Partition ratio, equation

Equations 17—20 result from contact between hot metal and slag, and the sulfur and carbon come dissolved in the hot metal. Likewise, the manganese, siUcon, and phosphoms which are produced are dissolved into the hot metal. The heats of solution for these elements in some cases depend on concentration, and are not included in the heats of reaction Hsted above. The ratio of the concentration of the oxide (or element for sulfur) in the slag to the concentration of the element in the hot metal is the partition ratio, and is primarily a function of slag chemistry and temperature. 

The 0.865 factor is used to match this equation to the Brenner and Gaydos expression for = 0.2. In these cases, the pore concentration Cpi is related to the external concentration Cj by the partition ratio... 

Commonly used forms of this rate equation are given in Table 16-12. For adsorption bed calculations with constant separation factor systems, somewhat improved predictions are obtained using correction factors f, and fp defined in Table 16-12 is the partition ratio... 

Equation 4.139 has been written for the case where the isotopic substitution is on reactant molecule A only. Therefore the qs ratio in the numerator cancels. The partition function ratio qA2/qAi in the numerator can be replaced by isotopic ratios of translational, rotational, and vibrational partition functions as in Equation 4.76. However, in the denominator one has to be careful to remember that the isotopic partition ratio involves the q functions which contain only 3N -7 (for a linear... 

The selectivity of an extraction system for two solutes i and j is the ratio of their partition coefficients (equation (8)). 

Dividing equation 13.25 by 13.27 and substituting 13.24 gives the relative partitioning ratio for the correct and incorrect substrates ... 

This procedure provides a very simple means of calculating partitioning ratios where there is a branch point in a pathway. For example, suppose that in equation 3.59, A may also give directly a product P with rate constant kP as well as giving F via B, C, D, and E ... 

Comparing equation 13.30 with 13.29 and substituting 13.28 for the partitioning ratio gives the cost-selectivity equation.52... 

The partition ratio (k) is defined as the amount of solute in the stationary phase compared to the amount in the mobile phase. The value of k is calculated for each component from the corrected retention time (t r) and the gas holdup time (tj by the equation ... 

Equation (14) can also be written to include the partition ratio ... 

The three variables are n (column efficiency), a (column selectivity), and kB, which is the partition ratio for the second of the two analytes being separated. (Several similar equations are also in common use, and the relationships between them have been discussed by Said.2) Since good... 

While the dynamic affinity plot provides a simple graphical representation of the order of elution in a displacement, that order is restricted to the particular operating conditions chosen for that experiment (i.e., for a specified value of A). In contrast, the affinity ranking plot can show the variation of the dynamic affinity of a molecule over a range of A values. To enable this comparison, the dynamic affinity A (which is the criterion for displacement) can be plotted against the displacer partition ratio A (which is the operating variable for displacement). The equation for such a plot can be determined by rearrangement of Eq. (6) as... 

The resolution (Rs) of compounds on capillary GC columns is a function of the column efficiency (N effective), the ability of the stationary phase to separate the compounds (separation factor, a), and the ratio of the amount of time the compounds spend in the stationary phase vs. the time the compounds spend in the carrier gas phase (partition ratio, k ). Resolution of two compounds can be defined by the equation ... 

In the G(w)-approximation, introduced by Bigeleisen and Mayer (8) and later extended to higher orders by Bigeleisen (4), the reduced partition function ratio (Equation 1) is expanded in terms of the isotope frequency shifts, Au, = — Ui. The first three terms are... 

Partition ratio. The partition ratio is the ratio of product release to enzyme inactivation and is a measure of the efficiency of the mechanism-based inhibitor. Formally, it refers to the ratio (Equation 17.46). The most efficient inactivators will have partition ratio of zero. In those cases, theoretically, every enzymatically processed inhibitor molecule will result in the inactivation of a molecule of enzyme. Even though the partition ratio is independent of... 

An adaptation of the distribution constant defined in Equation (23-3) could be made for solutes in chromatojp-aphy. As in liquid-liquid extraction, however, solutes may be present in several chemical forms, and therefore a quantity analogous to the distribution ratio (Section 23-1), called the partition ratio, is preferred. The partition ratio must be a somewhat more broadly defined term than the distribution ratio in liquid-liquid extraction for two reasons. First, in chromatography, concentrations of solute in the two phases are usually unknown and may be unmeasurable, as when adsorption is important. Second, instead of the two phases being merely an aqueous phase and an immiscible organic solvent, in chromatography they can be any one of innumerable combinations of solid or liquid stationary phases and liquid or gas... 

This expression for resolution may be written in an alternative form in terms of the relative retention Fj/Kj (Section 24-1) and the partition ratio k. Thus it can be shown that (24-34) is equivalent to the following fundamental equation involving three nearly independent factors ... 

In (24-35) the term V /4 is influenced by many factors [Equation (24-14)], but mainly reflects the characteristics of a particular column and its mode of operation. This plate-munber factor is described in the preceding sections (24-2 and 24-3). The factors of relative retention and partition ratio in (24-35) depend on the solutes, the nature of the mobile and stationary phases, and the temperature. The factor A /(l -I- k) also strongly depends on the dead-space volume in a column. Figure 24-8 illustrates how it varies according to the dead-space volume per gram of stationary phase. When the specific retention volume of a solute is relatively low and a column... 

FIGURE 24-9 Number of theoretical plates required to attain a resolution of 1.0 as a function of partition ratio for values of relative retention ranging from 1.005 to 1.1 [Equation (24-35)]. (From Tang and Harris. )... 

Resolution in temperature programming is calculated by means of Equation (24-30) without alteration. Equation (24-35), however, has no practical analog in temperature programming because relative retention has little direct significance and the partition ratio has meaning only at a particular temperature. Nevertheless, it can be concluded in a qualitative way that low partition ratios must be avoided if the best resolution is to be attained. 

The activity coefficients in Equation (25-5), and hence the selectivity coefficient and partition ratio, depend on the concentration of electrolyte in solution and taken up by the resin. The fraction a. for metal ions depends on factors such as hydrolysis, complexation, and masking (Section 23-5). 

Loren C. Wilson, B.S. Sr. Research Specialist, The Dow Chemical Company (Liquid Density, Viscosity, and Interfacial Tension Phase Diagrams Liquid-Liquid Equilibrium Experimental Methods Data Correlation Equations Table of Selected Partition Ratio Data)... 

Temperature Effect The effect of temperature on the value of the partition ratio can vary greatly from one system to another. This depends on how the activity coefficients of the components in each phase are affected by changes in temperature, including any effects due to changes in mutual solubility with temperature. For a given phase, the Gibbs-Helmholtz equation indicates that... 

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