Desorption rate determining

Physically speaking, this relation expresses the fact that for an overall process involving (as in the HER) an adsorption step and a desorption step, kinetics will not be good if the surface is extensively filled by a strongly adsorbed intermediate (since then discharge on the 1 - 0 fraction of the surface will tend to be slow) or, alternatively, if the surface is relatively empty, since then the desorption rate, determined by 0, will tend to be slow. Optimum conditions obviously arise when 0 1 - 0 0.5. 

It might be thought that since chemisorption equilibrium was discussed in Section XVIII-3 and chemisorption rates in Section XVIII-4B, the matter of desorption rates is determined by the principle of microscopic reversibility (or, detailed balancing) and, indeed, this principle is used (see Ref. 127 for... 

The sequence of events in a surface-catalyzed reaction comprises (1) diffusion of reactants to the surface (usually considered to be fast) (2) adsorption of the reactants on the surface (slow if activated) (3) surface diffusion of reactants to active sites (if the adsorption is mobile) (4) reaction of the adsorbed species (often rate-determining) (5) desorption of the reaction products (often slow) and (6) diffusion of the products away from the surface. Processes 1 and 6 may be rate-determining where one is dealing with a porous catalyst [197]. The situation is illustrated in Fig. XVIII-22 (see also Ref. 198 notice in the figure the variety of processes that may be present). 

Sorbed pesticides are not available for transport, but if water having lower pesticide concentration moves through the soil layer, pesticide is desorbed from the soil surface until a new equiUbrium is reached. Thus, the kinetics of sorption and desorption relative to the water conductivity rates determine the actual rate of pesticide transport. At high rates of water flow, chances are greater that sorption and desorption reactions may not reach equihbrium (64). NonequiUbrium models may describe sorption and desorption better under these circumstances. The prediction of herbicide concentration in the soil solution is further compHcated by hysteresis in the sorption—desorption isotherms. Both sorption and dispersion contribute to the substantial retention of herbicide found behind the initial front in typical breakthrough curves and to the depth distribution of residues. 

With the availabihty of computers, the transfer matrix method [14] emerged as an alternative and powerful technique for the study of cooperative phenomena of adsorbates resulting from interactions [15-17]. Quantities are calculated exactly on a semi-infinite lattice. Coupled with finite-size scaling towards the infinite lattice, the technique has proved popular for the determination of phase diagrams and critical-point properties of adsorbates [18-23] and magnetic spin systems [24—26], and further references therein. Application to other aspects of adsorbates, e.g., the calculation of desorption rates and heats of adsorption, has been more recent [27-30]. Sufficient accuracy can usually be obtained for the latter without scaling and essentially exact results are possible. In the following, we summarize the elementary but important aspects of the method to emphasize the ease of application. Further details can be found in the above references. 

Wetness of a metal surface The lime of wetness of the metal surface is an exceedingly complex, composite variable. It determines the duration of the electrochemical corrosion process. Firstly it involves a consideration of all the means by which an electrolyte solution can form in contact with the metal surface. Secondly, the conditions under which this solution is stable with respect to the ambient atmosphere must be considered, and finally the rate of evaporation of the solution when atmospheric conditions change to make its existence unstable. Attempts have been made to measure directly the time of wetness , but these have tended to use metals forming non-bulky corrosion products (see Section 20.1). The literature is very sparse on the r61e of insoluble corrosion products in extending the time of wetness, but considerable differences in moisture desorption rates are found for rusted steels of slightly differing alloy content, e.g. mild steel and Cor-Ten. 

The ability to use the Tafel slope as a diagnostic criterion can be exemplified by considering a discharge-chemical desorption mechanism for the h.e.r. in which either discharge or chemical desorption may be rate determining. ... 

If chemical desorption is rate determining, the rate will be independent of overpotential since no charge transfer occurs in this step, and... 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

Fig. 4. Dependence of relative concentrationa nj/nt of reaction components A, B, and C on time variable r (arbitrary units) in the case of consecutive (— — ) reactions according to scheme (Ha) or parallel (C ) reactions according to scheme (lib). Ads X, Ads A, Des Y denotes that the rate determining step in the overall transformation is adsorption or desorption of the respective substance Des (B + C) denotes that the overall rate is determined by simultaneous desorption of the substance B and C. Ki/Ki = 0.5 for consecutive, and Ki /Ki — 0.5 for parallel reactions, b nxVn. 0 = 2.5 for consecutive reactions Kt = 0.5, and for parallel reactions Ki/Ki — 0.5. c nxVnA0 = 2.5 fcdesBKi Ky/fcdesoXj Kx = 10 [cf. (53)]. d Ki = 1.75 for consecutive, and Ki/Ki = 1.75 for parallel reactions.

They varied only the values of the adsorption and desorption rate constants of the reaction intermediate B, and by using the simplest Langmuir kinetics, they calculated time-concentration curves of compounds A, B, and C shown in Fig. 5. Also from this example, which does not consider any step as clearly rate determining, it is evident how very different concentration versus time plots can be obtained for the same sequence of surface reactions if adsorption and desorption of the intermediate B proceed by different rates, which are, however, comparable with the rate of surface reactions. In particular, the curves in the first and second columns of Fig. 5 simulate the parallel formation of substances B and C, at least... 

Using similar arguments as with the demethylation of xylenes (p. 31) we can assume from the form of the integral dependences shown in Fig. 7 that here also neither adsorption nor desorption is a rate-determining step. This is, after all, in agreement with the form of the best equations (19a) and (19b) found for the initial reaction rates of single reactions. 

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

The required distribution of initial populations ntu can be obtained in the following manner (32). Let us consider a system with Ed mi = 20 kcal/ mole and Ed max = 45 kcal/mole. Assuming that kd = 1013 sec-1 and x = 1, we can calculate theoretical desorption rates dnai/dt for Ed = 20, 21, 22,..., 45 kcal/mole as a function of nBOi. With increasing temperature, 25 values of dnjdt are measured at temperatures corresponding to Ed of 20, 21, 22,. . ., 45 kcal/mole. Since the total desorption rate at any moment must be equal to the sum of the individual desorption processes, we obtain 25 linear equations. Their solution permits the computation of the initial populations of the surface sites in the energy spectrum considered, i.e. the function n,oi(Edi). From the form of this function, desorption processes can be determined which exhibit a substantial effect on the experimental desorption curve. 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

The partial oxidation of propylene occurs via a similar mechanism, although the surface structure of the bismuth-molybdenum oxide is much more complicated than in Fig. 9.17. As Fig. 9.18 shows, crystallographically different oxygen atoms play different roles. Bridging O atoms between Bi and Mo are believed to be responsible for C-H activation and H abstraction from the methyl group, after which the propylene adsorbs in the form of an allyl group (H2C=CH-CH2). This is most likely the rate-determining step of the mechanism. Terminal O atoms bound to Mo are considered to be those that insert in the hydrocarbon. Sites located on bismuth activate and dissociate the O2 which fills the vacancies left in the coordination of molybdenum after acrolein desorption. 

The evolution of methylchlorosilanes between 450 and 600 K is consistent with the 550 - 600 K typical for the catalytic Rochow Process [3]. It is also reasonably consistent with the evolution of methylchlorosilanes at 500 - 750 K reported by Frank and Falconer for a temperature programmed reaction study of the monolayer remaining on a CuaSi surface after catalytic formation of methylchlorosilanes from CHaCl at higher pressures [5]. Both of these observations suggest that the monolayer formed by methyl and chlorine adsorption on pure CuaSi is similar to that present on active catalysts. For reference, methylchlorosilanes bond quite weakly to tiie surface and desorb at 180 - 220 K. It can thus be concluded that the rate-determining step in the evolution of methylchlorosilanes at 450 - 600 K is a surface reaction rather an product desorption. 

GP 11] ]R 5] The addition of up to 7 vol.-% of water has no detectable impact on the oxygen reaction rate [121]. This is a hint that desorption of water generated is not the rate-determining step (Figure 3.51). 

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