Chemical potential immiscible solvents

In the previous sections, we indicated how, under certain conditions, pressure may be used to induce immiscibility in liquid and gaseous binary mixtures which at normal pressures are completely miscible. We now want to consider how the introduction of a third component can bring about immiscibility in a binary liquid that is completely miscible in the absence of the third component. Specifically, we are concerned with the case where the added component is a gas in this case, elevated pressures are required in order to dissolve an appreciable amount of the added component in the binary liquid solvent. For the situation to be discussed, it should be clear that phase instability is not a consequence of the effect of pressure on the chemical potentials, as was the case in the previous sections, but results instead from the presence of an additional component which affects the chemical potentials of the components to be separated. High pressure enters into our discussion only indirectly, because we want to use a highly volatile substance for the additional component. 

The isopiestic method is based upon the equality of the solvent chemical potentials and fugacities when solutions of different solutes, but the same solvent, are allowed to come to equilibrium together. A method in which a solute is allowed to establish an equilibrium distribution between two solvents has also been developed to determine activities of the solute, usually based on the Henry s law standard state. In this case, one brings together two immiscible solvents, A and B, adds a solute, and shakes the mixture to obtain two phases that are in equilibrium, a solution of the solute in A with composition. vA, and a solution of the solute in B with composition, a . 

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... 

If a quantity of a solute A is distributed between two immiscible solvents, for example I2 between carbon tetrachloride and water, then at equUibrium the chemical potentials or escaping tendencies of the solute are the same in both phases thus, for A(in solvent a) = A(in solvent b)... 

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 ... 

A three component system consisting of a solvent (0) and two further components (1 and 2) can be considered. The phase equilibrium between the solid (s) and liquid (1) phases is characterized by equality of the chemical potentials of a given component in the two phases. Supposing that the component are completely immiscible in the solid phase we obtain from the condition of equality of chemical potentials ... 

When a solute distributes at constant temperature between two solvents, which are immiscible or partially miscible, there exists the equality of the chemical potentials of the solute in the two phases. This situation is described by Eq. (5) in the form ... 

Inclusion of this technique to the BOHLM has to be explained. Solvent extraction or partition of the solute between two immiscible phases is an equilibrium-based separation process. So, the membrane-based or nondispersive solvent extraction process has to be equilibrium based also. Liquid membrane separation is a rate process and the separation occurs due to a chemical potential gradient, not by equilibrium between phases [114]. According to these definitions, many authors who refer to their works as membrane-based or nondispersive solvent extraction processes are not correct. 

If a dilute solution of iodine in water is shaken with carbon tetrachloride, the iodine is distributed between the two immiscible solvents. If and are the chemical potentials of iodine in water and carbon tetrachloride, respectively, then at equilibrium n = /t. If both solutions are ideal dilute solutions, then, choosing Eq. (14.18) to express jj, and fx, the equilibrium condition becomes fx + RT nx = n + RT In x, which can be rearranged to... 

If two immiscible phases are placed adjacent to each other, with one containing a solute soluble in both phases, the solute will distribute itself between two immiscible phases until equilibrium is attained therefore, no further transfer of solute occurs. At equilibrium, the chemical potential of the solute (free energy of the solute in solvent) in one phase is equal to its chemical potential in the other phase. If we consider an aqueous (w) and an organic (o) phase, we write according to theory ... 

The liquid-liquid interface is not only a boundary plane dividing two immiscible liquid phases, but also a nanoscaled, very thin liquid layer where properties such as cohesive energy, density, electrical potential, dielectric constant, and viscosity are drastically changed along with the axis from one phase to another. The interfacial region was anticipated to cause various specific chemical phenomena not found in bulk liquid phases. The chemical reactions at liquid-liquid interfaces have traditionally been less understood than those at liquid-solid or gas-liquid interfaces, much less than the bulk phases. These circumstances were mainly due to the lack of experimental methods which could measure the amount of adsorbed chemical species and the rate of chemical reaction at the interface [1,2]. Several experimental methods have recently been invented in the field of solvent extraction [3], which have made a significant breakthrough in the study of interfacial reactions. 

A second physicochemical parameter influencing chemical penetration through membranes is the relative lipid solubility of the potential toxicant that can be ascertained from its known partition coefficient. The partition coefficient is a measure of the ability of a chemical to separate between two immiscible phases. The phases consist of an organic phase (e.g., octanol or heptane) and an aqueous phase (e.g., water). The lipid solvent used for measurement is usually octanol because it best mimics the carbon chain of phospholipids, but many other systems have been reported (chloroform/water, ether/water, olive oil/water). The lipid solubility and the water solubility characteristics of the chemical will allow it to proportionately partition between the organic and water phase. The partition coefficients can be calculated using the following equation ... 

In any chemical separation scheme, the original sample becomes divided into at least two firactions through the application of a driving force across a functional boundary in such a way that the resulting firactions have a chemical fingerprint that is distinctly different from that of the initial sample. Typical driving forces are concentration gradients, solvent flow, or electrochemical potential. Typical separation boundaries include immiscible liquid-liquid or liquid-solid interfaces. The effectiveness of the separation of contaminant A from desired material B can be expressed in terms of a decontamination factor D ... 

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