Adsorption, coefficient isotherms

An analogous law was established in 1803 by W. Henry for the solubilities of gases in water hence, this expression is called the Henry isotherm. The adsorption coefficient B (units dmVmol) depends on the heat of adsorption B = B° e,xp(q RT). The Henry isotherm is valid for low surface coverages (e.g., at 9 < 0.1). 

Fig.3.1.9 (a) The adsorption-desorption isotherm (circles, right axis) and the self-diffusion coefficients D (triangles, left axis) for cyclohexane in porous silicon with 3.6-nm pore diameter as a function of the relative vapor pressure z = P/PS1 where Ps is the saturated vapor pressure, (b) The self-diffusion coefficients D for acetone (squares) and cyclohexane (triangles) as a function of the concentration 0 of molecules in pores measured on the adsorption (open symbols) and the desorption (filled symbols) branches. 

The adsorption coefficients (K) were determined using the equation for the Freundlich adsorption isotherm ... 

Monkiedje et al. [10] investigated the fate of niclosamide in aquatic system both under laboratory and field conditions. The octanol/watcr partition coefficient (Kaw) of niclosamide was 5.880 x 10 4. Adsorption isotherm studies indicated that the Freundlich parameters (K, n) for niclosamide were 0.02 and 4.93, respectively, for powder activated carbon (PAC), and 9.85 x 10 5 and 2.81, respectively, for silt loam soil. The adsorption coefficient (Aoc) for the drug was 0.02 for PAC, and 4.34 x 10-3 for the same soil. Hydrolysis of niclosamide occurred in distilled water buffer at pH above 7. No photolysis of the drug was observed in water after exposure to long-wave UV light for 4 h. Similarly, neither chemically volatilized from water following 5 h of sample aeration. Under field conditions, niclosamide persisted in ponds for over 14 days. The half-life of niclosamide was 3.40 days. 

At low temperature the difference in mobility is even more striking AH = 120 Hz (247 K) for C of trans 2-butene and only 80 Hz for C2 of 1-butene (250 K). The adsorption coefficients determined from adsorption isotherms and kinetic data which are 5xlO 2 torr for 1-butene and 8.2x10 torr l for trans 2-butene (4) support entirely this difference in mobility. 

Tables 12.2 and 12.3. The effect of vertical variability is shown in Table 12.2, while the lateral spatial variability is shown in Table 12.3. The vertical and lateral spatial variabilities were defined on the basis of either the measured adsorption coefficient K), as generated from adsorption isotherms on soil profiles, or on adsorption coefficients on soil organic matter calculated as adsorption on organic carbon per unit weight of soil. We see that both vertical (Table 12.2) and lateral (Table 12.3) variability of soil affect the adsorption coefficients. A comparison between the bromide (conservative) and the two nonconservative herbicides distributions with depth after about 900mm of leaching is shown in Fig. 12.3. We see that, in the case of bromide, there is a continuous displacement of the center of mass with cumulative infiltration. In contrast, the bulk of the herbicide contaminant mass remains in the upper soil layer, with very little displacement.

SULFATE ADENYLYLTRANSFERASE (ADP) ADRENODOXIN ADSORPTION ABSORPTION BIOMINERALIZATION MICELLAR CATALYSIS LANGMIUR ISOTHERM Adsorption coefficient LANGMUIR ISOTHERM Adsorption of gases,... 

Thus, the passage from an adsorption isotherm of a pure substance to the corresponding adsorption isotherm of a mixture is very easy, supposing that the model of a nonuniform surface is applicable and adsorption coefficients are proportional. If, for instance, adsorption of pure gas A is described by the Freundlich isotherm (135), then for adsorption of A from mixture... 

The fractional factor with p of Equation (1) according to the accepted view corresponds to Langmuir s adsorption isotherm for mixtures on an almost covered homogeneous surface or on like active centers and the z are the relative adsorption coefficients. This fraction was so interpreted for other cases by Hinshelwood 13), Schwab 9), the author 1, 14), Frost 15), Hougen 16), and others. Two questions now arise ... 

Is the factor in general an adsorption isotherm, i.e., do the 2 s have the significance of relative adsorption coefficients ... 

TABLE 4.7. Adsorption Coefficients (K) and Distribution Coefficients (Kd) for Adsorption of Triallate (Linear Isotherms) and trans- and c/s-Chlordane (Langmuir Isotherms) on Humic Acids (HAs) Isolated from Pig Slurry (PS) and Surface (1) and Whole (2) Horizons of Two Soils (UK and PO)... 

Geochemical models of sorption and desorption must be developed from this work and incorporated into transport models that predict radionuclide migration. A frequently used, simple sorption (or desorption) model is the empirical distribution coefficient, Kj. This quantity is simply the equilibrium concentration of sorbed radionuclide divided by the equilibrium concentration of radionuclide in solution. Values of Kd can be used to calculate a retardation factor, R, which is used in solute transport equations to predict radionuclide migration in groundwater. The calculations assume instantaneous sorption, a linear sorption isotherm, and single-valued adsorption-desorption isotherms. These assumptions have been shown to be erroneous for solute sorption in several groundwater-soil systems (1-2). A more accurate description of radionuclide sorption is an isothermal equation such as the Freundlich equation ... 

There are several theoretical derivations of adsorption isotherms. The simple Langmuir equation [Eq. (4.2), named after the American chemist and 1932 Nobel laureate Irving Langmuir], describes the formation of a monolayer on a surface [81]. This corresponds to the type I isotherm shown in Figure 4.15. Here Vis the amount adsorbed, Vm is the amount adsorbed in one monolayer, p is the pressure and b is the adsorption coefficient, which depends exponentially on the heat of adsorption. 

The adsorption coefficients of the substances present during the dehydration of ethyl alcohol (i.e., water, ethylene, and ethanol) over alumina were determined kinetically and from the adsorption isotherms. The values of these adsorption coefficients are listed in Table IV. The values of the adsorption coefficients determined from the adsorption isotherms greatly exceed those calculated from the kinetic data thus the catalytically active centers are characterized by a smaller adsorption capacity for the reaction product, water, than other sections of the surface. Antipina and Frost, therefore, assert that the dehydration of ethyl alcohol occurs on sections possessing a smaller adsorption for water than those upon which water vapor alone is adsorbed. 

Comparison of the Values of the Adsorption Coefficients Found from Kinetic Measurements and from Adsorption Isotherms... 

It is at this point that the Langmuir and Michaelis-Menten approaches diverge. The development of the Langmuir isotherm (Eqn. 7.7) was based on the adsorption coefficient of the catalyst-substrate complex (Eqn. 7.4) while the Michaelis-Menten equation is based on the dissociation constant of this complex (Eqn. 7.16). 

Approximation of the linear form is not necessary for the Langmuir isotherm, and the first plot of the adsorption data will determine whether or not the model is applicable, and also will allow calculation of the adsorption coefficients. Usually a single model will not be satisfactory for a wide range of adsorbate concentrations but will only serve in narrow range of concentration. At low concentrations, C/C 1, the BET model reduces to a Langmuir model. 

The Thiele modulus for the mesoporous structure of the eatalyst, ( ) i, was calculated using the following parameters particle size, Rp = 0.0137 cm mean pore radius, rpore.ave = 20 10 cm catalyst porosity, e = 0.52 catalyst density, pg = 1210 g 1. N2 adsorption-desorption isotherms were used for measurement. The calculated value of effective diffusivity coefficient in the mesoporous structure of the catalyst is Dg = 9.71 10 2 cm min . This value is not affeeted by coke deposition. 

For experimental verification of these models, Foplewska et al. [33] used binary mixtures of methanol-water and acetonitrile-water as the mobile phases and measured the adsorption equilibrium isotherms of cyclopentanone on two similar adsorbents having different degrees of sruface heterogeneity, a Cis non-endcapped and a Cig endcapped silica. Ehie to its structure, cyclopentanone exhibits affinity for adsorption on the bonded alkyl chains and for the polar, im-covered silica sruface of the adsorbent. Overloaded elution bands of cyclopentanone in piue water were recorded (Figrue 15.3) and the isotherms were derived using an inverse method (see Chapter 3). Five independent parameters (the excess coefficients and the eqiulibrirun constants for partition-adsorption and for... 

Adsorption. The solution used to evaluate the pesticide transport equation, Equation 4a, assumes a linear adsorption isotherm that is constant with depth. However, linearity may not be the case for some pesticides and the adsorption coefficient will almost never be constant with depth. The rationale for using a linear model is initially based on the Freundlich isotherm... 

Fig. 10. UOP Sorbex operation with linear isotherms. Slope of = Klm, slope of (D = K2. Conditions for separation Kl > K2i Lzj S > Kly k2 < l2/s < k19 k2 Ll — L2 = F where K = adsorption coefficient, L = net liquid flow rate, S = net solids flow rate, and...

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