Adsorption kinetics first order

Adsorption of organic phosphorus on soil minerals initially proceeds by a fast reaction that is often considered to reach an equilibrium value. However, a true equilibrium is not found for phosphate ions within a very long period. For example, one study showed that phosphate adsorption on to soils had not reached equilibrium after 1000 days at 25°C (Barrow and Shaw, 1975). The longterm adsorption processes for organic phosphorus compounds on to soils and oxides have not been well studied. Shang et al. (1990) compared the kinetics of adsorption of phosphate and selected organic phosphates on aluminium precipitates. They found that adsorption obeyed first-order... 

In contrast to white oil, light catalytic cycle oil is highly aromatic. These aromatics con ietitively adsorb and inhibit the desulfurization reaction. At high aromatics concentration, the dlbenzothlophene adsorption would be masked by aromatic adsorption. Apparent first order kinetics with respect to dlbenzothlophene would then be observed. 

Even if the peak behavior fits well for a given apparent desorption order, the real kinetic situation may be a different one. As a rate controlling step in a second-order desorption, random recombination of two particles is assumed most frequently. However, should the desorption proceed via a nonrandom recombination of neighboring particle pairs into an ordered structure, the resulting apparent first-order desorption kinetics is claimed to be possible (36). The term pseudo-first-order kinetics is used in this instance. Vice versa, second-order kinetics of desorption can appear for a nondissociative adsorption, if the existence of a dimer complex is necessary before the actual desorption step can take place (99). A possibility of switching between the apparent second-order and first-order kinetics by changing the surface coverage has also been claimed (60, 99, 100). 

The first-order and second-order kinetics of desorption are by far the most common and practically considered cases. Less than first-order desorption kinetics indicates multilayer adsorption or transport limited desorption (101). An actual significance of the third-order kinetics in desorption has been found recently by Goymour and King (102, 103). 

As in a monolayer adsorption process, we consider that the rate of filling of sites by TCP molecules follows first-order kinetics. If No represents the total number of free sites per unit area at time t = 0, and N(t) is the number of sites available at time t, then dN(t)ldt = -kN(t), where k is the rate constant of the adsorption process. Therefore, N(t) decreases as No exp(-kt), and the number of sites occupied by TCP molecules at t becomes [No -N(t)], a quantity that determines directly the parameter (t) in Eq. (25). So Wo(t) can be written as... 

In general, if an adsorbing molecule A occupies a single adsorption site, the adsorption process follows first-order kinetics ... 

While first-order kinetics are observed with most diatomic gases that adsorb in molecular form, dissociative adsorption of gases such as H2 and N2 follows second order kinetics. In the limit of the empty surface the rate of adsorption is... 

Spirodela intermedia, L. minor, and P. stratiotes were able to remove Pb(II), Cd(II), Ni(II), Cu(II), and Zn(II), although the two former ions were removed more efficiently. Data fitted the Langmuir model only for Ni and Cd, but the Freundlich isotherm for all metals tested. The adsorption capacity values (K ) showed that Pb was the metal more efficiently removed from water solution (166.49 and 447.95 mg/g for S. intermedia and L. minor, respectively). The adsorption process for the three species studied followed first-order kinetics. The mechanism involved in biosorption resulted in an ion-exchange process between monovalent metals as counterions present in the macrophytes biomass and heavy metal ions and protons taken up from water.112... 

Adsorption and desorption. The user can choose to handle this using either temperature-corrected first order reaction kinetics, in which case the concentrations are always moving towards equilibrium but never quite reach it, or he can use a Freundlich isotherm, in which instantaneous equilibrium is assumed. With the Freundlich method, he can elect either to use a single-valued isotherm or a non-single-valued one. This was included in the model because there is experimental evidence which suggests that pesticides do not always follow the same curve on desorption as they do on adsorption. 

Adsorption and desorption between the solution phase and sand, silt and clay in suspension and on the bed. First order reaction kinetics are used. 

Once adsorbed, we assume that M is internalised following a first-order kinetic process in each of the sites, with internalisation rate constants k and k2 respectively [9,16-18], For each kind of adsorption site, we have an uptake flux given by ... 

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]). 

For simplicity, up to now, first-order kinetics have been assumed, but obviously other rate laws may apply. Further complications can be generated by the presence of multiple paths for M on a variety of sites exhibiting different kinetics [5,11] or sequential enzymatic processes [100], Some complexes, labelled as lipophilics , have been shown to cross the membrane without the need for specific pre-adsorption sites [5,11,18,19,50] see also Chapters 5, 6 and 10 in this volume. Fortin and Campbell [76] have recently reported the accidental uptake of Ag+ induced by thiosulfate ligand. 

Modelling biouptake requires the judicious consideration and selection of the underlying physical phenomena responsible for the experimental observations. We have seen that three fundamental phenomena may play a key role in biouptake mass transfer, adsorption, and internalisation. The inclusion of additional phenomena or refinements (such as nonexcess ligand complexation, non-first-order kinetics, nonlinear isotherms, etc.) may be essential to describe certain cases, but they have handicaps, such as ... 

Reaction kinetics. The time-development of sorption processes often has been studied in connection with models of adsorption despite the well-known injunction that kinetics data, like thermodynamic data, cannot be used to infer molecular mechanisms (19). Experience with both cationic and anionic adsorptives has shown that sorption reactions typically are rapid initially, operating on time scales of minutes or hours, then diminish in rate gradually, on time scales of days or weeks (16,20-25). This decline in rate usually is not interpreted to be homogeneous The rapid stage of sorption kinetics is described by one rate law (e.g., the Elovich equation), whereas the slow stage is described by another (e.g., an expression of first order in the adsorptive concentration). There is, however, no profound significance to be attached to this observation, since a consensus does not exist as to which rate laws should be used to model either fast or slow sorption processes (16,21,22,24). If a sorption process is initiated from a state of supersaturation with respect to one or more possible solid phases involving an adsorptive, or if the... 

Abstract Removal of catechol and resorcinol from aqueous solutions by adsorption onto high area activated carbon cloth (ACC) was investigated. Kinetics of adsorption was followed by in-situ uv-spectroscopy and the data were treated according to pseudo-first-order, pseudo-second-order and intraparticle drfiusion models. It was fotmd that the adsorption process of these compotmds onto ACC follows pseudo-second-order model. Furthermore, intraparticle drfiusion is efiective in rate of adsorption processes of these compoimds. Adsorption isotherms were derived at 25°C on the basis of batch analysis. Isotherm data were treated according to Langmuir and Freundhch models. The fits of experimental data to these equations were examined. 

Three kinetic models were applied to adsorption kinetic data in order to investigate the behavior of adsorption process of adsorbates catechol and resorcinol onto ACC. These models are the pseudo-first-order, the pseudo-second-order and the intraparticle diffusion models. Linear form of pseudo-first-order model can be formulated as... 

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