Surface reaction first-order

If the reaction of A at the surface obeys first-order kinetics, then... 

The decomposition of titanium hydride in vacuum between 523 and 773 K was slower than the rate predicted by diffusion calculations and the controlling step was identified [12] as the surface combination of hydrogen atoms. The rate of reaction was sensitive to traces of gaseous Hj, but not to Oj. The inhibiting effect exerted by the presence of helium was ascribed to opposition to the diffusive dispersal of product from the vicinity of the desorption interface. The rates of decomposition of the hydrides of four related metals [13] (TiHj, ZrHj, NbH and TaH) studied between 343 and 973 K pass through a temperature maximum. This was explained by the occurence of two consecutive reactions first-order decomposition of the hydride, followed by second-order combination of the hydrogen atoms before desorption. 

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). 

In this case the catalyst has caused a radical reduction in overall activation energy, presumably by replacing a difficult homogeneous step by a more easily executed surface reaction involving adsorbed ethylene. The results lead to the kinetics observed by Wynkoop and Wilhelm," a reaction first order in H2 and zero order in strongly adsorbed ethylene. 

In this equation we suppose that the rate of the forward reaction is first order in A on the solid surface and first order in B in the gas phase. Similarly, the rate of the reverse process is first order in C on the surface. 

FIGURE 12.6 Schematic of how lateral intermolecular energy transfer across the semiconductor surface can lead to a second-order excited-state annihilation reaction. First-order excited-state relaxation was observed for sensitizers with short excited-state lifetimes, t < 50 ns, and was predominant at low irradiances and surface coverages for all sensitizers. 

Intrinsic rate constant per unit (internal) surface area of catalyst, k is defined as the number of molecules (or moles) reacted/second/cm. area when there is unit concentration of reactant adjacent to the surface. For first order reaction the units of k are cm./sec. 

A graphical representation of these equations is given in Fig. 6.4-14. van Kievelen and Hoftijzer originally developed their correlation only for irreversible second-order reactions (first-order in each reactant) and for equal difiusivities of the two reactants. Danckwetts pointed out that the results also are applicable to the case where is not equal to Dg. Decoursey developed an approximate solution for absorption with irreversible second-order reaction based on the Danckwerts surface-renewal model. The resulting expression, which is somewhat easier to use than the van Krevelen-HofUJzer approach, is... 

HyperChem can calculate transition structures with either semi-empirical quantum mechanics methods or the ab initio quantum mechanics method. A transition state search finds the maximum energy along a reaction coordinate on a potential energy surface. It locates the first-order saddle point that is, the structure with only one imaginary frequency, having one negative eigenvalue. 

This difference is a measure of the free-energy driving force for the development reaction. If the development mechanism is treated as an electrode reaction such that the developing silver center functions as an electrode, then the electron-transfer step is first order in the concentration of D and first order in the surface area of the developing silver center (280) (Fig. 13). Phenomenologically, the rate of formation of metallic silver is given in equation 17,... 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Reactants must diffuse through the network of pores of a catalyst particle to reach the internal area, and the products must diffuse back. The optimum porosity of a catalyst particle is deterrnined by tradeoffs making the pores smaller increases the surface area and thereby increases the activity of the catalyst, but this gain is offset by the increased resistance to transport in the smaller pores increasing the pore volume to create larger pores for faster transport is compensated by a loss of physical strength. A simple quantitative development (46—48) follows for a first-order, isothermal, irreversible catalytic reaction in a spherical, porous catalyst particle. 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

Decompositions may be exothermic or endothermic. Solids that decompose without melting upon heating are mostly such that can give rise to gaseous products. When a gas is made, the rate can be affected by the diffusional resistance of the product zone. Particle size is a factor. Aging of a solid can result in crystallization of the surface that has been found to affect the rate of reaction. Annealing reduces strains and slows any decomposition rates. The decompositions of some fine powders follow a first-order law. In other cases, the decomposed fraction x is in accordance with the Avrami-Erofeyev equation (cited by Galwey, Chemistry of Solids, Chapman Hall, 1967)... 

The surface reaction is reversible and is first order in the surface concentrations of A and ofB ... 

The NO reduction over Cu-Ni-Fe alloys has been studied recently by Lamb and Tollefson. They tested copper wires, stainless steel turnings, and metal alloys from 378 to 500°C, at space velocities of 42,000-54,000 hr-1. The kinetics is found to be first order with respect to hydrogen between 400 and 55,000 ppm, and zero order with respect to NO between 600 and 6800 ppm 104). The activation energies of these reactions are found to be 12.0-18.2 kcal/mole. Hydrogen will reduce both oxygen and NO when they are simultaneously present. CO reduction kinetics were also studied over monel metals by Lunt et al. 43) and by Fedor et al. 105). Lunt speculated that the mechanism begins by oxidant attack on the metal surface... 

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

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