressed by ... 

On the other hand, the electrochemical potentials of electrons, pe, oxygen ions, jIo2, and gaseous oxygen, po2 are related via the charge transfer equilibrium at the three-phase-boundaries (tpb) metal-support-gas38"40 ... 

Membrane Reactors. Consider the two-phase stirred tank shown in Figure 11.1 but suppose there is a membrane separating the phases. The equilibrium relationship of Equation (11.4) no longer holds. Instead, the mass transfer rate across the interface is given by... 

Molecular views of the rates of solid-liquid phase transfer of a pure liquid and a solution at the normal freezing point. The addition of solute does not change the rate of escape from the solid, but it decreases the rate at which the solid captures solvent molecules from the solution. This disrupts the dynamic equilibrium between escape and capture. 

SECM-induced transfer [SECMIT Fig. 2(b)] can be used to characterize reversible phase transfer processes at a wide variety of interfaces. The basic idea is to perturb the process, initially at equilibrium, through local amperometry at the UME. Hitherto, diffusion-limited electrolysis has mainly been used in conjunction with metal tips, but ion transfer voltammetric probes (discussed briefly in Section III, and in detail in Chapter 15) can also be used. The application of a potential to the tip, sufficient to deplete the... 

Depicted in Fig. 2, microemulsion-based liquid liquid extraction (LLE) of biomolecules consists of the contacting of a biomolecule-containing aqueous solution with a surfactant-containing lipophilic phase. Upon contact, some of the water and biomolecules will transfer to the organic phase, depending on the phase equilibrium position, resulting in a biphasic Winsor II system (w/o-ME phase in equilibrium with an excess aqueous phase). Besides serving as a means to solubilize biomolecules in w/o-MEs, LLE has been frequently used to isolate and separate amino acids, peptides and proteins [4, and references therein]. In addition, LLE has recently been employed to isolate vitamins, antibiotics, and nucleotides [6,19,40,77-79]. Industrially relevant applications of LLE are listed in Table 2 [14,15,20,80-90]. 

For the transfer equilibrium between a solution and a solid phase of the electrolyte BA it holds that... 

If this binding does occur, then one would expect very strongly bound compounds to show an unusual affinity for the aqueous phase. This could increase the mobility of these compounds in the environment. It is likely that the bound fraction will undergo phase transfers and degradation at different rates than the free truly dissolved fraction of a dissolved pollutant. If this is the case, then an observed equilibrium between a pollutant in the free and bound states could significantly affect its environmental behavior. 

Acetylene is sufficiently acidic to allow application of the gas-phase proton transfer equilibrium method described in equation l7. For ethylene, the equilibrium constant was determined from the kinetics of reaction in both directions with NH2-8. Since the acidity of ammonia is known accurately, that of ethylene can be determined. This method actually gives A f/ acid at the temperature of the measurement. Use of known entropies allows the calculation of A//ac d from AG = AH — TAS. The value of A//acij found for ethylene is 409.4 0.6 kcal mol 1. But hydrocarbons in general, and ethylene in particular, are so weakly acidic that such equilibria are generally not observable. From net proton transfers that are observed it is possible sometimes to put limits on the acidity range. Thus, ethylene is not deprotonated by hydroxide ion whereas allene and propene are9 consequently, ethylene is less acidic than water and allene and propene (undoubtedly the allylic proton) are more acidic. Unfortunately, the acidity of no other alkene is known as precisely as that of ethylene. 

The equilibrium constant is then connected to the thermodynamics of the mobile phase-stationary phase transfer process using classical expressions. 

As pointed out earlier, the conventional method of treating the problem is by assuming an interfacial equilibrium between C2 Cj. Based on the reported solubility, 50 ppm, of TBTC1 in sea water (12), "m" may be assigned a value of 5 x 10-5. However, an assumption is being made here that the equilibration is fast. Since Cardarelli has pointed out the possibility of a rate controlling interfacial transfer, we have decided to consider the phase transfer rate rather than interfacial equilibrium. 

The highly hydrophilic alcohols, pentaerythritol and 2-ethyl-2-hydroxymethyl-propan-l,3-diol, can be converted into their corresponding ethers in good yields under phase-transfer catalytic conditions [12]. Etherification of pentaerythritol tends to yield the trialkoxy derivative and kinetics of the reaction have been shown to be controlled by the solubility of the ammonium salt of the tris-ether in the organic phase and the equilibrium between the tris-ether and its sodium salt [13]. Total etherification of the tetra-ol is attained in good yield when reactive haloalkanes are used, and tetra-rt-octylammonium, in preference to tetra-n-butylammonium, bromide [12, 13]. 

Difluorocarbene cannot be generated (<1%) under liquiddiquid phase-transfer catalytic conditions [29] owing to the rapid hydrolysis of the carbene at the interface [30], although it has been indicated that it is possible to obtain low yields of 1,1-difluorocyclopropanes under soliddiquid conditions [1]. More successful is the reaction of dibromomethane and dibromodifluoromethane under basic conditions. It is assumed that the initially formed dibromomethyl anion is transported into the organic phase where an equilibrium reaction with dibromodifluoromethane produces the bromodifluoromethyl anion and, subsequently, the difluorocarbene [31]. 

The condition of Equation (13.7) can be met only if p,j = p,n, which is the condition of transfer equilibrium between phases. Or, to put the argument differently, if the chemical potentials (escaping tendencies) of a substance in two phases differ, spontaneous transfer will occur from the phase of higher chemical potential to the phase of lower chemical potential, with a decrease in the Gibbs function of the system, until the chemical potentials are equal (see Section 10.5). For each component present in aU p phases, (p 1) equations of the form of Equation (13.7) provide constraints at transfer equilibrium. Furthermore, an equation of the form of Equation (13.7) can be written for each one of the C components in the system in transfer equUibrium between any two phases. Thus, C(p — 1) independent relationships among the chemical potentials can be written. As chemical potentials are functions of the mole fractions at constant temperamre and pressure, C(p — 1) relationships exist among the mole fractions. If we sum the independent relationships for temperature. 

Where C and D are two components of the feed represented in percent weight and the subscripts A and U represent the adsorbed and the non-adsorbed phases, respectively. Equilibrium conditions are achieved when the feed passing over a bed of adsorbent does not change composition and there is no net transfer of material occurring between the non-adsorbed and adsorbed phases. Relative selectivity can be expressed not only for one feed compound as compared to another but can also be expressed between any feed mixture component and the desorbent material. 

A mechanistic study of acetophenone keto-enol tautomerism has been reported, and intramolecular and external factors determining the enol-enol equilibria in the cw-enol forms of 1,3-dicarbonyl compounds have been analysed. The effects of substituents, solvents, concentration, and temperature on the tautomerization of ethyl 3-oxobutyrate and its 2-alkyl derivatives have been studied, and the keto-enol tautomerism of mono-substituted phenylpyruvic acids has been investigated. Equilibrium constants have been measured for the keto-enol tautomers of 2-, 3- and 4-phenylacetylpyridines in aqueous solution. A procedure has been developed for the acylation of phosphoryl- and thiophosphoryl-acetonitriles under phase-transfer catalysis conditions, and the keto-enol tautomerism of the resulting phosphoryl(thiophosphoryl)-substituted acylacetonitriles has been studied. The equilibrium (388) (389) has been catalysed by acid, base and by iron(III). Whereas... 

Consider now two practically immiscible solvents that form two phases, designated by and ". Let the solute B form a dilute ideal solution in each, so that Eq. (2.19) applies in each phase. When these two hquid phases are brought into contact, the concentrations (mole fractions) of the solute adjust by mass transfer between the phases until equilibrium is established and the chemical potential of the solute is the same in the two phases ... 

An alternative formulation of the phase-transfer DCC concept was reported in 2008 by the Sanders group [75]. In this case, thiol monomers were dissolved in water on either side of a U-tube containing chloroform (Fig. 1.23). After allowing the system to reach equilibrium, monomer distribution was identical in both aqueous solutions, and mixed species (e.g., 51) were observed in the chloroform layer. 

---