Linear Henry isotherm

In principle, the FIAM does not imply that the measured flux. / s should be linear with the metal ion concentration. The linear relationship holds under submodels assuming a linear (Henry) isotherm and first-order internalisation kinetics [2,5,66], but other nonlinear functional dependencies with for adsorption (e.g. Langmuir isotherm [11,52,79]) and internalisation (e.g. second-order kinetics) are compatible with the fact that the resulting uptake is a function (not necessarily linear) of the bulk free ion concentration cjjjj, as long as these functional dependencies do not include parameters corresponding with the speciation of the medium (such as or K [11]). 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

For small pressures the Langmuir isotherm becomes the Henry isotherm describing the domain of linear adsorption... 

The simplest adsorption isotherm is that of Henry s law (linear adsorption isotherm),... 

In other words, the model predicts a limiting form of a linear (Henry s Law) type of isotherm as the polymer concentration tends to zero. 

The relationship between r, r2 and has to be specified via the adsorption isotherm. Let us first proceed with the simplest case of the linear Henry regime. 

Earlier work on the application of the concept of dual mode sorption and diffusion to glassy polymer-gas systems has been reviewed in detail 6) and important aspects of more recent work have been dealt with in more recent reviews 7 10). Eq. (5) was first applied by Michaels et al U). Sorption in the polymer matrix and in the specific sorption sites was represented by linear (Henry s law) and Langmuir isotherms respectively so that Sj in Eq. (5) is given by... 

At sufficiently low concentrations on a homogeneous surface the equilibrium isotherm for physical adsorption will always approach linearity (Henry s law). The limiting slope of the isotherm [limp o(dq/dp)T] is referred to as the Henry constant K . It is evident that the Henry con-... 

Inspection of the common normalized isotherm in Figure 9.3 reveals a number of distinctive features. At very low plp°, the isotherm is slightly convex with respect to the p/p° axis and it is evident that the linear, Henry s law region does not extend above p/p° 5x 10-4. Although the isotherm is not truly stepwise (i.e. not a true Type VI isotherm), it does exhibit a characteristic monolayer step. This is followed by a wavy second layer region and then a smooth multilayer curve. Thus, as the multilayer coverage is increased, the isotherm appears to conform to the normal Type II shape. 

At room temperature only a small amount of hydrogen is stored in porous materials and the adsorption isotherm typically does not show any saturation described by a plateau. Instead a linear increase in the hydrogen uptake is observed up to relatively high pressure. Therefore, at room temperature the adsorption is better described by a linear Henry type isotherm [Ij. 

In principle, all Isotherms approach the linear (Henry) range for p- 0, but for heterogeneous surfaces It is often difficult to attain this range. 

Of these shapes, long linear isotherms are uncommon for adsorption on solids (Just like type c in fig. 2.8) and occur only if penetration into the solid takes place, leading to a Nemst-type distribution law as in liquid-liquid partitioning, see (1.2.20.1]. Linearity is also found for the (relatively short) initial parts of all isotherms on homogeneous surfaces. We shall call them, as before, Henry isotherms or the Henry parts of curved Isotherms. 

For the simple Henry region everything is linear. The isotherm is N° / A = K x... 

To examine the effect of reaction kinetics on the reaction region the derived design criteria are applied for the reversible solid-phase reaction A B + C. A linear adsorption isotherm of the components is assumed, with Henry coefficients of 0.4 (reactant), 0.2 and 0.6 (products) respectively. A process with an equal number of columns in sections II and III is considered. The conversion that has to be reached is set to 99.99%. 

The analytical solutions presented above are most of all derived on the basis of the very simple Henry isotherm or the more physically sensible Langmuir isotherm. Beside these analytical solutions a direct integration of the initial and boundary value problem of the diffusion-controlled model is possible. To do so differentials are replaced by differences. This approximation leads to linear equation systems for each time step which have to be solved. As... 

Equation (9-34) is the Langmuir isotherm equation. At low partial pressures, if Kp 1, it reduces to the linear Henry s law form of equation (9-31), while at high partial pressures, if Kp 1, q = qm. 

The selection of a suitable zeolite adsorbent for CO2 removal from flue gas (mixture of CO2 and N2) has been carried out. The limiting heats of adsorption, Henry s Law constants for CO2 and N2, CO2 pure component adsorption isotherms and expected working capacity curves for Pressure Swing Adsorption (PSA) separation application were determined. The results show that the most promising adsorbent characteristics are a near linear CO2 isotherm and a low Si02/Al203 ratio with a cation in the zeolite structure that has strong electrostatic interaction. 

The deviation of the adsorption isotherm at a uniform electrode surface from the linear behavior (Henri isotherm) is related to the interaction between the adsorbed species. A substantiated derivation of its form can only be made on the basis of an analysis of the statistical-mechanical properties of the whole ensemble of adsorbed ions, which, in turn, requires the knowledge of the interaction potential between the ions, U, as a function of their distance, R, along the surface. This quantity is defined as a difference between the energies of the system, when these two ions are fixed at distance R or are very far from each other. 

During the diffusion of solute molecules through the network of pores, some of the solute molecules are adsorbed onto the interior surface of the particle. This process of adsorption is normally very fast relative to the diffusion process, and so we can model it as local equilibrium between the solute in the pore fluid and the solute bound to the interior surface of the particle. This partitioning is often referred to as the adsorption isotherm, which implies constant temperature conditions. When the solute concentration in the pore is low enough, the relationship becomes linear (Henry s law) hence, mathematically, we can write... 

This is a linear relationship between activity and amount sorbed, having the same form as Henry s law in solution chemistry, so that it is often termed Henry isotherm, and K, is the Henry constant. In principle, it is expected that isotherm equations should approximate to the Henry isotherm for low sorbate activities. 

General.—Adsorption from dilute solutions can, in the limit of sufficiently low concentrations, be described by a linear (Henry s law) isotherm, which may, however, be expressed in various forms. Among the possible definitions are the... 

Stadnik and Eltekov have considered again their thermodynamic approach to adsorption from dilute aqueous solutions of microporous active carbons. An important problem in the use of the Dubinin-Radushkevich (D.R.) equation for both gas/solid and solution/solid systems is the mode of transition from this equation to the linear (Henry s law) region of the isotherm (see this Vol. p. 65). In a previous papers they found an empirical relationship between the quantity B/ 3 in the D.R. equation ... 

For a multistage process involving N stages the general result for a linear (Henry s law) isotherm is ... 

Assuming a linear Henry-like absorption isotherm, for polymer membranes the permeability P. (molmm h Pa ) can be expressed as product of solubility S (mol Pa" m" ) and diffusivity D (m h ). For pore membranes, however, this simple relation is not valid because the limited pore volume the amount adsorbed does not increase linearly with the pressure (Henry-like behavior only for permanent gases at relative high temperatures) and the adsorption isotherm is usually curved (Langmuir-like). 

The ideal gas law equation of state thus leads to a linear or Henry s law isotherm. A natural modification adds a co-area term ... 

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

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