Surface reaction rate constant

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... 

In the presence of substances that react with Ag , the 340 nm absorption decays more rapidly and the rate constant of reaction can be calculated from this decay. It was found in this way that free silver atoms are indeed a strongly reducing species. They reduce Fe to Fe and Cu to Cu (note that these reactions would not occur with the silver atoms at the surface of a compact electrode ) organic compounds containing electrophilic groups such as CICH2COOH or CH3NO2 are reduced by Ag via electron transfer... 

Transition State Theory [1,4] is the most frequently used theory to calculate rate constants for reactions in the gas phase. The two most basic assumptions of this theory are the separation of the electronic and nuclear motions (stemming from the Bom-Oppenheimer approximation [5]), and that the reactant internal states are in thermal equilibrium with each other (that is, the reactant molecules are distributed among their states in accordance with the Maxwell-Boltzmann distribution). In addition, the fundamental hypothesis [6] of the Transition State Theory is that the net rate of forward reaction at equilibrium is given by the flux of trajectories across a suitable phase space surface (rather a hypersurface) in the product direction. This surface divides reactants from products and it is called the dividing surface. Wigner [6] showed long time ago that for reactants in thermal equilibrium, the Transition State expression gives the exact... 

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

Alfassi, Z. B S. Padmaja, P. Neta, and R. E. Huie, Rate Constants for Reactions of NO, Radicals with Organic Compounds in Water and Acetonitrile, J. Phys. Chem., 97, 3780-3782 (1993). Allen, H. C., J. M. Laux, R. Vogt, B. J. Finlayson-Pitts, and J. C. Hemminger, Water-Induced Reorganization of Ultrathin Nitrate Films on NaCI—Implications for the Tropospheric Chemistry of Sea Salt Particles, J. Phys. Chem., 100, 6371-6375 (1996). Allen, H. C., D. E. Gragson, and G. L. Richmond, Molecular Structure and Adsorption of Dimethyl Sulfoxide at the Surface of Aqueous Solutions, J. Phys. Chem. B, 103, 660-666 (1999). Anthony, S. E R. T. Tisdale, R. S. Disselkamp, and M. A. Tolbert, FTIR Studies of Low Temperature Sulfuric Acid Aerosols, Geophys. Res. Lett., 22, 1105-1108 (1995). 

It is also clear that during periods of low surface ozone, chlorine atoms are a major reactant for hydrocarbons (e.g., Jobson et al., 1994 Solberg et al., 1996 Ariya et al., 1998). Figure 6.39, for example, shows the measured ratios of isobutane, n-butane, and propane during an ozone depletion event (Jobson et al., 1994). These particular pairs of hydrocarbons were chosen to differentiate chlorine atom chemistry from OH reactions. Thus isobutane and propane have similar rate constants for reaction with Cl but different rate constants for reaction with OH. If chlorine atoms are responsible for the loss of these organics, their ratio should remain relatively constant in the air mass, as indicated by the line marked Cl. Similarly, isobutane and n-butane have similar rate constants for removal by OH but different rate constants for reactions with... 

As pointed out in Section 16.2 (Eq. 16-2), the major source for COj" radicals in advanced oxidation processes, and possibly also in surface water, is reaction of HCO3 and CO3 with hydroxyl radical (HO ). The major sink for COj is regarded to be DOM. The rate constant for reaction of COj" with DOM is in the order of 4x10 L-(mg.oc)-1 s-1 (Larson and Zepp, 1988), which is about 600 times smaller than for the reaction of HO with DOM constituents (see Illustrative Example 16.1). 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

Based on our calculations, performed on literature data, most likely candidates among DOM components for reaction with N02 are the phenolic moieties. However, given the usual DOM loading in surface waters and the expected second-order rate constants for reaction with N02, we have shown that hydrolysis would usually be the most important sink of nitrogen dioxide in aqueous solution [104, 111-113]. 

Here and in what follows the subscripts in and out indicate the Chi molecules localized near the inner and outer surfaces of the vesicle membranes. If no more than one pair of Chl+ and A- particles is generated on the inner surface of each vesicle, the recombination by reaction (7) may be described in terms of first-order kinetics. Having in mind that the number of D, A and Chlout molecules considerably exceeds the number of 3Chl and Chl+ particles, one can treat all the remaining rate constants of reaction sequence (5)-(9) also as pseudo first-order ones. In accord with this reaction scheme, the quantum yield of the transfer of the first electron through the vesicle membrane can be expressed as ... 

Surface water i/2 = 0.62.4-3840 h, based on estimated rate constants for reactions of aromatic amines with OH and R02 radicals in aqueous solutions (Howard et al. 1991). 

Surface water t,/2 = 62.0-3840 h, based on estimated rate constants for reactions of aromatic amines with OH and R02 radicals in aqueous solutions (Giiesten et al. 1981 Mill Mabey 1985 quoted, Howard et al. 1991). Groundwater t1/2 = 1344-8640 h, based on estimated unacclimated aqueous aerobic biodegradation half-life (Howard et al. 1991). 

Surface water photooxidation t/2 = 125 d to 22 yr, based on measured rate constant for reaction with hydroxyl radical in water (Dorfman Adams 1973 Anbar Neta 1967 quoted, Howard et al. 1991) estimated t,/ = 0.3 - 3.0 d in rivers (Zoeteman et al. 1980) ... 

The effectiveness factor is a function of a dimensionless group termed the Thiele modulus, which depends on the diffusivity in the pore, the rate constant for reaction, pore dimension, and external surface concentration Cs-... 

As shown above, the most important radiolytical oxidant in view of interfacial reactions in aqueous systems is H2O2. For this reason, rate constants for reactions between H2O2 and solid surfaces are of crucial importance. The reactivity of H2O2 towards a number of different solid oxide materials has been studied. All these studies were performed using particle suspensions. In Table 1, activation energies for some of these solid materials are presented. 

Here, K2 is the dissociation constant for bicarbonate, Kc is the solubility product constant for calcite, ki is the rate constant for reaction (11), and the subscript (s) refers to concentrations in the surface adsorption layer. Chou et al. (1989) suggested a... 

The D-model was further based on the assumption that all radical intermediates R , R , and S possessed identical reactivities and rates of diffusion First, they would all have the same rate constant for reaction with the solvent (sec ). Second, they would have the same diffusion coefficient D (cm sec" ). Third, they would have the same rate constant (cm mol" for reaction with each other. Finally, they would return to the surface to react in an identical manner and with the same reactivity parameter S (Fig. 8). 

Similarly, rate constants for reaction of photogenerated surface reductants on p-type semiconductors can be measured. 

These studies indicated that the photoproduction rates in solutions of varying composition were approximately proportional to the dissolved organic carbon (DOC) content. Assuming that the lifetime of the solvated electron in air-saturated water is 0.2 ps and that halocarbon concentrations are much lower than that of oxygen (and thus have little effect on the electron lifetime), the photoproduction rate observed in the Greifensee (DOC = 4 mg of C/L) corresponded to estimated near-surface pseudo-first-order photoreduction rate constants of about lOVh for several halocarbons known to be present in natural waters (Table V). These estimates were derived by using previously measured rate constants for reaction of solvated electrons with the halocarbons (48). 

Barrow [772] derived a kinetic model for sorption of ions on soils. This model considers two steps adsorption on heterogeneous surface and diffusive penetration. Eight parameters were used to model sorption kinetics at constant temperature and another parameter (activation energy of diffusion) was necessary to model kinetics at variable T. Normal distribution of initial surface potential was used with its mean value and standard deviation as adjustable parameters. This surface potential was assumed to decrease linearly with the amount adsorbed and amount transferred to the interior (diffusion), and the proportionality factors were two other adjustable parameters. The other model parameters were sorption capacity, binding constant and one rate constant of reaction representing the adsorption, and diffusion coefficient of the adsorbate in tire solid. The results used to test the model cover a broad range of T (3-80°C) and reaction times (1-75 days with uptake steadily increasing). The pH was not recorded or controlled. 

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