Adsorption isotherms excess isotherm

An adsorption isotherm known as the Temkin equation [149] has the form tt = ofF /F where a is a constant and F" is the limiting surface excess for a close-packed... 

Fig. XI-10. Isotherm of composition change or surface excess isotherm for the adsorption of (1) benzene and (2) n-heptane on Graphon. (From Ref. 141.)...

The ACR Process. The first step in the SCR reaction is the adsorption of the ammonia on the catalyst. SCR catalysts can adsorb considerable amounts of ammonia (45). However, the adsorption must be selective and high enough to yield reasonable cycle times for typical industrial catalyst loadings, ie, uptakes in excess of 0.1% by weight. The rate of adsorption must be comparable to the rate of reaction to ensure that suitable fronts are formed. The rate of desorption must be slow. Ideally the adsorption isotherm is rectangular. For optimum performance, the reaction must be irreversible and free of side reactions. 

The equlibrium between the bulk fluid and fluid adsorbed in disordered porous media must be discussed at fixed chemical potential. Evaluation of the chemical potential for adsorbed fluid is a key issue for the adsorption isotherms, in studying the phase diagram of adsorbed fluid, and for performing comparisons of the structure of a fluid in media of different microporosity. At present, one of the popular tools to obtain the chemical potentials is an approach proposed by Ford and Glandt [23]. From the detailed analysis of the cluster expansions, these authors have concluded that the derivative of the excess chemical potential with respect to the fluid density equals the connected part of the fluid-fluid direct correlation function (dcf). Then, it follows that the chemical potential of a fluid adsorbed in a disordered matrix, p ), is... 

The retention of analyses in RP-HPLC markedly depends on the adsorption of the organic constituent of the mobile phase on the surface of the stationary phase. The excess adsorption isotherms of ACN, THF and methanol were measured on silica support modified with C, C6, C8, C10, C12 and C18 monomeric phase and a model was developed for the description of the retention of solutes from the binary mobile phase. The dependence of the retention factor on the partition coefficient can be described by... 

Y.V. Kazakevich, R. LoBrutto, F. Chan and T. Patel, Interpretation of the excess adsorption isotherms of organic components on the surface of reversed-phase adsorbents. Effect on the analyte retention. J. Chromatogr.A 913 (2001) 75-87. 

Gibbs adsorption equation phys chem A formula for a system involving a solvent and a solute, according to which there Is an excess surface concentration of solute if the solute decreases the surface tension, and a deficient surface concentration of solute if the solute increases the surface tension. gibz ad sorp shan i.kwa-zhon Gibbs adsorption isotherm physchem An equation for the surface pressure of surface [< ... 

Fluoride in minor concentrations is beneficial for animals and humans, bnt it becomes toxic when ingested in excessive amounts. Bar-Yosef et al. (1989) investigated adsorption kinetics and isotherms of K -montmorillonite and a series of soils (clay, 4-61% organic matter, 2-7%), as affected by solution pH. The flnoride... 

Acid/hase potentiometry enables the surface charge density to be measured. This involves comparison of the titration curves obtained for the suspension of oxide at several different ionic strengths (10 10" M) with that of the electrolyte alone, followed by calculation of the net consumption of protons or hydroxyl ions (mol g ) at each pH. The data is presented as a plot of excess of acid or base (Fh - Toh ) mol g or mol m ) vs pH (adsorption isotherm) or as a plot of surface charge, cr, (coulombs m ) vs pH (charging curve) (Figure 10.5). 

The second concept that has to be considered is that of absolute adsorption or adsorption of an individual component. This can be considered as the true adsorption isotherm for a given component that refers to the actual quantity of that component present in the adsorbed phase as opposed to its relative excess relative to the bulk liquid. It is a surface concentration. From a practical point of view, the main interest lies in resolving the composite isotherm into individual isotherms. To do this, the introduction of the concept of a Gibbs dividing surface is necessary. Figure 10.6 shows the concept of the surface phase model. 

The adsorption of reactant in the system Cd(II) +1 M KBr/Cd(Hg) was investigated by using chronocoulometry [41]. The values of the reactant surface excess were calculated. The authors proposed the adsorption isotherm, which allows the adsorption of the reactant and ligand to... 

A scintillation counter is used to measure tritium /3 particles adjacent to the surfaces of tritiated sodium dodecyl sulfate in 0.115 M aqueous NaCl solution and tritiated dodeca-nol in dodecanol. The former system is surface active and the latter is not, so the difference between the measured radioactivity above the two indicates the surface excess of sodium dodecyl sulfate. The number of counts per minute arising from the surface excess As is related to the surface excess in moles per square centimeter r by the relationship As = 4.7 x 1012 T1. Use the following data (25°C) to construct the adsorption isotherm for sodium dodecyl sulfate on 0.115 M NaCl ... 

The adsorption isotherm was calculated from the measured concentration change. The number of points and their precision suggests that the adsorption values are good to 5%, except at the very lowest concentrations. The absolute accuracy depends on the cleanliness of the carbon surface, which could contain chemisorbed oxygen, and on the completeness of the dispersion process. These possible errors would lead to low values for the experimental surface excess. Comparison of the area per adsorbed ion at apparent surface saturation with the calculated area in different orientations suggests that the entire B.E.T. area is available for adsorption in the dispersions. 

An adsorption isotherm for a single gaseous adsorptive on a solid is the function which relates at constant temperature the amount of substance adsorbed at equilibrium to the pressure (or concentration) of the adsorptive in the gas phase. The surface excess amount rather than the amount adsorbed is the quantity accessible to experimental measurement, but, at lower pressures, the difference between the two quantities becomes negligible (see Appendix II, Part I, 1.1.11). 

The Gibbs adsorption isotherm is a relationship between the surface tension and the excess interfacial concentrations. To derive it we start with Eqs. (3.27) and (3.28). Differentiation of... 

The choice of the ideal interface in the Gibbs adsorption isotherm (3.52) for a two-component system is, in a certain view, arbitrary. It is, however, convenient. There are two reasons First, on the right side there are physically measurable quantities (a, 7, T), which are related in a simple way to the interfacial excess. Any other choice of the interface would lead to a more complicated expression. Second, the choice of the interface is intuitively evident, at least for ci > C2. One should, however, keep in mind that different spatial distributions of the solute can lead to the same T. Figure 3.6 shows two examples of the same interfacial excess concentration In the first case the distribution of molecules 2 stretches out beyond the interface, but the concentration is nowhere increased. In the second case, the concentration of the molecules 2 is actually increased. 

For solutions the Gibbs dividing plane is conveniently positioned so that the surface excess of the solvent is zero. Then the Gibbs adsorption isotherm (Eq. 3.52) relates the surface tension to the amount of solute adsorbed at the interface ... 

The interfacial tension decreases with increasing amount of surface potential. The reason is the increased interfacial excess of counterions in the electric double layer. In accordance with the Gibbs adsorption isotherms, the interfacial tension must decrease with increasing interfacial excess. At charged interfaces ions have an effect similarly to surfactants at liquid surfaces. 

An adsorption isotherm is a graph of the amount adsorbed versus the pressure of the vapor phase (or concentration in the case of adsorption from solution). The amounts adsorbed can be described by different variables. The first one is the surface excess I in mol/m2. We use the Gibbs convention (interfacial excess volume Va = 0). For a solid surface the Gibbs dividing plane is localized directly at the solid surface. Then we can convert the number of moles adsorbed Na to the surface excess by... 

For ionic surfactants another effect often dominates and usually salt tends to stabilize emulsions. Reason without salt the distance between surfactants in the interface is large because the molecules electrostatically repel each other. This prevents a high surface excess. The addition of salt reduces this lateral repulsion and more surfactant molecules can adsorb at the interface. Then, according to the Gibbs adsorption isotherm Eq. (3.52), the surface tension is reduced and the emulsion is stabilized. 

If we compress a surfactant film on water we observe that the surface tension decreases and the surface pressure increases. What is the reason for this decrease in surface tension We can explain it by use of the Gibbs adsorption isotherm (Eq. (3.52)). On compression, the surface excess increases and hence the surface tension has to decrease. This, however, is relatively abstract. A more illustrative explanation is that the surface tension decreases because the highly polar water surface (high surface tension) is more and more converted into a nonpolar hydrocarbon surface (low surface tension). 

With surfactant the surface tension is reduced according to the Gibbs adsorption isotherm Eq. (3.52). To apply Eq. (3.52) we need to know the surface excess ... 

Figure 6.11 Composite (surface excess) isotherms for the adsorption of (a) benzene from solution in methanol on to charcoal177 and (b) chloroform from solution in carbon tetrachloride on to charcoal178 (By courtesy of (a) American Chemical Society, (b) Journal of the Chemical Society)...

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