Adsorption single-component equilibrium

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of soration equilibrium for single component adsorption or binary ion exchange (monovariance) is usually in the form of isotherms [n = /i,(cd or at constant T] or isosteres = pi(T) at constant /ij. Representative forms are shown in Fig. I6-I. An important dimensionless group dependent on adsorption equihbrium is the partition ratio (see Eq. 16-125), which is a measure of the relative affinities of the sorbea and fluid phases for solute. 

Eqs. (1,4,5) show that to determine the equilibrium properties of an adsorbate and also the adsorption-desorption and dissociation kinetics under quasi-equilibrium conditions we need to calculate the chemical potential as a function of coverage and temperature. We illustrate this by considering a single-component adsorbate. The case of dissociative equilibrium with both atoms and molecules present on the surface has recently been given elsewhere [11]. 

Single component system (SCS) adsorption models actually mean one pollutant component in aqueous system or in a SWM leachate [34]. Since water is simply assumed to be inert, and the pollutant/leachate adsorption is assumed to be unaffected by water, the system is treated as an SCS. To represent the equilibrium relation for SCS adsorption, a number of isotherm models reported in the literature are reviewed in the following. 

For single-component gas permeation through a microporous membrane, the flux (J) can be described by Eq. (10.1), where p is the density of the membrane, ris the thermodynamic correction factor which describes the equilibrium relationship between the concentration in the membrane and partial pressure of the permeating gas (adsorption isotherm), q is the concentration of the permeating species in zeolite and x is the position in the permeating direction in the membrane. Dc is the diffusivity corrected for the interaction between the transporting species and the membrane and is described by Eq. (10.2), where Ed is the diffusion activation energy, R is the ideal gas constant and T is the absolute temperature. 

The Langmuir adsorption isotherm describes the equilibrium between a single-component gas A and adsorbed species A(s) at a surface [237]. The expression relates the fraction of the surface 6a covered by adsorbed species as a function of the partial pressure pa exposed to the surface. The usual form of the Langmuir adsorption isotherm is... 

Ideal Adsorbed Solution Theory. Perhaps the most successful general approach to the prediction of multicomponent equilibria from single-component isotherm data is ideal adsorbed solution theory. In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equilibrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equilibrium pressure for the pure component at Ike same spreading pressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption. Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, are not consistent with an ideal adsorbed phase and there is no way of knowing a priori whether or not a given system will show ideal behavior. 

A cell model is presented for the description of the separation of two-component gas mixtures by pressure swing adsorption processes. Local equilibrium is assumed with linear, independent isotherms. The model is used to determine the light gas enrichment and recovery performance of a single-column recovery process and a two-column recovery and purification process. The results are discussed in general terms and with reference to the separation of helium and methane. 

In carrying out material balance over a small control volume of a fixed bed, it is considered that fluoride removal is solely by adsorption onto the zeolite particles. Additionally, the system is assumed to be isothermal, non-equilibrium and non-adiabatic single-component fixed-bed adsorption. For the control volume (Fig. 6), Axdz, for a limiting situation z->0, the material balance is given by... 

When the relative volumes are known and the diffusion coefficients in the capsule core and capsule membrane can be estimated a priori in single component adsorption, the parameter to work with is the effective diffusivity in the adsorbent pore (Dn). Then, with the above estimated parameter values, the parameters of competitive adsorption are the maximum concentration at the solid phase of the adsorbent (CsmT), and the equilibrium constants of the target product (KS1) and byproduct (KS2)-... 

At this point, it is feasible to correlate the liquid-phase adsorption equilibrium single component data, with the help of isotherm equations developed for gas-phase adsorption, since, in principle, it is feasible to extend these isotherms to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [92], These equations are the Langmuir, Freundlich, Sips, Toth, and Dubinin-Radushkevich equations [91-93], Nevertheless, the Langmuir and Freudlich equations are the most extensively applied to correlate liquid-phase adsorption data. [2,87],... 

The Langmuir isotherm equation for the correlation of the liquid-phase adsorption equilibrium of a single component, can, in principle, as was previously stated, be extended to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [2,87] ... 

In the case of a single-component system, the adsorption isotherm gives the concentration in the stationary phase C (in moles per liter of bead or grams per liter of bead) versus the mobile phase concentration C when equilibrium is reached (in the same units as for C), at a given temperature. 

Equation (2-46) is only applicable for binary systems (analyte—single component mobile phase). Similar expression could be derived if we assume that the adsorption of the analyte does not disturb the equilibrium of the binary eluent system. 

In our previous works [1-3], we reported experimental and theoretical equilibrium isotherms for adsorption of L-glutamic acid in the single component system on polyaminated highly porous chitosan (hereafter called PEl-CH), weakly basic ion exchanger, and crosslinked chitosan fiber. We found that the adsorption of L-glutamic acid, which is a kind of acidic amino acid, was controlled by the acid/base neutralization reaction between neutral L-glutamic acid (zwitterion, A and those adsorbents. 

The equilibrium parameters used in this study have been taken from independent single-component experiments using volumetric method at several temperatures. Adsorption isotherms on each adsorbent are shown in Figures 2 and 3. 

Figure 1 shows experimental and predicted TPA results for single component on LOC 1. Hydrocarbon used was 224 trimethylpentane and toluene. Fluid velocity (7.57E-2 m/s) and concentration of supplied O2 concentration (0.18 kPa) for each hy ocarbon were same. In the result of adsorption equilibrium, the amount of toluene adsorbed seemed to be higher than 224 trimethylpentane. As can be expected, toluene was emitted more lately. However, Toluene was converted more rapidly than toluene over 380 K. 

Having obtained the adsorption equilibrium and mass transfer parameters of single component systems (Tables 1 to 2), we are ready to examine the predictability of the model in simulating the sorption kinetics of multicomponent systems on Norit activated carbon. 

In contrast to the well-developed thermodynamic methods for determining gas/ liquid equilibriums the theoretical determination of adsorption isotherms is not yet feasible. Only approaches to determining multi-component isotherms from experimentally determined single-component isotherms are known. Such approaches are explained in more detail in Section 2.5.2.3. Careful experimental determination of the adsorption isotherm is therefore absolutely necessary. The different approaches for isotherm determination are discussed in Chapter 6.5.7. 

Equilibrium stage model Adsorption chromatography for products with low molecular weights Accuracy only for single components or small differences in Ni for all components... 

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