The Separation Factors

We next turn to the ion-exchange separation and the liquid-liquid (solvent) extraction of the lanthanides and the actinides. Except in a few cases, the actual values of the distribution coefficient 0) defined as 

In the original paper of Sinha (58), the log values of the solvent extraction of the lanthanides by HTTA in C6H6 was plotted giving an inclined W plot. We have now plotted the log , the change in the free energy (— AG), enthalpy (— AH), and the 

The plots of the logs/ values (normalized to Gd(III)) for a-hydroxyisobutyric acid HIB), lactate (Lact) for the cation exchange (Dowex 50-WX8) elution (61), and 2-hydroxy-2-methylbutyric acid (HIMBUT) (normalized to La(III)) (62) against the 

L-values of the lanthanides also reproduced the generic form (Fig. 11—13) of the inclined W. The gadolinium point for HIB and Lact seems to be common for both second and third tetrad. From the plots the following missing values of log for the lactate 

For one non-phosphorous extracting agent methyl-iso-butyl ketone (MIBK) enough data (63) are available for the inclined W plot (Fig. 14). From this plot it is also possible to predict the log r values for the missing members 

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To accomplish any separation of two cations (or two anions) of the same net charge, the stationary phase must show a preference for one more than the other. No variation in the eluant concentration will improve the separation. However, if the exchange involves ions of different net charges, the separation factor does depend on the eluant concentration. The more dilute the counterion concentration in the eluant, the more selective the exchange becomes for polyvalent ions. 

To accomplish any separation of two cations (or two anions), one of these ions must be taken up by the resin in distinct preference to the other. This preference is expressed by the separation factor (or relative retention), using K+ and Na+ as the example ... 

An analysis to determine the concentration of Cu in an industrial plating bath uses a procedure for which Zn is an interferent. When a sample containing 128.6 ppm Cu is carried through a separation to remove Zn, the concentration of Cu remaining is 127.2 ppm. When a 134.9-ppm solution of Zn is carried through the separation, a concentration of 4.3 ppm remains. Calculate the recoveries for Cu and Zn and the separation factor. 

In an ideal separation = I, Rj = 0, and Sj a = 0. In general, the separation factor should be approximately 10 for the quantitative analysis of a trace analyte in the presence of a macro interferent, and 10 when the analyte and interferent are present in approximately equal amounts. 

A sample contains a weak acid analyte, HA, and a weak acid interferent, HB. The acid dissociation constants and partition coefficients for the weak acids are as follows Ra.HA = 1.0 X 10 Ra HB = 1.0 X f0 , RpjHA D,HB 500. (a) Calculate the extraction efficiency for HA and HB when 50.0 mF of sampk buffered to a pH of 7.0, is extracted with 50.0 mF of the organic solvent, (b) Which phase is enriched in the analyte (c) What are the recoveries for the analyte and interferent in this phase (d) What is the separation factor (e) A quantitative analysis is conducted on the contents of the phase enriched in analyte. What is the expected relative erroi if the selectivity coefficient, Rha.hb> is 0.500 and the initial ratio ofHB/HA was lO.O ... 

To calculate the separation factor, we must determine the recovery of solute B in tubes 85-99. This is determined by calculating the fraction of solute B in tubes 85-100 and subtracting the fraction of solute B in tube 100. By calculating z and using Appendix lA, we find that approximately 10.6% of solute B is in tubes 85-100, and that essentially no solute B is in tube 100. The separation factor, Sb,a therefore, is... 

For an equiUbrium-based separation, a convenient measure of the intrinsic selectivity of the adsorbent is provided by the separation factor which is defined by analogy with the relative volatility as... 

The separating power of a chromatographic process arises from the development of many theoretical plates to achieve adsorption equiUbrium within a column of moderate length. Even though the separation factor between two components may be small, any desired resolution may be achieved with sufficient theoretical plates. 

Fig. 8. Ion-exchange isotherm. The separation factor is given by the ratio of area 1/area II (1). See text.

Another solvent extraction scheme uses the mixed anhydrous chlorides from a chlorination process as the feed (28). The chlorides, which are mostly of niobium, tantalum, and iron, are dissolved in an organic phase and are extracted with 12 Ai hydrochloric acid. The best separation occurs from a mixture of MIBK and diisobutyl ketone (DIBK). The tantalum transfers to the hydrochloric acid leaving the niobium and iron, the DIBK enhancing the separation factor in the organic phase. Niobium and iron are stripped with hot 14—20 wt % H2SO4 which is boiled to precipitate niobic acid, leaving the iron in solution. 

Two ions a and b can be separated by countercurrent extraction as long as the ratio of the distribution coefficients, that is, the separation factor Q, is not unity ... 

Irreversible Processes. Irreversible processes are among the most expensive continuous processes. These are used only in special situations, such as when the separation factors of more efficient processes (that is, processes that are theoretically more efficient from an energy point of view) are found to be uneconomicaHy small. Except for pressure diffusion, the diffusion methods discussed herein are essentially irreversible processes. Thus,... 

Irreversible processes are mainly appHed for the separation of heavy stable isotopes, where the separation factors of the more reversible methods, eg, distillation, absorption, or chemical exchange, are so low that the diffusion separation methods become economically more attractive. Although appHcation of these processes is presented in terms of isotope separation, the results are equally vaUd for the description of separation processes for any ideal mixture of very similar constituents such as close-cut petroleum fractions, members of a homologous series of organic compounds, isomeric chemical compounds, or biological materials. 

It should be noted that the separation factor for the centrifuge process is a function of the difference in the mol wts of the components being separated rather than, as is the case in gaseous diffusion, a function of their ratio. The gas centrifuge process would therefore be expected to be relatively more suitable for the separation of heavy molecules. As an example of the equiUbrium separation factor of a gas centrifuge, consider the Zippe centrifuge, operating at 60°C with a peripheral velocity of 350 m/s. From equation 68, OC is calculated to be 1.0686 for uranium isotopes in the form of UF. ... 

When the gas speed is sufficiently high, the separation factor corresponding to a given value of the cut is essentially independent of the gas velocity and, hence, at high speeds, is given (104) to a good approximation as... 

The separation factor / identifies the equihbrium increase in /if from 0 to 1, which accompanies an increase in cf from 0 to 1. For a concentration change over only part of the isotherm, a separation factor R can be defined for the dimensionless transition variables [Eq. (16-11)]. This separation factor is... 

FIG. 16-7 Constant separation factor isotherm as a function of the separation factor r (or interchangeably R). Each isotherm is symmetric about the perpendicular hne connecting (0,1) and (1,0). Isotherms for r and 1/r are symmetric about the 45 hne. 

Constant Separation-Factor Treatment If the valences of all species are equal, the separation factor Oti applies, where... 

Separation Factor The separation factor, a, is defined consistent with other separation methods. It is important to recall that in membranes, a is the result of differing rates, and that it has no eqm-librium implications. The convention in membrane separations is to define the separation so that a > I. 

This method uses the separation factor given in the section titled Vapor Residence Time. The first three steps use equations and a graph (or alternate equation) in that section to get Kv and Uvapormax- Nomenclature is explained there. 

Enantioseparation is typically achieved as a result of the differences in interaction energies A(AG) between each enantiomer and a selector. This difference does not need to be very large, a modest A(AG) = 0.24 kcal/mol is sufficient to achieve a separation factor a of 1.5. Another mechanism of discrimination of enantiomers involves the preferential inclusion of one into a cavity or within the helical structure of a polymer. The selectivity of a selector is most often expressed in terms of retention of both enantiomers using the separation factor a that is defined as ... 

The rapid increase in the separation factors observed for the individual series of columns reflected not only the improvement in the intrinsic selectivities of the individual selectors but also the effect of increased loading with the most potent selector. Although the overall loading determined from nitrogen content remained virtually constant at about 0.7 mmol g for all CSPs, the fractional loading of each selector increased as the number of selectors in the mixture decreased. Thus, the whole method of building block selection and sublibrary synthesis can be also viewed as an amplification process. 

In the elucidation of retention mechanisms, an advantage of using enantiomers as templates is that nonspecific binding, which affects both enantiomers equally, cancels out. Therefore the separation factor (a) uniquely reflects the contribution to binding from the enantioselectively imprinted sites. As an additional comparison the retention on the imprinted phase is compared with the retention on a nonimprinted reference phase. The efficiency of the separations is routinely characterized by estimating a number of theoretical plates (N), a resolution factor (R ) and a peak asymmetry factor (A ) [19]. These quantities are affected by the quality of the packing and mass transfer limitations, as well as of the amount and distribution of the binding sites. 

Fig. 6-10. Influence of the number of basic interaction sites of the template versus the separation factor measured in chromatography for the corresponding racemate. The templates were imprinted using MAA as functional monomer by thermochemical initiation at 60/90/120 °C (24 h at each temperature) and using acetonitrile as porogen. (From Sellergren et al. [15].)...

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,... 

Resolution The degree to which two peaks are separated. This is a function of the number of theoretical plates, N, in a column and the separation factor between the two components. 

The separation factors are relatively low and consequently the MR is not able to approach full conversion. With a molecular sieve silica (MSS) or a supported palladium film membrane, an (almost) absolute separation can be obtained (Table 10.1). The MSS membranes however, suffer from a flux/selectivity trade-off meaning that a high separation factor is combined with a relative low flux. Pd membranes do not suffer from this trade-off and can combine an absolute separation factor with very high fluxes. A favorable aspect for zeoHte membranes is their thermal and chemical stability. Pd membranes can become unstable due to impurities like CO, H2S, and carbonaceous deposits, and for the MSS membrane, hydrothermal stability is a major concern [62]. But the performance of the currently used zeolite membranes is insufficient to compete with other inorganic membranes, as was also concluded by Caro et al. [63] for the use of zeolite membranes for hydrogen purification. 

Particle separation can be characterized by the separation factor, Rp, which is the ratio of eluant to particle elution volumes, or, by the difference in elution voliame, AV, between particle and eluant marker turbidity peaks. For polystyrene monodisperse standards, a linear relationship occ irs between the log of the particle diameter and AV, with a series of parallel lines resulting for different concentration of either salt or surfactant below its critical micelle concentration (IT>18,19) The separation factor has also been shown to be independent of eluant... 

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