Equilibrium rate factors

Displacement Development A complete prediction of displacement chromatography accounting for rate factors requires a numerical solution since the adsorption equilibrium is nonlinear and intrinsically competitive. When the column efficiency is high, however, useful predictious can be obtained with the local equilibrium theoiy (see Fixed Bed Transitions ). 

The method includes the mass unit vent flow capacity per unit area. G. This allows using any applicable vent capacity calculation method. The method incorporates the equilibrium rate model (ERM) for vent flow capacity when friction is negligible. Additionally, a coiTection factor is used for longer vent lines of constant diameter and with negligible static head change. ... 

The lack of a substrate isotope effect suggests very extensive internal return and is readily explained in terms of the fact that conversion of the hydrocarbon to the anion would require very little structural reorganisation. Since koba = k 1k 2/(kLl+k 2) and k 2 is deduced as > k2, then kobs = Kk 2, the product of the equilibrium constant and the rate of diffusion away of a solvent molecule, neither of the steps having an appreciable isotope effect. If the diffusion rates are the same for reactions of each compound then the derived logarithms of partial rate factors (above) become pAT differences between benzene and fluorobenzene hydrogens in methanol. However, since the logarithms of the partial rate factors were similar to those obtained with lithium cyclohexylamide, a Bronsted cor-... 

Fig. 2. Variation of the logarithms of the rate factors (23) and (24) for charge-state changes as the band potential, and hence the height of the hydrogen donor level eD is changed (a) relative to an equilibrium Fermi level eF for the carriers or (b) relative to an arbitrary level, when the electron and hole Fermi levels eFe and rFh, respectively, are made different by application of a reverse bias to a p-n junction.

Chemical kinetics is concerned with the rate of reaction and factors affecting the rate, and chemical thermodynamics is concerned with the position of equilibrium and factors affecting equilibrium. 

There is also a diffusion rate factor when polymers are exposed to any gas or liquid. Usually absorption of fluid (swelling) takes place faster than extraction of soluble constituents of the polymer and builds up to an equilibrium condition as shown in Figure 4.2 (curve A). If extraction is also taking place, for example from a plasticised material, a maximum swelling may be reached (curve B). If the absorption of fluid is accompanied by oxidation, the volume may continue to increase (curve C). 

Forward and backward reaction rates are not identical in systems that are not at isotopic equilibrium. Reactions may, in fact, be unidirectional if reaction products become physically isolated from the reactants. The reaction rates depend on the ratios of the masses of the isotopes and their vibrational energies hence, such reactions result in kinetic isotope fractionations. The magnitude of a kinetic isotope fractionation depends on the reaction pathway and the relative energies of the bonds being severed or formed by the reaction. The kinetic fractionation factor is typically larger than the equilibrium fractionation factor for the same reaction. As a rule, bonds of light isotopes are broken more easily than equivalent bonds of heavier isotopes. Hence, light isotopes react faster than heavy isotopes. 

The sole factor determining the value of a rate or equilibrium constant is the difference in free energy between the reactants and either a transition state, in the case of a reaction rate, or the products, in the case of an equilibrium. Rate and equilibrium constants cannot therefore properly be correlated with any static property of the reactants themselves. This point cannot be emphasized too strongly in view of the many attempts that have been made to find such correlations. One might add that attempts of this kind are in any case basically unsatisfactory in that they ignore the transition state entirely and so can throw no light on its structure even if correlations of this kind can be established, they do not throw any light on the detailed mechanism of chemical process—and it is just in this field that quantum theory has most to offer to chemists. 

Bioconcentration of organic compounds by aquatic plants has received relatively little research attention. Curves showing uptake and loss of radioactivity by duckweed plants exposed to labelled compounds in axenic cultures are shown in Fig. 2. Rate constants and calculated equilibrium bioconcentration factors are shown in Table III. By comparison with fish data shown in Table I, the plants concentrated fenitrothion and fluorene rather poorly, and aminocarb surprisingly well. Lockhart et al. (14) presented a regression equation based on data from uptake curves ... 

For two-phase flow through pipes, an overall dimensionless discharge coefficient, /, is applied. Equation 12-11 is referred to as the equilibrium rate model (ERM) for low-quality choked flow. Leung [28] indicated that Equation 12-11 be multiplied by a factor of 0.9 to bring the value in line with the classic homogeneous equilibrium model (HEM). Equation 12-11 then becomes... 

The factor in the outer brackets accounts for the influence of polymer conformational relaxation on the equilibrium rates, and has values typically ranging from 0.01 to 0.5, depending on the depth of the binding potential When [Pg.460]

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