Langmuir isotherm, determination

These figures show the band profiles obtained for two consecutive injections of increasing volumes of solutions of S- and R-3CPP ca. 4.14 g/1). The numerical calculations with the ED model were carried out with an efficiency of 8000 plates (see Chapter 10). The solid lines show the best profiles calculated with the transport-dispersive model. The parameters of the Langmuir isotherm determined previously were used. A good agreement is observed between the profiles... 

DPM onto humic acid, 376t factors affecting, 370 Langmuir isotherm, determination... 

Using the Langmuir isotherm, determine the fraction of the surface covered at each pressure,... 

The initial formation of the monolayer is rapidly occurred within 30 minutes. If we assume that coverage is proportional to total amount of film material and all surface sites are equivalent, we can use Langmuir adsorption model. We compared experimental EPPI adsorption trend with theoretical Langmuir isotherm determined from ex-situ quartz crystal microbalance data that was indicated that the hypothetical Langmuir isotherm matches with the experimental isotherm in aspects of deposition time and trend of adsorption. The Langmuir isotherm dictates that fractional surface coverage is given by [17 -19]... 

The appropriate form of the Langmuir isotherm determined from equations 7.25 and 7.26 for each set of sites is substituted into equation 7.24, which gives ... 

Consider a binary adsorbed mixture for which each pure component obeys the Langmuir equation, Eq. (16-13). Let n = 4 mol/kg, nl =. 3 mol/kg, Kipi = K2P2 = 1. Use the ideal adsorbed-solution theory to determine ni and n. Substituting the pure component Langmuir isotherm... 

The knowledge of these adsorption isotherms allows quantification of the respective affinity for the stationary phase with respect to the different solutes. Many different isotherm equations have been described in the literature, and experimental methods allowing their determination are reviewed by [58]. As a first approximation, modified competitive Langmuir isotherms can often he used ... 

To understand the chemisorptive property of lr/ln/H-ZSM-5 in a comparison with that of ln/H-ZSM-5, the chemisorption data were analyzed in detail. The data shown in Fig. 3 are relatively well fitted to the Langmuir isotherm, as shown in Fig. 5. From these relations, the equilibrium constant (K) and the amount of NO2 adsorbed at saturation (Vo) were determined according to the following equations ... 

Often, mnltistep reactions are enconntered where a reactant j first becomes adsorbed on the electrode, then is converted electrochemically (or chemically) to a desorbing prodnct. We shall consider the case where the electrochemical step involving adsorbed particles is rate determining. With a homogeneons electrode surface and without interaction forces between the adsorbed particles [i.e., in conditions when the Langmuir isotherm (10.14) can be apphed], the assumption can be made that the rate of this step is proportional not to the bulk concentration Cy j but to the surface concentration Aj or to the degree of surface coverage 0 hence. 

A typical N2 adsorption measurement versus relative pressure over a solid that has both micropores and mesopores first involves essentially a mono-layer coverage of the surface up to point B shown in isotherm IV (lUPAC classification) in Figure 13.1. Up to and near point B the isotherm is similar to a Langmuir isotherm for which equilibrium is established between molecules adsorbing from the gas phase onto the bare surface and molecules desorbing from the adsorbed layer. The volume of adsorbed N2 that covers a monolayer volume, hence the surface area of N2 can then be determined from the slope of the linearized Langmuir plot when P/V is plotted against P ... 

The superficial characteristics of atmospheric corrosion products of steel depend on the type of atmosphere where the sample has been exposed. The way of adsorption of the corrosion products obtained in the coastal atmosphere is polymolecular due to a higher content of salts. This makes easier the presence of water in the metal-corrosion products interface and determines a high corrosion rate. The adsorption of water of a corrosion product formed in a rural zone obeys a Langmuir isotherm, i.e. a monomolecular adsorption takes place. It causes a lower corrosion rate. 

Some conclusions pertaining to adsorption of 1-pentanol riboflavin and thioctic acid on Au electrode have been drawn from differential capacity-potential curves [274]. It has been found, for instance, that adsorption of these compounds obeys the Langmuir isotherm. Moreover, the free energies of adsorption have been determined. 

The maximum surface concentration of benzoic acid obtained by extrapolation of the experimental data is rmax = 5.1 X 1014 molecules cm-2. Determine the parameters P and A in the Frumkin equation of adsorption. Calculate the Gibbs energy of adsorption. Compare the results with the Langmuir isotherm. (Sobkowski)... 

The common shape observed for Tq as a function of the substrate or catalyst concentration depending on the primary events depicted in Eqs. (la)-(lf) is normally reported of saturative type as if the rate would be determined by adsorption properties of the substrate on the catalyst surface according to a Langmuir isotherm ... 

It might also be noted that K (Equation (62)) may be related to AG° for the adsorption process if the model applies to the experimental system. Therefore, from studies of adsorption at different temperatures, values of AH° and AS0 may be determined for the process described by Equation (61). It must be emphasized that compliance with the form predicted by the Langmuir isotherm is not a sensitive test of the model therefore interpretations of this kind must be used cautiously. 

Schuldiner (1959) studied the effect of Hi pressure on the hydrogen evolution reaction at bright (polished) Pt in sulphuric acid. The mechanism of the reaction was assumed to be as in equations (3.3) and (3.4). The step represented by equation (3.3) was assumed to be at equilibrium at all potentials and equation (3.4) represented the rate-determining step. The potentials were measured as overpotentials with respect to the hydrogen potential, i.e. the potential of the H +/H2 couple in the solution (0 V vs. RHE). The experiments were performed at 25CC, where the adsorption of both forms of hydride was assumed to follow the Langmuir isotherm. Thus, the current for the forward (cathodic) and reverse (anodic) reactions in equation (3.3) can be written as ... 

In heterogeneous systems, the rate expressions have to be developed on the basis of (a) a relation between the rate and concentrations of the adsorbed species involved in the rate-determining step and (b) a relation between the latter and the directly observable concentrations or partial pressures in the gas phase. In consequence, to obtain adequate kinetic rate expressions it is necessary to have a knowledge of the reaction mechanism, and an accurate means of relating gas phase and surface concentrations through appropriate adsorption isotherms. The nature and types of adsorption isotherm appropriate to chemisorption processes have been discussed in detail elsewhere [16,17] and will not be discussed further except to note that, in spite of its severe theoretical limitations, the Langmuir isotherm is almost invariably used for kinetic interpretations of surface hydrogenation reactions. The appropriate equations are... 

Assuming that the second process is rapid, we obtain the following standard picture of adsorption on a uniform surface the equilibrium concentration q, which depends on the pressure of the gas, is determined by the Langmuir isotherm. The only difference from the standard picture is that the statistical sum for all states of the adsorbed molecule in a potential hole must be replaced by a combination of two statistical sums for all states of the adsorbed molecule and for all possible states of the surface element. This, of course, has no effect on the form of the Langmuir equation. Under very simple assumptions the kinetics of establishment of equilibrium will also not differ from those on a uniform surface. Thus, the initial velocity is proportional to the pressure and approaches equilibrium exponentially. 

Although the rotational anisotropy scans are informative, considerably more information can be obtained by separate determination of changes in the isotropic and anisotropic components of the surface susceptibility tensor as done by Koos et al. [122]. The experiments consist of monitoring the SH intensity at a fixed angle of 0 = 30° where / oc a 2 and Tj a b0) 2. The results shown in Fig. 5.16 are displayed in terms of thallium coverage. The data has been fitted to a simple linear Langmuir isotherm model of Heinz [79] where the adsorbate contribution to x(2) varies linearly with coverage such that... 

Langmuir isotherms indicate that there are limits to the amount of arsenic that an adsorbant may adsorb. Knowing these limits are important in developing effective treatment technologies for removing arsenic from water (Chapter 7) and determining the ability of soils, sediments, or other natural materials to remove arsenic from natural waters or acid mine drainage (Chapter 3). 

Determination of Correction for Sample Loss Due to Adsorption. Adsorption of the PGS to glassware can be a cause of significant losses of samples. The problem is particularly pronounced for relatively pure samples of PGS. The adsorption process described by the Langmuir isotherm indicates that, at very low concentrations, most material is adsorbed to the glassware. 

---