Temperature distribution coefficients

Temperature programming was introduced in the early days of GC and is now a commonly practiced elution technique. It follows that the temperature programmer is an essential accessory to all contemporary gas chromatographs and also to many liquid chromatographs. The technique is used for the same reasons as flow programming, that is, to accelerate the elution rate of the late peaks that would otherwise take an inordinately long time to elute. The distribution coefficient of a solute is exponentially related to the reciprocal of the absolute temperature, and as the retention volume is directly related to the distribution coefficient, temperature will govern the elution rate of the solute. 

Among the properties sought in the solvent are low cost, avadabihty, stabiUty, low volatiUty at ambient temperature, limited miscibility in aqueous systems present in the process, no solvent capacity for the salts, good solvent capacity for the acids, and sufficient difference in distribution coefficient of the two acids to permit their separation in the solvent-extraction operation. Practical solvents are C, C, and alcohols. For industrial process, alcohols are the best choice (see Amyl alcohols). Small quantities of potassium nitrate continue to be produced from natural sources, eg, the caUche deposits in Chile. 

Whenever data are available for a given system under similar conditions of temperature, pressure, and composition, equilibrium distribution coefficients (iC = y/x) provide a much more rehable tool for predicting vapor-liquid distributions. A detailed discussion of equilibrium iC vahies is presented in Sec. 13. 

For a ternai y system, the phase diagram appears much like that in conventional liquid-liquid equilibrium. However, because a SCF solvent is compressible, the slopes of the tie lines (distribution coefficients) and the size of the two-phase region can vary significantly with pressure as well as temperature. Furthermore, at lower pressures, LLV tie-triangles appear upon the ternary diagrams and can become quite large. 

It is clear that the separation ratio is simply the ratio of the distribution coefficients of the two solutes, which only depend on the operating temperature and the nature of the two phases. More importantly, they are independent of the mobile phase flow rate and the phase ratio of the column. This means, for example, that the same separation ratios will be obtained for two solutes chromatographed on either a packed column or a capillary column, providing the temperature is the same and the same phase system is employed. This does, however, assume that there are no exclusion effects from the support or stationary phase. If the support or stationary phase is porous, as, for example, silica gel or silica gel based materials, and a pair of solutes differ in size, then the stationary phase available to one solute may not be available to the other. In which case, unless both stationary phases have exactly the same pore distribution, if separated on another column, the separation ratios may not be the same, even if the same phase system and temperature are employed. This will become more evident when the measurement of dead volume is discussed and the importance of pore distribution is considered. 

By measuring the retention volume of a solute, the distribution coefficient can be obtained. The distribution coefficient, determined over a range of temperatures, is often used to determine the thermodynamic properties of the system this will be discussed later. From a chromatography point of view, thermodynamic studies are also employed as a diagnostic tool to examine the actual nature of the distribution. The use of thermodynamics for this purpose will be a subject of discussion in the next chapter. It follows that the accurate measurement of (VV) can be extremely... 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

This, as is shown by the theory, is due to the evolution of the heat of absorption, during solute adsorption at the front part of the peak. Conversely, the back of the peak is eluted at a lower temperature than the surroundings throughout the length of the column due to the absorption of the heat of solute desorption. As a result, the distribution coefficient of the solute at the front of the peak, and at a higher temperature, will be less than the distribution coefficient at the back of the peak, at the... 

This equation, although originating from the plate theory, must again be considered as largely empirical when employed for TLC. This is because, in its derivation, the distribution coefficient of the solute between the two phases is considered constant throughout the development process. In practice, due to the nature of the development as already discussed for TLC, the distribution coefficient does not remain constant and, thus, the expression for column efficiency must be considered, at best, only approximate. The same errors would be involved if the equation was used to calculate the efficiency of a GC column when the solute was eluted by temperature programming or in LC where the solute was eluted by gradient elution. If the solute could be eluted by a pure solvent such as n-heptane on a plate that had been presaturated with the solvent vapor, then the distribution coefficient would remain sensibly constant over the development process. Under such circumstances the efficiency value would be more accurate and more likely to represent a true plate efficiency. 

In the range of operating temperatures and compositions, the equilibrium relations are monotonic functions of temperature of the MSA. This is typically true. For instance, normally in gas absorption Henry s coefficient monotonically decreases as the temperature of the MSA is lowered while for stripping the gas-liquid distribution coefficient monotonically increases as the temperature of the stripping agent is increased. 

Various amines find application for pH control. The most commonly used are ammonia, morpholine, cyclohexylamine, and, more recently AMP (2-amino-2-methyl-l-propanol). The amount of each needed to produce a given pH depends upon the basicity constant, and values of this are given in Table 17.4. The volatility also influences their utility and their selection for any particular application. Like other substances, amines tend towards equilibrium concentrations in each phase of the steam/water mixture, the equilibrium being temperature dependent. Values of the distribution coefficient, Kp, are also given in Table 17.4. These factors need to be taken into account when estimating the pH attainable at any given point in a circuit so as to provide appropriate protection for each location. 

This may be illustrated by the following example. Suppose that 50 mL of water containing 0.1 g of iodine are shaken with 25 mL of carbon tetrachloride. The distribution coefficient of iodine between water and carbon tetrachloride at the ordinary laboratory temperature is 1 /85, i.e. at equilibrium the iodine concentration in the aqueous layer is 1 /85th of that in the carbon tetrachloride layer. The weight of iodine remaining in the aqueous layer after one extraction with 25 mL, and also after three extractions with 8.33 mL of the solvent, can be calculated by application of the above formula. In the first case, if x, g of iodine remains in the 50 mL of water, its concentration is x,/50 gmL 1 the concentration in the carbon tetrachloride layer will be (0.1 —x1)/25gmL 1. 

Voltaic cells 64. 504 Voltammetry 7, 591 anodic stripping, 621 concentration step, 621 mercury drop electrode, 623 mercury film electrode, 623 peak breadth, 622 peak current, 622 peak potential, 622 purity of reagents, 624 voltammogram, 622 D. of lead in tap water, 625 Volume distribution coefficient 196 Volume of 1 g of water at various temperatures, (T) 87... 

Kaufman, J. J. Semo, N. M. Koski, W. S., Microelectrometric titration measurement of the pKa s and partition and drug distribution coefficients of narcotics and narcotic antagonists andtheirpH and temperature dependence, 7. Med. Chem. 18,647-655 (1975). 

In closing, recovery of technetium from waste solution should be touched upon. Studies of the base hydrolysis of technetium P-diketone complexes revealed that all of the complexes studied decompose in an alkaline solution even at room temperature, until technetium is finally oxidized to pertechnetate. These phenomena are very important for the management of technetium in waste solutions. Since most metal ions precipitate in alkaline solution, only technetium and some amphoteric metal ions can be present in the filtrate [29]. A further favorable property of pertechnetate is its high distribution coefficient to anion exchangers. Consequently, it is possible to concentrate and separate technetium with anion exchangers from a large volume of waste solution this is especially effective using an alkaline solution [54],... 

Tmax Tmin)/lodo stand for potential and temperature distribution coefficients. 

The choice of operating temperature can have a profound effect on a chromatographic separation due to the temperature dependence of the distribution ratio D of each solute or to be strict, of the distribution coefficient A , (cf. solvent extraction, p. 56). The relation is an exponential one,... 

Sablani, S.S. and Rahman Shafiur, M. 2003. Effect of syrup concentration, temperature and sample geometry on equilibrium distribution coefficients during osmotic dehydration of mango. Food Res. Int. 36, 65-71. 

Distribution coefficients describe in a summarizing way the distribution of an element between the dissolved and solid phases. They are conditional constants valid for a given pH, temperature and other conditions they are independent of the concentrations of solids in water. They are usually defined (Chapter 4.8) as... 

Boltzmann s constant temperature charge of ion distribution coefficient activity coefficient of species i potential at o-plane potential at (5-plane potential at d-plane... 

Thermodynamic calculations based on the compositional dependence of the equilibrium constant are applied to solubility data in the KCl-KBr-H20 system at 25°C. The experimental distribution coefficient and activity ratio of Br /Cl in solution is within a factor of two of the calculated equilibrium values for compositions containing 19 to 73 mole percent KBr, but based on an assessment of uncertainties in the data, the solid solution system is clearly not at equilibrium after 3-4 weeks of recrystallization. Solid solutions containing less than 19 and more than 73 mole percent KBr are significantly farther from equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. 

Although equilibrium was not established, it was more closely approached in the KCl-KBr-H20 system than in carbonate systems. For example, in a similar analysis of the strontianite-aragonite solid solution system (4 ), it was found that the experimental distribution coefficient for Sr substitution from seawater into aragonite is 12 times larger than the expected equilibrium value. Most of the distribution coefficients for the KCl-KBr-H20 system are within a factor of two of the equilibrium value, but clearly not at equilibrium. Considerable caution should be exercised before reaching the conclusion that equilibrium is established at relatively low temperatures in other solid solution-aqueous solution systems. 

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