Retention equilibrium

As follows from Figure 2-2, the lower the particle diameter, the wider the range of the flow rates where the highest column efficiency is achieved. For columns packed with smaller particles, efficiency is not as adversely affected at faster flow rates, because the mass-transfer term is lower for these columns. Essentially, this means that retention equilibrium is achieved much faster in these columns. 

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

Ion-Exchange Equilibrium. Retention differences among cations with an anion exchanger, or among anions with a cation exchanger, are governed by the physical properties of the solvated ions. The stationary phase will show these preferences ... 

Two variations of the technique exists isocratic elution, when the mobile phase composition is kept constant, and gradient elution, when the mobile phase composition is varied during the separation. Isocratic elution is often the method of choice for analysis and in process apphcations when the retention characteristics of the solutes to be separated are similar and not dramaticallv sensitive to vei y small changes in operating conditions. Isocratic elution is also generally practical for systems where the equilibrium isotherm is linear or nearly hnear. In all cases, isocratic elution results in a dilution of the separated produces. 

In ion-exchange chromatography (lEC), the mobile phase modulator is typically a salt in aqueous solution, and the stationary phase is an ion-exchanger. For ddnte conditions, the solute retention faclor is commonly found to be a power-law function of the salt uormahty [cf. Eq. (16-27) for ion-exchange equilibrium]. 

Solute equilibrium parameters (X5,S for RPC and (Xz,Z for lEC Solute retention factor for initial mobile phase A ... 

Algebraic Comptttation This method starts with calculation of the quantities and compositions of all the terminal streams, using a convenient quantity of one of the streams as the basis of calculation. Material balance and stream compositions are then computed for a terminal ideal stage at either end of an extraction battery (i.e., at Point A or Point B in Fig. 18-81), using equilibrium and solution-retention data. Calculations are repeated for each successive ideal stage from one end of the system to the other until an ideal stage which corresponds to the desired conditions is obtained. Any solid-hquid extraction problem can be solved by this method. 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

This PUCI3 also acts as a salt-phase buffer to prevent dissolution of trace impurities in the metal feed by forcing the anode equilibrium to favor production (retention) of trace impurities as metals, instead of permitting oxidation of the impurities to ions. Metallic impurities in the feed fall into two classes, those more electropositive and those less electropositive than plutonium. Since the cell is operated at temperatures above the melting point of all the feed components, and both the liquid anode and salt are well mixed by a mechanical stirrer, chemical equlibrium is established between all impurities and the plutonium in the salt even before current is applied to the cell. Thus, impurities more electropositive than the liquid plutonium anode will be oxidized by Pu+3 and be taken up by the salt phase, while impurities in the electrolyte salt less electropositive than plutonium will be reduced by plutonium metal and be collected in the anode. 

Halide exchange, sometimes call the Finkelstein reaction, is an equilibrium process, but it is often possible to shift the equilibrium." The reaction is most often applied to the preparation of iodides and fluorides. Iodides can be prepared from chlorides or bromides by taking advantage of the fact that sodium iodide, but not the bromide or chloride, is soluble in acetone. When an alkyl chloride or bromide is treated with a solution of sodium iodide in acetone, the equilibrium is shifted by the precipitation of sodium chloride or bromide. Since the mechanism is Sn2, the reaction is much more successful for primary halides than for secondary or tertiary halides sodium iodide in acetone can be used as a test for primary bromides or chlorides. Tertiary chlorides can be converted to iodides by treatment with excess Nal in CS2, with ZnCl2 as catalyst. " Vinylic bromides give vinylic iodides with retention of configuration when treated with KI and a nickel bromide-zinc catalyst," or with KI and Cul in hot HMPA." ... 

The reaction has also been used to prepare 1,3-dilithiopropanes" and 1,1-dilithio-methylenecyclohexane" from the corresponding mercury compounds. In general, the equilibrium lies in the direction in which the more electropositive metal is bonded to that alkyl or aryl group that is the more stable carbanion (p. 228). The reaction proceeds with retention of configuration an Sgi mechanism is likely. Higher order cuprates (see Ref. 1277 in Chapter 10) have been produced by this reaction starting with a vinylic tin compound ... 

The enantiomerization of phenoxyalkanoic acids containing a chiral side chain has been studied in soil using (Buser and Muller 1997). It was shown that there was an equilibrium between the R- and S- enantiomers of 2-(4-chloro-2-methylphenoxy)propionic acid (MCPP) and 2-(2,4-dichlorophenoxy)propionic acid (DCPP) with an equilibrium constant favoring the herbicidally active f -enantiomer. The exchange reactions proceeded with both retention and inversion of configuration at the chiral sites. 

Consequences of the Snyder and Soczewinski model are manifold, and their praetieal importance is very signifieant. The most speetaeular conclusions of this model are (1) a possibility to quantify adsorbents ehromatographic activity and (2) a possibility to dehne and quantify chromatographic polarity of solvents (known as the solvents elution strength). These two conclusions could only be drawn on the assumption as to the displacement mechanism of solute retention. An obvious necessity was to quantify the effect of displacement, which resulted in the following relationship for the thermodynamic equilibrium constant of adsorption, K,, in the case of an active chromatographic adsorbent and of the monocomponent eluent ... 

Retention of solute molecules (X) is performed by the equilibrium displaeement of mobile phase moleeules M) from the adsorbed monolayer. There is a eompetition between solute and solvent molecules for a site on the adsorbent surfaee in a hquid-sohd adsorption proeess, whieh is expressed by the Equation 4.29 [13] ... 

In its simplest form the competition model assumes the entire adsorbent surface is covered by a monolayer of solute and mobile phase molecules. Under normal chromatographic conditions, the concentration of sample molecules will be small and the adsorbed monolayer will consist mainly of mobile phase molecules. Retention of a solute molecule occurs by displacing a roughly equivalent volume of mobile phase molecules from the monolayer to make the surface accessible to the adsorbed solute aiolecule. For elution of the solute to occur -the above process must be reversible, and can be represented by the equilibrium depicted by equation (4.6)... 

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