Adsorption isotherms surface area occupied

Most commercial instruments using gas adsorption for surface area and porosity determination are based on the BET isotherm. In Eq. (1.45), the monolayer capacity Vm can be used to calculate the surface area on the basis of the area occupied by each adsorbed gas molecule. According to Eq. (1.45), a plot of p/[Va(p0 - p)] versus p/po is linear. From the slope and the intercept, Vm can be obtained. Thus, the specific surface area S can be obtained as... 

Ferro-Garcia et al. studied the removal of lead from aqueous solutions by activated carbons prepared from almond shells, (Sample A), olive stones (Sample H) and peach stones (Sample P), and by conventional activated carbon (Sample M). The adsorption isotherms were Type H of the BET classification (Figure 6.38). The adsorption capacity of Pb + ions varied between 17.5 mg/g for carbon P to 22.7 mg/g for carbon A. The adsorption increased with increase in the surface area of the activated carbon. The surface areas occupied by the Pb + ions were calculated using 0.802 nm as the diameter of the ion, assuming it to be hydrated with hydration... 

First, we note that the line shape of the plot of surface tension for UI in Fig. 2C differs from that of I" and II The surface tension of aqueous solutions of III decreases abruptly at a concentration of 0.003 mM whereas the surface tensions of solutions of I" " and IIdecrease gradually with increasing concentration. The adsorption isotherm of III cannot be described by the Langmuir model of adsorption. The limiting area occupied by III" ( < 28 A /molec) is also substantially less than either I (55 A /molec) or II (85 A /molec). 

Nitrogen adsorption at low temperature is a routine characterization technique of nanoporous materials. For instance, the specific surface of porous materials is usually assessed from adsorption experiments (prior to capillary condensation of the fluid) on the basis of the Brunauer, Emmett, and Teller (BET) method. The BET model corresponding to the N2 adsorption isotherm at 77 K in the atomistic model of MCM-41 materials fits very well the simulated data with a correlation coefficient = 0.999 (see [39] for the comparison). We found Sbet 1000 m /g (the latter value is obtained by considering as the surface area occupied by an adsorbed N2 molecule, A 2 = 0.162 nm ) and C = 100. The value obtained for C... 

At pH 10.6, the surface of the substrate is negatively charged and sodium ions are adsorbed as counterions in the inner Helmholtz plane (IHP) of the electrical double layer (e.d.L). Adsorption of HDP gives a high-affinity isotherm, which reaches the plateau at equilibrium concentrations consistent with the critical micelle concentration (CMC) of HDPCl, 0.9 mmol/dm [36]. The adsorbed amount is 0.7 mmol/g at saturation, and the surface area occupied by one molecule is about 0.2 nm. This means that the adsorbed amount is somewhat higher than would be expected for close-packed monolayer coverage (0.3 nmVmolecule). 

Many adsorption phenomena especially of surfactants, polymers, proteins and the chemical adsorption of gases on solids can be well represented by the Langmuir adsorption isotherm. This equation can be expressed in a suitable linear form and we can obtain the two parameters of the model, of which one is the concentration or volume at maximum (full) coverage or the so-called monolayer coverage. Knowledge of this monolayer coverage and of the specific surface area of the solid can help us estimate the surface area occupied by a molecule at the interface and thus the amount needed for stabilization. The specific solid surface area can be obtained from gas adsorption measurements on the same solid. 

This is the most commonly used isotherm. This adsorption assumes that at higher concentration the rate of adsorption decreases because of lack of space on the adsorbent surface. Therefore, the adsorption is proportional to concentration as well as empty surface available and rate of desorption is proportional to the surface area occupied by adsorbate. The general form of this isotherm is given below... 

In Table 5.3, is compared with the total hydroxyl concentration (Ni, + N ) of the corresponding fully hydroxylated, sample. The results clearly demonstrate that the physical adsorption is determined by the total hydroxyl content of the surface, showing the adsorption to be localized. It is useful to note that the BET monolayer capacity n JH2O) (= N ) of the water calculated from the water isotherm by the BET procedure corresponds to approximately 1 molecule of water per hydroxyl group, and so provides a convenient means of estimating the hydroxyl concentration on the surface. Since the adsorption is localized, n.(H20) does not, of course, denote a close-packed layer of water molecules. Indeed, the area occupied per molecule of water is determined by the structure of the silica, and is uJH2O) 20A ... 

The principle underlying surface area measurements is simple physisorb an inert gas such as argon or nitrogen and determine how many molecules are needed to form a complete monolayer. As, for example, the N2 molecule occupies 0.162 nm at 77 K, the total surface area follows directly. Although this sounds straightforward, in practice molecules may adsorb beyond the monolayer to form multilayers. In addition, the molecules may condense in small pores. In fact, the narrower the pores, the easier N2 will condense in them. This phenomenon of capillary pore condensation, as described by the Kelvin equation, can be used to determine the types of pores and their size distribution inside a system. But first we need to know more about adsorption isotherms of physisorbed species. Thus, we will derive the isotherm of Brunauer Emmett and Teller, usually called BET isotherm. 

Figure 5.19 shows an idealized form of the adsorption isotherm for physisorption on a nonporous or macroporous solid. At low pressures the surface is only partially occupied by the gas, until at higher pressures (point B on the curve) the monolayer is filled and the isotherm reaches a plateau. This part of the isotherm, from zero pressures to the point B, is equivalent to the Langmuir isotherm. At higher pressures a second layer starts to form, followed by unrestricted multilayer formation, which is in fact equivalent to condensation, i.e. formation of a liquid layer. In the jargon of physisorption (approved by lUPAC) this is a Type II adsorption isotherm. If a system contains predominantly micropores, i.e. a zeolite or an ultrahigh surface area carbon (>1000 m g ), multilayer formation is limited by the size of the pores. 

Data taken from the adsorption leg of the isotherm of Figure 17.11 are listed in the first two columns of the following table. Test the applicability of the following equilibrium theories (a) Langmuir (b) infinite BET and (c) Harkins and Jura. From (a) and (b) obtain estimates of the surface area of the adsorbent and compare the values with that obtained by the point B method. One molecule of nitrogen adsorbed on alumina occupies 0.162 nm2. 

Figure 7-24 Adsorption equilibrium apparatus to determine adsorption isotherms and surface areas of catalysts. From the saturation of a sample of known weight, the surface area can be determined if the area occupied by a...

The adsorption isotherms were discussed extensively in the previous paper (5). The surface area that the adsorbed surfactant molecules occupy at the range of plateau ( 9 = 1) is different because it depends on the chemical composition of the mineral and its clevage plane. 

Typical adsorption isotherms that obey Eqs. (5) and (7) are shown in Figs. 2.1 and 2.2, respectively. It should be noted that a linear Langmuir plot can be obtained by plotting l/[nA]s against 1/P where the slope is 1/k and the intercept is l/[ng] as seen after rearrangement of Eq. (7). The adsorption isotherms are utilized primarily to determine the surface area of porous solids and the heats of adsorption. The isotherms yield the amount of gas adsorbed. By multiplying with the area occupied per molecule... 

Adsorption Isotherms. The dependence of the amount of selenite adsorbed on pH and solution concentration of selenite is illustrated by the curves in Figures 1 and 2. These show that the amount of selenite taken up by goethite reaches a maximum value, r0(PH), at constant pH which cannot be exceeded by increasing the solution concentration and that this maximum value varies with pH. In the pH region studied ion size is unlikely to be the only factor limiting adsorption because even at low pH, where the maximum is greatest, the area of surface available to the ion is always greater than the area it would be expected to occupy ( 20 A.2/ion). 

Kern and Findenegg measured the adsorption of n-docosane (C22H46) in heptane solution to graphite [403], They used a porous graphite with a specific surface area of 68 m2g 1 as determined from BET adsorption isotherms with N2. Tmax, which is assumed to correspond to monolayer coverage, is found to be 88.9 /.xmol/g. Can you conclude something about the structure of the adsorbed molecules What is the area occupied by one molecule compared to its size ... 

Using these equations, we can estimate the number of molecules in a monolayer for compounds with type I, II, and IV isotherms. From that, we can determine the solid s monolayer capacity. This is the amount of adsorbate needed to cover 1 g of solid. The specific surface area for this solid is given dividing this capacity by the average area which one adsorbate molecule occupies. To obtain meaningful values, the dimensions of the adsorbate must be small compared to the pore diameter. The best results are obtained with small spheres, e.g., Ar or Kr. For practical and traditional reasons, however, N2 adsorption at 77 K is used as the IUPAC standard, even though it is not a spherical molecule. 

In adsorption, the amount adsorbed on a surface is most fundamentally characterized by the fraction of surface sights, 9,, that are occupied by i adsorbate molecules. Because the surface area is often not well known, adsorption isotherms are often reported as the amount adsorbed on the surface per gram of adsorbent. In gas adsorption, this amount is traditionally given as the volume of adsorbate at standard temperature and pressure (STP), v. This volume depends on temperature and on the pressure of the adsorbate in the gas phase. v(T, P) is an equation of state for the surface and, when reported at a constant T, is known as an adsorption isotherm. 

This can be used for calculating the area occupied by the adsorbed molecule and hence to predict its orientation on the surface. The surface coverage is commonly related to the bulk concentration via the adsorption isotherm. One of the most frequently used at present is the Langmuir isotherm... 

The specific surface area of the adsorbent can be obtained from the adsorption data if the number of molecules in the monolayer and the area effectively occupied by an adsorbed molecule in the monolayer, Am (i.e., its cross-sectional area), are known. The amount adsorbed per gram of solid to complete a monolayer, nm, can be obtained by applying Equations 4.4 and 4.5 to the adsorption isotherm. The surface area of the adsorbent (S) expressed in m2/g, is... 

The majority of surface area determinations are carried out by making use of the area occupied by a nitrogen molecule as the yardstick, the nitrogen adsorption isotherm being measured at the boiling point of nitrogen, 77.4 K. 

From measuring adsorption isotherms one obtains n(p), and the integral can be solved. The specific surface area is determined by measuring the adsorption isotherm n(p) with a reference gas (e.g.. nitrogen), where the area occupied by an adsorbed molecule is known. Therefore the adsorption isotherms are fitted... 

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