Chemical reaction sorption rates

Wu and Gschwend (1986) reviewed and evaluated several kinetic models to investigate sorption kinetics of hydrophobic organic substances on sediments and soils. They evaluated a first-order model (one-box) where the reaction is evaluated with one rate coefficient (k) as well as a two-site model (two-box) whereby there are two classes of sorbing sites, two chemical reactions in series, or a sorbent with easily accessible sites and difficultly accessible sites. Unfortunately, the latter model has three independent fitting parameters kx, the exchange rate from the solution to the first (accessible sites) box k2, the exchange rate from the first box to the... 

The overall reaction occurring at an Fe° surface involves a series of steps including (1) mass transport to the reactive site, (2) chemical reaction at the surface (e.g., sorption, electron transfer, etc.), (3) desorption, and (4) mass transport to the bulk solution (recall Fig. 7). Any one of these steps can limit the rate of contaminant removal by Fe°, so the observed... 

Duration of a cycle of HHP operation is defined as time required for reaction hydrogenation/dehydrogenation in pair hydride system. This time determines heat capacity of HHP. Duration of a cycle depends on kinetics of hydrogenation reactions, a heat transfer between the heated up and cooling environment, heat conductivities of hydride beds. Rates of reactions are proportional to a difference of dynamic pressure of hydrogen in sorbers of HHP and to constants of chemical reaction of hydrogenation. The relation of dynamic pressure is adjusted by characteristics of a heat emission in beds of metal hydride particles (the heat emission of a hydride bed depends on its effective specific heat conductivity) and connected to total factor of a heat transfer of system a sorber-heat exchanger. The modified constant of speed, as function of temperature in isobaric process [1], can characterize kinetics of sorption reactions. In HHP it is not sense to use hydrides with a low kinetics of reactions. The basic condition of an acceptability of hydride for HHP is a condition of forward rate of chemical reactions in relation to rate of a heat transmission. 

It is interesting to note that since sorption will be exothermic for most processes, rates of sorption will usually exceetl rates of desorption. This means that product molecules in the homogeneous phase will usually be in equilibrium with the sorbed phase. That is not necessarily true for reactants when sorption, being in many cases a chemical reaction with the surface atoms, may have an activation energy and be quite slow. 

The bulk of evidence which we have discussed so far indicates that the mechanism of catalysis at solid surfaces takes place via the reaction of catalyst atoms (or ions) with the adsorbate to form a monolayer of chemically active intermediates. Since the initial act of chemisorption is a chemical reaction, it is not surprising to find that it may be accompanied by an activation energy of sorption. In general, however, the act of chemisorption is very rapid and occurs at a reasonable proportion of the estimated collisions of the gas molecule with the geometrical surface. Even when we might expect the rates of sorption to decrease as the surface monolayer nears completion, it is often found that the rate is only slightly diminished. This has been interpreted as due to the formation of a loosely held second sorbate layer, fonned on top of the monolayer, which is capable of migrating fairly rapidly to uncovered sorption sites. 

Practically any experimental kinetic curve can be reproduced using a model with a few parallel (competitive) or consecutive surface reactions or a more complicated network of chemical reactions (Fig. 4.70) with properly fitted forward and backward rate constants. For example, Hachiya et al. used a model with two parallel reactions when they were unable to reproduce their experimental curves using a model with one reaction. In view of the discussed above results, such models are likely to represent the actual sorption mechanism on time scale of a fraction of one second (with exception of some adsorbates, e.g, Cr that exchange their ligands very slowly). Nevertheless, models based on kinetic equations of chemical reactions were also used to model slow processes. For example, the kinetic model proposed by Araacher et al. [768] for sorption of multivalent cations and anions by soils involves several types of surface sites, which differ in rate constants of forward and backward reaction. These hypothetical reactions are consecutive or concurrent, some reactions are also irreversible. Model parameters were calculated for two and three... 

Considerable sorption occurs before the first measurement can be made, particularly if batch and flow techniques are employed where the fastest that a measurement can be made is about 15 seconds. For such rapid reactions, chemical relaxation techniques, and preferably real-time molecular-scale techniques, can be used. The latter are discussed later in the chapter. One might ask why it is important to measure such reactions if they are so rapid. Since the reactions are occurring so far from equilibrium, back reactions are insignificant and one can determine chemical reaction rates, devoid of mass transfer processes. Therefore, chemical kinetic measurements are being made, and details about molecular processes and mechanisms can be ascertained. 

Nonequilibrium transport of solutes through porous media occurs when ground-water velocities are sufficiently fast to prevent attainment of chemical and physical equilibrium. Chemical reactions in porous media often require days or weeks to reach equilibrium. For example. Fuller and Davis Q) reported that cadmium sorption by a calcareous sand was characterized by multiple reactions, including a recrystallization reaction that continued for a period of days. Sorption of oxyanions by metal oxyhydroxides often occurs at an initially rapid rate the rate then decreases until steady-state is achieved (2-4). Unless ground-water velocity in such a situation is extremely slow, nonequilibrium transport will occur. 

It seems that the zeolites have been well screened in a qualitative sense, for their catalytic properties. This paper is concerned with the quantitative aspects of catalytic reaction rates in zeolites. The question whether the model of coupled surface adsorption and reaction is still meaningful in the case of zeolite catalysis was already raised by Weisz and Frilette (4) when they wrote In conventional surface catalysis the termination of a three-dimensional solid structure is considered to be the locus of activity. For these zeolites the concept of surface loses its conventional meaning.. . It is the purpose of the present article to examine critically some possibile models representing equilibrium and rate phenomena in gas-zeolite systems, in order to obtain an understanding of the kinetics of chemical reactions in zeolites. Sorption equilibria, on the one hand, and rates of sorption/desorption, exchange, and catalytic reaction on the other hand are closely related and therefore have to be represented in terms of the same model. 

This equation follows from continuity (Eq. 3.3.2) and the Nernst—Planck relation (Eq. 3.4.1). The overbars indicate that the variable has been averaged over the tube cross-section (Eq. 4.6.19), and R and R" are the molar rates of production due to chemical reactions and sorption, respectively. 

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