Adsorption kinetics second order

This rate-limiting step is third order in the forward direction (i.e., adsorption) and second order in the reverse direction (i.e., desorption). Since two active sites are required for dual-site adsorption, one predicts that the kinetic model is proportional to the square of the vacant-site fraction. Substitution for a from (14-144) leads to... 

RCCM showed considerable adsorption properties for citric acid [54]. Static adsorption experiments were carried out to study the adsorption kinetics and thermodynamics of citric acid on RCCM. The results indicated that the adsorption of RCCM on citric acid followed the Langmuir isotherm. The adsorption followed second-order kinetic equation. The adsorption rates of citric acid on RCCM were controlled by the intraparticle diffusion. 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

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). 

Second-order enzymatic reactions require two adsorption events at the same site. For the reaction A + B — P, there may be a compulsory order of adsorption (e.g., first A, then B) or the two reactants may adsorb in a random order. Different assumptions lead to slightly different kinetic expressions, but a general form with theoretical underpinnings is... 

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... 

The results of a similar experiment with adsorbed hydrogen is shown in Fig. 2.3b. Only one desorption peak was observed in the temperature range studied [50], The desorption peak temperature lies at 420 K for the experiment with 0.8 L and is shifted to lower temperatures as the H2 concentration increases indicating second order desorption kinetics. Surface states with desorption temperatures at 165 K, 220 K, 280 K and 350 K were reported for the adsorption of H2 and D2 at 120 K [51]. Thermal desorption experiments after H2 adsorption at 350 K show only one desorption state at ca. 450 K [52],... 

Loukidou et al. (2005) fitted the data for the equilibrium sorption of Cd from aqueous solutions by Aeromonas caviae to the Langmuir and Freundlich isotherms. They also conducted, a detailed analysis of sorption rates to validate several kinetic models. A suitable kinetic equation was derived, assuming that biosorption is chemically controlled. The so-called pseudo second-order rate expression could satisfactorily describe the experimental data. The adsorption data of Zn on soil bacterium Pseudomonas putida were fit with the van Bemmelen-Freundlich model (Toner et al. 2005). 

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]). 

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... 

Adsorption kinetic and adsorption isotherm of pesticide metobromuron at the high area ACC were investigated in relation to water treatment. The ACC used in this study seems to be quite effective in adsorption of metobromnron from aqueous solutions. Adsorption of that pesticide was found to follow second-order kinetic model and the adsorption isotherm is well represented by Frenndlich model. 

The decomposition behavior of formic acid on the close-packed Ru(lOTO) surface parallels the reaction on nickel, except that the autocatalytic process was not observed (lOJ). Water was desorbed at 183 K by apparent second-order kinetics following adsorption of HCOOH at 100 K. Subsequent desorption of Hj, COj, and CO suggested the formation of the surface anhydride. The rate constant for decomposition was 2.6 x 10 sec exp —26.9 kcal/mol// r. ... 

The second-order reaction with adsorption of the ligand (2.210) signifies the most complex cathodic stripping mechanism, which combines the voltammetric features of the reactions (2.205) and (2.208) [137]. For the electrochemically reversible case, the effect of the ligand concentration and its adsorption strength is identical as for reaction (2.205) and (2.208), respectively. A representative theoretical voltammo-gram of a quasireversible electrode reaction is shown in Fig. 2.86d. The dimensionless response is controlled by the electrode kinetic parameter m, the adsorption... 

Based on these rate laws, various equations have been developed to describe kinetics of soil chemical processes. As a function of the adsorbent and adsorbate properties, the equations describe mainly first-order, second-order, or zero-order reactions. For example. Sparks and Jardine (1984) studied the kinetics of potassium adsorption on kaolinite, montmorillonite (a smectite mineral), and vermiculite (Fig. 5.3), finding that a single-order reaction describes the data for kaolinite and smectite, while two first-order reactions describe adsorption on vermiculite. 

The solution of the simplest kinetic model for nonlinear chromatography the Thomas model [9] can be calculated analytically. The Thomas model entirely ignores the axial dispersion, i.e., 0 =0 in the mass balance equation (Equation 10.8). For the finite rate of adsorption/desorption, the following second-order Langmuir kinetics is assumed... 

The conclusion drawn from Worked Problem 6.14 is that changing the type of termination step from gas to surface alters the kinetics. This is because the order with respect to the radical differs between the second order recombination of the gas phase termination and surface termination where diffusion to the surface or adsorption on the surface is rate determining and first order. If, however, the rate-determining step in surface termination were bimolecular recombination on the surface, the order would not change between gas and surface termination. This is because both recombinations would now have the same order, i.e. 2 4[R ]2 and 2 7[R ]2, with the total rate of termination if both contributed being 2(k + 7)[R ]2. 

Blanding (10) first proposed the second order cracking kinetics for FCC. Krambeck (11) theoretically demonstrated that conversion in systems with a large number of parallel reactions can be approximated by simple second order kinetics. More recently, Ho and Aris (12) have developed a further mathematical treatment of this concept. An inhibition term was incorporated into the second order cracking kinetics for gas oil conversion to account for competitive adsorption. The initial cracking rate is then given by ... 

A reaction sequence analogous to that in Eq. 4.40 can also be developed for the specific adsorption of bivalent metal cations (e.g., Cu2+, Mn2 or Pb2+) by metal oxyhydroxides.21 In this application the abstract scenario in the first row of Table 4.3 is realized with A = =Al-OH, B = M2+, C = =Al-OH - - M2+, D = = Al-OM+, and E = H where M is the metal complexed by an OH group on the surface of an aluminum oxyhydroxide. Analysis of pressure-pulse relaxation kinetics data leads to a calculation of the second-order rate coefficient kf, under the assumption that the first step in the sequence in Eq. 4.40 is rate determining. Like k(l, the rate coefficient for the dissolution of a metal-containing solid (Section 3.1 cf. Fig. 3.4), measured values of k, correlate positively in a log log plot with kw,. , the rate coefficient for water exchange on the metal... 

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