Kinetics 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. 

St-Pierre (2009) developed a zero-dimensional model that considers competitive adsorption for a contaminant with O2 or H2 at the cathode or anode side, respectively. This model assumes that contaminant transport through the gas flow channels, GDLs and ionomer in the catalyst layers is much faster compared to surface kinetics. The rate determining step is considered to be due to contaminant reaction or desorption of reaction product from the platinum surface. Other model assumptions include the absence of lateral interaction between adsorbates, first-order reaction kinetics, constant pressure, and constant temperature at the cathode/anode sides. Using a set of parameters, St-Pierre (2009) successfully used his model in order to describe experimental transient data obtained in the presence of SOj, NOj, and HjS in the cathode airstreams. 

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. 

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. 

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... 

Applying the concept of the rate-determining step (see Section 5.4.2) one can derive the following kinetic equations for adsorption of A, surface reaction, and desorption of R or S, respectively, as rate-limiting processes ... 

To interpret the kinetics experimental data of an organic pollutant(s) or leachate from complex organic mixtures, it is necessary to determine the adsorption/ desorption process steps in a given experimental system which govern the overall adsorption/desorption rate. For instance, the adsorption process of an organic compound by a porous adsorbent can be categorized as three consecutive steps ... 

Thus, there are two kinetic paths for the hydrogen evolution. The first path consists of charge transfer (CT) followed by chemical desorption (CD) path CT-CD. The second path consists of charge transfer (CT) followed by electrochemical desorption (ED) path CT-ED. Within each path, either of the consecutive steps can be slow and thus can be the rate-determining step (RDS). Each of these paths has two pKJSsible mechanisms. 

Several authors have proposed that CH4 combustion over PdO occurs via a redox mechanism [82-85]. Methane activation through assisted hydrogen extraction is generally regarded as the rate-determining step, although there is not a general consensus on the nature of the adsorption sites. Further, desorption of H2O by decomposition of surface hydroxyls has been reported to play a key role in reaction kinetics at temperatures below 450 °C [67, 86]. 

In voltammetric experiments, electroactive species in solution are transported to the surface of the electrodes where they undergo charge transfer processes. In the most simple of cases, electron-transfer processes behave reversibly, and diffusion in solution acts as a rate-determining step. However, in most cases, the voltammetric pattern becomes more complicated. The main reasons for causing deviations from reversible behavior include (i) a slow kinetics of interfacial electron transfer, (ii) the presence of parallel chemical reactions in the solution phase, (iii) and the occurrence of surface effects such as gas evolution and/or adsorption/desorption and/or formation/dissolution of solid deposits. Further, voltammetric curves can be distorted by uncompensated ohmic drops and capacitive effects in the cell [81-83]. 

Figure 4.39. Sabatier desorption-limitation of the dissociation rate-determined kinetics.

The difficulty of dealing with a quantitative theory that involves peaks due to the adsorption or desorption of materials (i.e., 0 > 0) is that one has to know the kinetic rate constants for the surface reactions that are often part of an overall sequence. Equilibrium equations involving the adsorption energies of the intermediates (Gosser 1993) are not enough, i.e., the intermediate may be part of a rate-determining reaction and not at equilibrium. 

The obtainable current is limited by the maximum gas pressure that can be maintained without resulting in a discharge. Thus the rate-determining step is not the desorption of ions under the influence of the high field, but the diffusion of gas to the tip. The latter is an order of magnitude greater than would be expected from kinetic theory because gas near the tip is polarized and thus attracted. 

Kinetic investigations have appeared in the literature since 1965. A redox mechanism is generally accepted [254], and has been confirmed by pulse experiments which demonstrated the equal activity of the catalyst in the presence and absence of oxygen. The results of Pernicone [254] and Liberti et al. [187] seem to indicate that the rate-determining step is either hydrogen abstraction from methanol or desorption of formaldehyde. 

Adsorption of FeCp-PrOH on the droplet/water interface influences the MT processes. If the MT rate of FeCp-PrOH is determined by the saturated amount of the adsorbed molecules on the interface and successive desorption to the droplet interior, the rate is given by a sum of two exponentials with the fast and slow components corresponding to the adsorption and desorption rates, respectively. Using rcc = 2 x 10 11 mol cm-2, however, the amount of FeCp-PrOH adsorbed on the droplet surface (r = 4.3 /im and C0 = 0.047 M) is calculated to be 4.6 x 10 17 mol, and this corresponds to 4.5 pC as electric charge. The calculated electric charge is 170 times smaller than the observed saturated Q t) value (750 pC), indicating that the consecutive-reaction-type kinetics cannot explain the present results. Therefore, Q(t) should be analyzed on the basis of simultaneous-reaction-type kinetics. 

In the previous sections, the use of surfactants to increase the rate of desorption of hydrophobic organic contaminants was discussed. For the current study, several different surfactants were tested to determine whether the rate of TCE desorption from a peat soil could be increased. The effects of the surfactants on the rate of TCE desorption was tested using a continuous-flow stirred-tank reactor (CFSTR) methodology. The observed data were simulated using a distributed-rate kinetic desorption model. The parameters determined from the model simulation were then use to discern the effects of the surfactants on the rate of TCE desorption from the peat soil. The experimental methodology and the modeling procedure are now described in detail. 

It has to be clear that, once diluted and injected (or administered in ocular and other routes), the emulsion stability and fate are determined by three measurable parameters. The first is the partition coefficient of each emulsion component (including added drugs and agents) between the emulsion assembly and the medium. To some extent this partition coefficient is related to oil-water and/or octanol-water partition coefficients. For example, it was well demonstrated that per component of which logP is lower than 8, the stability upon intravenous (IV) injection is questionable [42,138], The other two parameters are kQff, a kinetic parameter which describes the desorption rate of an emulsion component from the assembly, and kc, the rate of clearance of the emulsion from the site of administration. This approach is useful to decide if and what application a drug delivery system will have a chance to perform well [89],... 

Lorenz and Sali610 also propose an alternative kinetic approach to the determination of / this assumes a potential dependence of the adsorption and desorption rates of the pet process of Eq. (1) which is entirely analogous to that of the Butler-Volmer equation ... 

Initial reaction rates obtained with a pure feed in which only reactants are present can be used for the discrimination between rival kinetic models, i.e. to identify whether adsorption, desorption, or surface reactions are the rate-determining steps. When pure A is fed to an integral reactor, for example, initial rates are observed at the inlet, where the product concentration is still zero. Comparing possible rate equations, which are often simpler in case of absence of products, with experimental data obtained at different concentrations of A, helps to reveal the appropriate [33,35]. 

Further research (22-24) has shown that butene oxidation can produce many selective reaction products (furan, acetaldehyde, and methyl vinyl ketone), which are not detected during butane oxidation. It cannot be assumed that the oxidation of butane and of the unsaturated reactants proceed along the same pathway. The kinetics data must be viewed with this point in mind, although butane activation is widely accepted to be the rate-determining step. The intermediates are capable of desorbing from the surface (as observed in the TAP investigations), but they do not, indicating that the further reactions occur more readily than desorption. 

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