Separations factors

SEPARATION FACTOR. The reader will recall that the separation factor, a, in Section 2.1.4, is the same as the relative volatility term used in distillation theory. In 1959, Purnell (32,33) introduced another separation factor (S) term to describe the efficiency of a column. It can be used very conveniently to describe efficiency of open tubular columns  

6 0 level or having a value of 1.5. Therefore, from Equation 

The separation factor (a) is used to describe the position of two peaks relative to each other and is measured using the following equation  

This factor is calculated using the retention factor (k ) for each of the component peaks, where 

As a measure of degree of separation, the ratio of distribution rations, DA/Dfi.is termed the separation factor a. While it is expected that an increased a signifies an improvement in separation, we must remember that the Da should be greater than one and Dg should be less. In fact, the best separation to be achieved at a particular a value is obtained at 

Example 14.1. Consider a mixture of two solutes A and B initially at the same concentration which are distributing between two phases characterized 

although both pairs have the same a = 100, the fraction of A in phase 1, 0.99, is only twice that of B, 0.50. The corresponding fractions of C and D are 0.91 and 0.09 which represents a 10-fold enrichment of C over D in phase 1. 

While single stage processes provide satisfactory solutions to many separation problems, there are at least two conditions that require more. 

When the separation factor is close to one, i.e. the distribution ratios of a pair of analytes are too close to obtain complete separation in a single stage separation, then multistage separations, usually in a counter current mode, must be employed (see Chapters 15 and 16). 

Raw Materials sourcing, purrry raquiremanti. spec Ticaiions Analytical Mathoda Developmeni. Validation artd Tranatef to Duality Assurance Cost Modei Operating and Capital Business Model 

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Recovery factor Reduced column length Reduced plate height Reduced velocity Relative retention ratio Retardation factor d Retention time Retention volume Selectivity coefficient Separation factor... 

Separation factor a Spin-spin coupling constant AB... 

Three separate factors affect resolution (1) a column selectivity factor that varies with a, (2) a capacity factor that varies with k (taken usually as fej). and (3) an efficiency factor that depends on the theoretical plate number. 

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 ... 

By comparing the ratio of the distribution coefficients for a pair of ions, a separation factor (or relative retention) is obtained for a specific experimental condition. 

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. 

Recoveries and separation factors are useful ways to evaluate the effectiveness of a separation. They do not, however, give a direct indication of the relative error introduced by failing to remove all interferents or failing to recover all the analyte. The relative error introduced by the separation, E, is defined as... 

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 ... 

For the countercurrent extraction in Example A6.2, calculate the recovery and separation factor for solute A if the contents of tubes 85-99 are pooled together. 

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. 

The selectivity or separation factor between the two solutes is defined as the ratio of the distribution ratios ... 

DifficultSepa.ra.tions, Difficult separations, characterized by separation factors in the range 0.95 to 1.05, are frequentiy expensive because these involve high operating costs. Such processes can be made economically feasible by reducing the solvent recovery load (260) this approach is effective, for example, in the separation of m- and -cresol, Hnoleic and abietic components of tall oil (qv), and the production of heavy water (see Deuteriumand TRITIUM, deuterium). 

Liquid—Liquid Extraction. The tiquid—tiquid extraction process for the rare-earth separation was discovered by Fischer (14). Extraction of REE using an alcohol, ether, or ketone gives separation factors of up to 1.5. The selectivity of the distribution of two rare-earth elements, REI and RE2, between two nonmiscible tiquid phases is given by the ratio of the distribution coefficients DI and D2 ... 

Fig. 2. Distribution of REE ia the HDEHP—perchlorate system. The lanthanide—yttrium separation factor, E(Ln/Y), is plotted as a function of lanthanide...

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. 

The equihbrium constant for this reaction is ca 1.022 at 100°C. The B concentrates in the Hquid phase (23). However, the vapor phase contains ca 40% undissociated complex, which lowers the effective single-stage separation factor to ca 1.014. 

The search for a system with less decomposition and a higher separation factor has been summarized (27—29). The most promising system is the BE —anisole system, in which BE (g) exchanges with the anisole [100-66-3] (methyl phenyl ether) -BF3 complex (1) (30) ... 

High molecular weight primary, secondary, and tertiary amines can be employed as extractants for zirconium and hafnium in hydrochloric acid (49—51). With similar aqueous-phase conditions, the selectivity is in the order tertiary > secondary > primary amines. The addition of small amounts of nitric acid increases the separation of zirconium and hafnium but decreases the zirconium yield. Good extraction of zirconium and hafnium from ca 1 Af sulfuric acid has been effected with tertiary amines (52—54), with separation factors of 10 or more. A system of this type, using trioctylarnine in kerosene as the organic solvent, is used by Nippon Mining of Japan in the production of zirconium (55). 

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