Equilibrium adsorption, determination

Most surface area measurements are based on the interpretation of the low temperature equilibrium adsorption of nitrogen or of krypton on the solid using the BET theory [33,269,276—278]. There is an extensive literature devoted to area determinations from gas adsorption data. Estimates of surfaces may also be obtained from electron micrographs, X-ray diffraction line broadening [279] and changes in the catalytic activity of the solid phase [ 280]. 

In a separate study, Igwe and Abia46 determined the equilibrium adsorption isotherms of Cd(II), Pb(II), and Zn(II) ions and detoxification of wastewater using unmodified and ethylenediamine tetraacetic acid (EDTA)-modified maize husks as a biosorbent. This study established that maize husks are excellent adsorbents for the removal of these metal ions, with the amount of metal ions adsorbed increasing as the initial concentrations increased. The study further established that EDTA modification of maize husks enhances the adsorption capacity of maize husks, which is attributed to the chelating ability of EDTA. Therefore, this study demonstrates that maize husks, which are generally considered as biomass waste, may be used as adsorbents for heavy metal removal from wastewater streams from various industries and would therefore find application in various parts of the world where development is closely tied to affordable cost as well as environmental cleanliness.46... 

An entirely different approach to equilibrium adsorption is to assume that adsorbed layers behave like liquid films, and that the adsorbed molecules are free to move over the surface. It is then possible to apply the equations of classical thermodynamics. The properties which determine the free energy of the film are pressure and temperature, the number of molecules contained and the area available to the film. The Gibbs free energy G may be written as ... 

The aims of this study are to investigate the removability of resorcinol and catechol from aqueous solutions by adsorption onto ACC in relation to waste water purification and to determine kinetic and equilibrium adsorption models. 

Point (3) has been interpreted by Kieboom and van Bekkum (59) as evidence of the similarity in the electronic character of the initial and transition states. However, an alternative explanation would be that the ratedetermining step does not involve the unsaturated compound but only the activation of hydrogen the overall rate then will be determined by the equilibrium adsorption of the unsaturated compound, the extent of which is sensitive to steric effects. 

Equation (46), one form of the Gibbs equation, is an important result because it supplies the connection between the surface excess of solute and the surface tension of an interface. For systems in which y can be determined, this measurement provides a method for evaluating the surface excess. It might be noted that the finite time required to establish equilibrium adsorption is why dynamic methods (e.g., drop detachment) are not favored for the determination of 7 for solutions. At solid interfaces, 7 is not directly measurable however, if the amount of adsorbed material can be determined, this may be related to the reduction of surface free energy through Equation (46). To understand and apply this equation, therefore, it is imperative that the significance of r2 be appreciated. 

In Figure 4 for Pocahontas coal the methane isotherms at —195°, —78°, 0°, 30°, and 50°C., determined in the sequence indicated, are shown as solid curves, and the isotherms at 0°, —78° and —195°C. after the initial sequence are shown as dashed curves. For the Pittsburgh coal, only the isotherms in a rising series of temperatures were determined (Figure 5). Figures 4 and 5 show a plot of methane isotherms at —195°C. on a relative pressure basis (pressure of methane/vapor pressure) because the vapor pressure is only about 10 torr. Isotherms determined at —195°C. represent metastable equilibrium and those at 30°, 50°, and possibly 0°C. equilibrium. Adsorption was... 

The most common method used for the determination of surface area and pore size distribution is physical gas adsorption (also see 1.4.1). Nitrogen, krypton, and argon are some of the typically used adsorptives. The amount of gas adsorbed is generally determined by a volumetric technique. A gravimetric technique may be used if changes in the mass of the adsorbent itself need to be measured at the same time. The nature of the adsorption process and the shape of the equilibrium adsorption isotherm depend on the nature of the solid and its internal structure. The Brunauer-Emmett-Teller (BET) method is generally used for the analysis of the surface area based on monolayer coverage, and the Kelvin equation is used for calculation of pore size distribution. 

The equilibrium adsorption isotherms of protium and deuterium were measured volumetrically at temperatures within 67-78 K in the pressure range from 10 Pa to 0.2 MPa. The adsorption cell was cooled in liquid nitrogen boiling under vacuum. The error of determination of adsorbent capacity is not above 2 cm3. 

In the single-flow technique, a carrier gas containing the molecules to be adsorbed pass continuously over the catalyst. The flow method of determining gas adsorption has the advantages that no vacuum system is required and no dead volume corrections need to be made. The method is also rapid and easy to use. Disadvantages are the need to use very pure carrier gases, and the fact that for slow or activated adsorption processes equilibrium adsorption may be difficult to determine. The flow method is not recommended for obtaining total isotherms. 

For practical heterogeneous catalyst kinetics this principle has the following consequence. Usually, the assumption of a homogeneous surface is not valid. It would be more realistic to assume the existence of a certain distribution in the activity of the sites. From the above, certain sites will, however, contribute most to the reaction, since these sites activate the reactants most optimally. This might result in an apparently uniform reaction behaviour, and can explain why Langmuir adsorption often provides a good basis for the reaction rate description. This also implies that adsorption equilibrium constants determined from adsorption experiments can only be used in kinetic expressions when coverage dependence is explicitly included otherwise they have to be extracted from the rate data. 

The equilibrium adsorption capacity for nitrogen was determined for each of the samples tested. Isotherms were measured in the range of 0.2 to 700 mmHg adsorbate gas pressure and at 22, 40 and 65 C. Due to the amount of data taken,... 

The special properties of thin liquid films, in particular of foam films, involve studying various colloid-chemical aspects, such as kinetics of thinning and rupture of films, transition from CBF to NBF, isotherms of disjoining pressure, thermodynamic (equilibrium) properties, determination of the electrical parameters of surfactant adsorption layer at the liquid/gas... 

A smooth fall of the equilibrium thickness is clearly seen when the counterion concentration is raised. For films of h = 60 - 80 nm the equilibrium is determined by the equality of Uei with the hydrostatic pressure (pa = 25.5 Pa) Ylvw was not accounted for. Studying films of small thickness, the authors considered for the first time film structure, i.e. the presence of a free aqueous core and adsorption layers (see Section 2.1.3). This is important for the treatment of not only the results from optical thickness measurements but of ne( and Ylvw as well. It was established that ne/ covered thickness h2 equal to the thickness of the... 

Where W is the equilibrium adsorption capacity. Wo is the total volume of the micropores aecessible to the given adsorbate, k is a characteristic constant related to the pore structure of the adsorbent, P is an affinity coefficient, Csai is the saturation concentration in the gas phase of liquid adsorbate at the adsorption temperature T, and C is the eoncentration of adsorbate vapor in equilibrium. Plotting ln(W) versus [RTln(Csai/C)] the parameters K/p and Wo in the DR equation were determined by the slope and the intercept of the linear lines respeetively. The obtained results and correlation coefficients are eompiled in Table 2. This Table shows the DR equation parameters and the... 

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