Isotherm slope: significance

The latter relationship is readily derived from a mass balance on the contaminant entering the column. This wave speed is referred to as the stoichiometric wave speed. It applies strictly only to one component. It will be recognized that manipulation of Eq. (9.11) with similar substitutions yields the wave speed result for bulk separations where the derivative of v with respect to the spatial variable does not drop out and where two or more components may adsorb. The result has a very similar form but of course depends on not one isotherm slope but on two or more and very significantly the wave speed depends on the relative mole fractions of the adsorbing species and the initial loadings in the column. 

This shows that, as long as these domains are a distance of some jim apart their interaction does not significantly contribute to the surface pressure. Hence interdomain repulsion is not responsible for the finite isotherm slope in the phase coexistence range. 

The adsorption of various aliphatic alcohols from benzene solutions onto silicic acid surfaces has been studied.t The experimental isotherms have an appearance consistent with the Langmuir isotherm. Both the initial slopes of an n/w versus c plot and the saturation value of n/w decrease in the order methanol > ethanol > propanol > butanol. Discuss this order in terms of the molecular structure of the alcohols and the physical significence of the initial slope and the saturation intercept. Which of these two quantities would you expect to be most sensitive to the structure of the adsorbed alcohol molecules Explain. 

The partial derivative, (3z/dp)r, is the slope of z-factor plotted against pressure at constant temperature. The slopes of the isotherms of Figures 3-2, 3-3, and 3-4 show that the second term of Equation 6-8 can be significantly large. 

Solid surfaces are usually heterogeneous therefore, since adsorption at the more active sites is favoured, heats of both monolayer physical adsorption and chemisorption might, in this respect, be expected to become significantly less exothermic as the surface coverage increases, as, for example, shown at low pressures in Figures 5.12a and 5.12b. This, in turn would cause the initial slope of an adsorption isotherm to be steeper than that predicted according to the Langmuir equation or the BET equation. 

Sorption and desorption isotherms were obtained for sorption of radionuclides under oxidizing and reducing conditions. The Freundlich equation accurately describes most of these isotherms. Most radionuclides are apparently irreversibly sorbed on each of the geologic solids since the slopes of sorption and desorption isotherms for a given radionuclide are different. This hysteresis effect is very large and will cause a significant delay in radionuclide transport. It, therefore, should be included in modeling radionuclide transport to accurately assess the isolation capabilities of a repository in basalt. 

An as-plot of Type 11(b) or 11(c) (cf. Figure 6.1) is obtained when the multilayer section of the experimental isotherm conforms to that of the standard, but the mono-layer section is different. The form of plot 11(b) is indicative of relatively strong adsorbent-adsorbate interactions, whereas plot 11(c) is associated with significantly weaker interactions. With either 11(b) or 11(c), a(S) may be calculated from the slope of the linear multilayer region. 

In order to clarify this deviation some additional experiments with zeolite NaY were completed. Thus, the CO2 adsorption isotherm at 273K was repeated in the same sample after evacuation at 373 K in vacuum (to remove the physisorbed CO2). The isotherm obtained is very similar to the first one and no hysteresis is observed. These results indicate that CO2 is not significantly chemisorbed on the zeolite NaY at the experimental conditions used. Additionally, CO2 adsorption was performed at a higher temperature (i.e., 298 K) in order to discard any diffusional limitations of this adsorptive. The characteristic curves for the isotherm at 273 and 298 K are shown in Figure 7. The shape of the characteristic curves at the two temperatures is similar. Both curves exhibit a downward deviation at high adsorption potentials and the slope at lower potentials as well as the ordinate at the origin are very close (see dashed line). These experiments confirm that the deviation observed in the CO2 characteristic curve of zeolite NaY is due to neither CO2 chemisorption nor to diffusional problems as it was expected because the CO2 can enter into smaller pores like in the case of zeolite NaA (Table 2). Therefore, this deviation at low relative pressures must be related with the surface chemistry of the zeolite. 

The transport of significant amounts of dissolved calcite by convection (Wood Hewett, 1984) can probably also be excluded, as convection cells are usually not active except in special settings with strongly sloping isotherms, such as adjacent to salt domes (Bjorlykke etal., 1988). This point of view is supported by the fact that we observe no systematic tendency for calcite cement to be concentrated near the base of a sandstone (i.e. a convection cell) and quartz cement near the top, as one would expect if convection were controlling cementation (Bjorlykke Egeberg, 1993). 

A typical n — A isotherm for a pure fatty acid or phospholipid is shown in Fig. 2. There are three regions of relatively steep slope separated by two distinct plateaus. The significance of these regions has generally been taken to be the following ... 

Another possible cause for such a behavior may not be due to the non-ideality of the system but may be rooted in the nature of the experimental technique and the method of data analysis. The binary sorption equilibria (total amount adsorbed and the composition of the adsorbed phase) are not measured directly in the chromatographic method but are deduced from integration of the slopes of the isotherms at different gas phase compositions. Such an integration may give rise to a significant cumulative error which, in turn, may be responsible for underpredicting the binary... 

At a concentration of >10 mol/1 (Region II), the slope of both curves increases significantly. This increased adsorption is attributed to possible precipitation of oleate on the mineral surface as well as in the bulk solution. The equation for both the isotherms is given below ... 

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