Rate of sorption

Influence of electronic impact in the rate of sorption of gases on the getter... 

We may also postulate that the rate of sorption or desorption can be described by a diffusive mechanism. The application of diffusion equations to describe the uptake of a sorbing solute can be... 

Several important assumptions were necessary to achieve the solution given in Equation 38. First, it is assumed that the rate of sorption is much faster than the rate of diffusion. This implies that all solute in the internal pores of the sorbent is at equilibrium with its immediate surroundings. In addition, it is assumed that the sorption sites are homogeneous and that once a compound is sorbed to the solid, it does not migrate along the surface. 

When the rates of sorption or desorption processes are known, environmental fate modeling can provide an educated estimate and prediction on the accessibility and bioavailability of a target pollutant to a specific transport mechanism in the environment. Hence, the present chapter is an attempt to assess fate (i.e., in terms of pollutant mobility using predictive sorption or desorption coefficients) as well as effects (i. e., in terms of bioavailability) of various pollutants and to correlate these observations for development of predictive relationships. 

RATE of SORPTION. The overall rate of benzene sorption for the different extracts varies, depending on the size of the added alkyl group (See Figures 2-5). For the extract and O-methylated extracts, equilibrium sorption was achieved in 30 to 100 hours, depending on the experiment. For the O-... 

Rates of sorption and desorption of phosphate. Eur. J. Soil Sd. 48 101-114 Strens, R.G.S. Wood, B.J. (1979) Diffuse reflectance spectra and optical properties of some iron and titanium oxides and oxyhydr-oxides. Min. Mag. 43 347—354 Stumm, W. Eurrer, G. (1987) The dissolution of oxides and aluminum silicates Examples of surface-coordination-controlled kinetics. 

If, however, the movement from zone to zone is fast enough that equilibrium does not occur, the fraction sorbed from solution can be calculated if the rate of sorption is known (or can be estimated). A parameter, F, is therefore defined... 

In this equation dW/dt is the rate of sorption, k. is the experimental rate constant for sorption, W, is the equilibrium sorption, W is the amount of sorption at time t = t, and h is the experimental rate constant for desorption. Thus, the sorption rate was found to be proportional to the square of the concentration of unoccupied sites, and the desorption rate was proportional to the square of the concentration of occupied sites. These rate equations are not general solutions to Fick s law of diffusion. The experimental rate constants for sorption were found to be non-linearly dependent on methanol pressure and seemed to correlate with the amount of surface sorbed methanol in different ways for coals of various rank. 

Kulai A. Kini It was mentioned that the rate of sorption of methanol is altered by partial acetylation. Have any surface area measurements been done on the coal samples before and after acetylation In absence of these it... 

Theory of Vapor-Particle Partitioning of PAH Compounds in the Atmosphere. Yamasaki et al. (64) treated semivolatile PAHs as inherently vapor-phase materials, existing in the particle phase only because of their tendency to sorb on nonvolatile materials. Under this assumption, the proportion in each phase should vary with the available surface area for sorption and with the ambient temperature. They assumed that sorption followed a Langmuir adsorption isotherm, requiring that there be only a low fractional coverage of the particulate matter with semivolatile material. In this case, competition for sorption sites can be ignored. At equilibrium, the rate of sorption equals the rate of evaporation. They derived this relationship ... 

Figure 5.8 (Bunzl et al., 1976) shows the initial rates of sorption and desorption during the first 10 s of exchange and corresponding half times for Pb2+, Cu2+, Cd2+, Zn2+, and Ca2+ by H-saturated peat using the same concentrations of metal and H30+ added for the experiments shown in Fig. 5.7. The absolute initial rates of sorption decreased in the order Pb > Cu > Cd > Zn > Ca, which is the order observed for the calculated distribution coefficients. This indicates that the higher the selectivity of peat for a given metal ion, the faster the initial rate of sorption. The relative rates of sorption, as shown by half-times (Fig. 5.8), shows that Ca2+ was sorbed the fastest, followed by Zn2+ > Cd2+ > Pb2+ > Cu2+. Thus, even though the absolute rate of Ca2+ adsorption by peat was low, the relative rate was comparatively high, since the total amount of Ca2+ adsorbed was small. The relative rates of desorption, as illustrated by the half-times, show longer times for Pb2+, Cu2+, and Ca2+ but shorter ones for Cd2+ and Zn2+.

Figure 5.8. Initial rates of sorption and subsequent desorption during the first 10 s of exchange on peat and corresponding half-times of lead (Pb2+), copper (Cu2+), cadmium (Cd2+), zinc (Zn2+), and calcium (Ca2+) obtained from similar curves and experimental conditions as given in Fig. 5.7. [From Bunzl et al. (1976), with permission.

The rate of sorption and desorption of pesticides on soils and soil constituents has been investigated by a number of workers (see, e.g., Hance, 1967) and is dependent on the type of sorbent, pesticide, and rate of mixing. For example, sorption seems much slower on humic substances (Khan, 1973). Other factors that may affect the kinetics are swelling of the sorbent and temperature (Hance, 1967). 

Hance (1967) investigated the rate of sorption and desorption of four pesticides (monuron, linuron, atrazine, and chlorpropham) on two soils, a soil organic matter fraction, and bentonite, a 2 1 smectitic clay mineral. An equilibrium in sorption was reached in 24 h for every system except one (Table 6.1). With eight of the 18 systems equilibrium was reached in less than 4 h, and in five cases equilibrium was established in 1 hr. Equilibrium was attained for most of the systems in 4-24 h. Desorption was slower than sorption. In only eight systems was an equilibrium reached in 24 h. Hance... 

Figure 6.2. Rate of sorption of 2,4-D on montmorillonite, kaolinite, and iilite, as shown by the decrease in the concentration of 2,4-D in the bulk solution with time. [From Haque et al. (1968), with permission.]...

The rate of sorption in Eq. (9.24) is proportional to the distance from equilibrium. As noted earlier, in deriving Eq. (9.24), which is based on the generalized equilibrium theory of Fava and Eyring (1956), it is assumed that the reverse reaction and desorption rate are small enough to be neglected. Haque et al. (1968) satisfied this assumption by using large amounts of each of the clays (5-15 g) and low 2,4-D solution concentrations (1.3 mg l-1). 

In order to assess the feasibility of any nuclear waste disposal concept, mathematical models of radionuclide sorption processes are required. In a later section kinetic descriptions of the three common sorption isotherms (3) are compared with experimental data from the mixing-cell tests. For a radionuclide of concentration C in the groundwater and concentration S on the surface of the granite, the net rate of sorption, by a first-order reversible reaction, is given by... 

Effect of Water. Wood is usually treated with ammonia in the presence of some amount of water. The effect of water depends not only on the amount of water but also somewhat on the history of the wood sample and the method of treatment. Thus, when oven-dried veneer strips were treated with cold liquid ammonia-water mixtures at ambient pressure, the flexibility of the treated wood was substantially decreased when the moisture content of the ammonia was much above 10% (26). Other protonic solvents act similarly (26). In apparent contrast, the rate of sorption of ammonia from the gas phase by wood is markedly enhanced by moisture in the wood (19). Bone dry wood absorbs ammonia quite slowly at ambient temperatures but if the wood has ten to twenty percent moisture content, sorption and plasticization occur much more rapidly. Presumably the moisture opens the pore structure of the wood and also dissolves ammonia much more readily than bone-dry wood. On continued treatment, the water is presumably displaced from the wood by the ammonia... 

Predicting fast and slow rates of sorption and desorption in natural solids is a subject of much research and debate. Often times fast sorption and desorption are approximated by assuming equilibrium portioning between the solid and the pore water, and slow sorption and desorption are approximated with a diffusion equation. Such models are often referred to as dual-mode models and several different variants are possible [35-39]. Other times two diffusion equations were used to approximate fast and slow rates of sorption and desorption [31,36]. For example, foraVOCWerth and Reinhard [31] used the pore diffusion model to predict fast desorption, and a separate diffusion equation to fit slow desorption. Fast and slow rates of sorption and desorption have also been modeled using one or more distributions of diffusion rates (i.e., a superposition of solutions from many diffusion equations, each with a different diffusion coefficient) [40-42]. 

Depending on the distribution chosen, as few as three fitting parameters may be required to define a distribution of diffusion rates. In some cases, a single distribution was used to describe both fast and slow rates of sorption and desorption, and in other cases fast and slow mass transfer were captured with separate distributions of diffusion rates. For example, Werth et al. [42] used the pore diffusion model with nonlinear sorption to predict fast desorption, and a gamma distribution of diffusion rate constants to describe slow desorption. 

Sorption of organic contaminants onto aquifer solids is frequently described as a partitioning process, where the hydrophobic organic compound partitions into natural organic material associated with the aquifer solids [8]. Sorption can be characterized as either an equilibrium or rate-limited phenomenon. Equilibrium sorption can be modeled as either a linear or non-linear process. Equilibrium sorption may be assumed when the flow of groundwater and other processes affecting contaminant transport are slow compared to the rate of sorption. In this event the sorption of the contaminant can be considered instantaneous. If we assume equilibrium sorption, the relationship between sorbed and aqueous contaminant concentrations may be described by a sorption isotherm. 

Mandelkern, L., and F. A. Long Rate of sorption of organic vapors by films of cellulose acetate. J. Polymer Sci. 6, 457 (1951). 

The rate of sorption and the absorptive capacity of starch has been analyzed by Sunner et al.396 using the equation... 

It is interesting to note that since sorption will be exothermic for most processes, rates of sorption will usually exceetl rates of desorption. This means that product molecules in the homogeneous phase will usually be in equilibrium with the sorbed phase. That is not necessarily true for reactants when sorption, being in many cases a chemical reaction with the surface atoms, may have an activation energy and be quite slow. 

In the original derivation given by Langmuir, the isotherm was derived by considerations of the rates of sorption and desorption at equilibrium. Since the rate constants do not appear in the final expression, this is not the most economical derivation, involving as it does needless assumptions about rates. 

The bulk of evidence which we have discussed so far indicates that the mechanism of catalysis at solid surfaces takes place via the reaction of catalyst atoms (or ions) with the adsorbate to form a monolayer of chemically active intermediates. Since the initial act of chemisorption is a chemical reaction, it is not surprising to find that it may be accompanied by an activation energy of sorption. In general, however, the act of chemisorption is very rapid and occurs at a reasonable proportion of the estimated collisions of the gas molecule with the geometrical surface. Even when we might expect the rates of sorption to decrease as the surface monolayer nears completion, it is often found that the rate is only slightly diminished. This has been interpreted as due to the formation of a loosely held second sorbate layer, fonned on top of the monolayer, which is capable of migrating fairly rapidly to uncovered sorption sites. 

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