Langmuir kinetics, modified

Figure 13.6 Step feed and shut-off of 700 ppm NH3 in He -I- 700 ppm NO -I- l%v/v Oj over VjO., WO,/liO, model catalyst at 220 C. Dashed lines, inlet NH, concentration solid lines, model fit with Temkin-type coverage dependence and modified Langmuir kinetics, Equation (13.10). (Adapted from ref. [52]).

The qualitative features pertinent to the present topic can even satisfactorily be modeled by an ansatz based on modified Langmuir kinetics for the above reaction scheme ... 

The rate of physical adsorption may be determined by the gas kinetic surface collision frequency as modified by the variation of sticking probability with surface coverage—as in the kinetic derivation of the Langmuir equation (Section XVII-3A)—and should then be very large unless the gas pressure is small. Alternatively, the rate may be governed by boundary layer diffusion, a slower process in general. Such aspects are mentioned in Ref. 146. 

Such a model should be as simple as possible, without however missing any of the underlying thermodynamic and physicochemical factors which cause electrochemical promotion. In particular it will be shown that even the use of Langmuir-type adsorption isotherms, appropriately modified due to the application of potential (or equivalently by the presense of promoters) suffice to describe all the experimentally observed rules G1 to G7 as well as practically all other observations regarding electrochemical promotion including the effect of potential on heats of adsorption as well as on kinetics and reaction orders. 

When one examines the rate of an electrochemical reaction and how it varies with overpotential, it is often found that equations such as (7.150) and (7.150a) (which depend on a Langmuir assumption as to the implied isotherm) are obeyed, and there is no need to modify the kinetic equations to allow for a special isotherm. 

Figure 6.18 Transient absorption spectra, uncorrected for luminescence, observed after 532 nm excitation of a [Ru(deebpy)(bpy)2]2+-modified Ti02 film in neat CH3CN under argon. The apparent negative absorption change observed beyond 570 nm is due to emission. This part of the spectrum is included to illustrate the correspondence between absorption and luminescence kinetics. Reprinted with permission from C. A. Kelly, F. Farzad, D. W. Thompson and G. J. Meyer, Langmuir, 15, 731 (1999). Copyright (1999) American Chemical Society...

Next, the drop in catalytic activity was determined as a function of temperature. The catalyst studied is an improved version of a commercial catalyst on which detailed kinetic experiments were carried out [13 The process occurring over the catalyst is described by a system of the oxidation reactions for o-xylene together with the Langmuir - Hinshelwood equation given by Skrzypek etal[ 3 Their equations (9) - (14) were, however, slightly modified by substituting the product of the activity s and the reaction rate rh R,-s rs> for the reaction rate rt. 

Figure 20. Effectiveness factor rj for a bimolecular irreversible reaction with Langmuir Hinshelwood-type kinetics versus the Weisz modulus ip. Influence of intraparticle diffusion on the effective reaction rate (isothermal reaction in a flat plate, modified stoichiometric excess E — 10, Kp it as a parameter, adapted from Satterfield [91]).

Rajadhyaksha and Vaduseva [9] introduced modified Thiele moduli for a sphere for nth-order kinetics, and for Langmuir-Hinshelwood kinetics assuming the rate equation... 

Other attempts have been made to arrive at modified Thiele moduli for different forms of reaction kinetics. For example, Valdman and Hughes [11] have proposed a simple approximate expression for calculating the effectiveness factor for Langmuir-Hin-shelwood kinetics of the type... 

Figure 6.7 Ratio of the modified Thiele moduli of Equation 6.35 over Equation 6.36 versus KCAj for Langmuir-Hinshelwood kinetics.

Figure 2,5 (a) An Arrhenius plot of log k versus I/TXK) for the dissolution rates of various silicate rocks and minerals. The data points and curves for rhyolite, basalt glass, and diabase are from Apps (1983), as is the curve labeled silicates, which Apps computed from the results of Wood and Walther (1983). Curves for the S1O2 polymorphs are based on Rimstidt and Barnes (1980). Modified from Langmuir and Mahoney (1985). Reprinted from the National Well Water Assoc. Used by permission, (b) An Arrhenius plot of log k versus 1 /T(K) for the precipitation of quartz and amorphous silica based on Rimstidt and Barnes (1980). Reprinted from Geochim. Cosmochim. Acta, 44, J.D. Rimstidt and H.L. Barnes, The kinetics of silica water reactions, 1683-99, 1980, with permission from Elsevier Science Ltd, The Boulevard. Langford Lane. Kidlington OXS 1GB, U.K. 

For both the Langmuir and Jovanovic isotherms several exact methods exist for the determination of the energy distribution function adsorption isotherm is precisely known. Rather than trying to modify these exact methods for desorption kinetics, this work will use two approximate methods which give simple analytical expressions for the distribution function in terms of derivatives of the overall isotherm, and which allow a better and more friendly analysis of results. 

The kinetics of photocatalytic degradation of the dye on the surface of the catalyst follows pseudo first-order kinetics. It is rationalized in terms of the Langmuir-Hinshelwood model, which is modified to accommodate reactions occurring at a solid-liquid interface, as shown by Eq. 1 [3] ... 

Acosta, E., Le, M.A., Harwell, J.H. and Sabatini, D.A. (2003) Coalescence and solubilization kinetics in linker-modified microemulsions and related systems. Langmuir, 19, 566-574. 

In the kinetic models discussed so far, the catalyst surface was assumed to be uniform and to have constant activity. In practice, catalysts often show a decline in activity with time, because of poisoning or fouling these changes are discussed later. Catalysts may also change activity because of reactions that alter the chemical composition of the surface. One example of this is the supported silver catalyst used for the partial oxidation of ethylene. Kinetic data suggest that the active catalyst is a partial layer of silver oxide and not metallic silver. But a modified form of the Langmuir-Hinshelwood model can still be used to correlate the data, as shown in the following example. 

When a poison is reversibly adsorbed and Langmuir-Hinshelwood kinetics apply, the rate equation can be modified by adding a term KpPp to the denominator ... 

Formation of such bidentate carbonate structure requires the existence and accessibility of appropriate anion vacancies on the oxide surface. Spectral evidence for unidentate carbonate species disappeared at 300°C, and was followed by complete removal of the bidentate structures at 350°C (Rosynek and Magnuson, 1977b). Similar IR results as those discussed above have been reported by Filippova et al. (1973) for CO2 adsorption on NdiOs and also by Pajares et al. (1976) on SC2O3. Pajares et al. (1978) have described the kinetics of CO2 adsorption on SC2O3 by a modified Langmuir equation, and have emphasized the influence of surface hydroxylation on the kinetics of CO2 adsorption. The influence of surface hydroxyl species on the adsorbed CO2 amount is shown in fig. 17. 

The kinetics of acid hydrolysis of the p-methoxybenzaldehyde-O-acyloximes (7) in SDS micelles modified by BuOH has also been fitted to the PIE model [86]. The substrates differ only in their hydrophobicities, and while the acetyl derivative partitions between water and micelles, the octanoyl derivative is wholly micelle-bound. The simple PIE model fits rate data in dilute HCl [Eq. (6)], but it underpredicts observed rate constants in more concentrated acid. This increased rate was analyzed in terms of a model that does not involve a constant value of a but allows concentrations of reactive and inert ions, and Na" ", in the micellar pseudophase to increase, following Langmuir isotherms [106]. This model was reasonably satisfactory except at high 1-butanol concentration. Alternatively, the rate data in more concentrated acid can be fitted in terms of Eq. (12). 

ABSTRACT Ephedra waste was modified by epichlorohydrin and diethylenetriamine to obtain aminated ephedra waste biosorbent. The factors affecting the adsorption efficiency, such as pH and contact time were investigated. The results showed that the optimum absorption conditions of aminated ephedra waste pH was 4.7 contact time was 3 h equilibrium was well described by Langmuir isotherms and kinetics was found to fit pseudo-second order type. According to the Langmuir equation, the maximum adsorption capacities of modified adsorbent for Cu + are 93.11 mg/g, which are higher than untreated adsorbent (17.61 mg/g). The aminated ephedra waste biosorbent had excellent absorbability toward heavy metal ions Cu f... 

In this study, ephedra waste was modified by epichlorohydrin and diethylenetriamine to obtain aminated ephedra waste biosorbent and absorbed for Cu +. By dint of static absorption test, the effects of pH and contact time on absorption were investigated. Biosorbent characterization was determined with FTIR analysis. Langmuir adsorption isotherm was applied to the experimental data. The pseudo second-order model was used for determining of the adsorption kinetics. 

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