Chemical Reaction Rate Surface Kinetics

Both the mass transfer kinetic parameters (diffusion in the phases, D, D j, surface renewal frequency, s) and chemical reaction rate constants (kg, kj) strongly influence enhancement of the absorption rate. The particle size, dp, the dispersed liquid holdup, e and the partition coefficient, H can also strongly alter the absorption rate [42-44,46,48]. Similarly, the distance of the first particle from the gas-liquid interface, 6q is an essential factor. Because the diffusion conditions are much better in the dispersed phase (larger solubility and, in most cases, larger diffusivity, as well) the absorption rate should increase with the decrease of the (5g value. 

The kinetics of chemical reactions on surfaces is described using a microscopic approach based on a master equation. This approach is essential to correctly include the effects of surface reconstruction and island formation on the overall rate of surface reactions. The solution of the master equation using Monte Carlo methods is discussed. The methods are applied to the oxidation of CO on a platinum single crystal surface. This system shows oscillatory behavior and spatio-temporal pattern formation in various forms. 

The kinetics of chemical reactions on surfaces is normally described using macroscopic rate equations. The master equation can be used to derive such macroscopic rate equations. Sometimes this derivation is exact, but we often will have to make approximations, which may or may not be appropriate. This will depend on the system. If the approximation to derive the macroscopic rate equations are too crude, the master equation shows, however, how to add corrections to rate equations. It is in general necessary to make approximations even with these corrections, but one has the choice what approximations to make. Of course, in practice one may... 

Most important, heterogeneous surface-catalyzed chemical reaction rates are written in pseudo-homogeneous (i.e., volumetric) form and they are included in the mass transfer equation instead of the boundary conditions. Details of the porosity and tortuosity of a catalytic pellet are included in the effective diffusion coefficient used to calculate the intrapellet Damkohler number. The parameters (i.e., internal surface area per unit mass of catalyst) and Papp (i.e., apparent pellet density, which includes the internal void volume), whose product has units of inverse length, allow one to express the kinetic rate laws in pseudo-volumetric form, as required by the mass transfer equation. Hence, the mass balance for homogeneous diffusion and multiple pseudo-volumetric chemical reactions in one catalytic pellet is... 

Minerals with Kinetic Dissolution Condition Minerals of this group are considered in everyday life insoluble. Ihey include mostly metal oxides, hydroxides, sulphides and aluminum sihcates. The mechanism of their dissolution is dominated by hydrolysis whose nature depends on the structure and composition of minerals. Their dissolution under any conditions has kinetic condition, i.e., it is controlled by extremely slow chemical reactions of surface complexation. The rate of their dissolution is noticeably lower than 10 ° mole m s and the solubility does not exceed 10" mole l Besides, both their dissolution rate and solubility depend on pH values. These minerals are most common in the Earth crust and often play a leading role in the formation of imderground water composition. It is convenient to subdivide minerals with kinetic dissolution regime into three groups 1- silica, 2 - oxides, hydroxides and sulphides of metals, 3-aluminum silicates. 

Despite the similar reaction mechanism, a completely different type of behavior was found for the TAME process [71-73]. This is due to the fact that the rate of reaction is one order of magnitude slower for TAME synthesis compared to MTBE synthesis. The behavior of the TAME process is illustrated in Fig. 10.14. In contrast to the MTBE process the TAME column is operated in the kinetic regime of the chemical reaction at a pressure of 2 bar. Under these conditions large parameter ranges with multiple steady states occur. The more detailed analysis by Mohl et al. [73] reveals that steady state multiplicity of the TAME process is caused by self-inhibition of the chemical reaction by the reactant methanol, which is adsorbed preferably on the catalyst surface. Steady state multiplicity is therefore caused by the nonlinear concentration dependence of the chemical reaction rate. Consequently, a similar type of behavior can be observed for an isothermal CSTR. This effect is further in-... 

All these reactions required some heat or temperature on the catalyst surface for the reaction to occur. When the automobile first starts, both the engine and the catalyst are cold. After startup, the heat of combustion is transferred from the engine and the exhaust piping begins to heat up. Finally, a temperature is reached within the catalyst that initiates the catalytic reactions. This light-off temperature and the concurrent reaction rate are kinetically controlled, that is, depends on the chemistry of the catalyst, since the transport reactions are fast. Typically, the CO (and H2) reaction begins first, followed by the HC and NO reaction. Upon further heating, the chemical reaction rates become fast and the overall conversions are controlled by pore diffusion and/or bulk mass transfer. 

The degree of involvement of inner surface is related with the ratio of the diffusion rate of the gas passing through the pore in particles to the reaction rate on the surface of pore. If the diffusion rate is higher than the reaction rate of reductant with the solid oxide, then H2 concentration in pore is the same as that on surface of particles, and the entire inner smface completely participates in the process. This process is called as the kinetically controlled process. When the gas diffusion rate in pore is the opposite proportional with the chemical reaction rates, the amount of reducing agent provided by the diffusion to inner surface is less than that is able to take advantage on the smface of pore, in which case, H2 concentration drops to equilibrium value, and most of surface area is not involved in reduction. Such a system is called as the internal diffusion system. 

TTie best way to measure surface areas is by using rapid chemical reactions with known kinetics, that take place in a very thin zone close to the interface. Since the rate is proportional to the surface area, the latter can be calculated from rate measurements. The relevant principles are presented in section 5,42J. Surface areas can also be calculated from measured values of the bubble holdup and the mean bubble diameter, according to eq. (4.51). From the two empirical relations by Van Dierendonck (1970), eqs. (4.54) and (4.57), a third can be derived, giving the specific interfacial area a for solutions of electrolytes and liquid mixtures ... 

The conversion rate of the solid is determined by the smallest value of Equations (5.18) to (5.16). Figure 5.1 shows that at elevated temperatoes (e.g., >1100 °C for hard coal) chemical reaction rates increase exponentially and pore and bulk surface diffusion occur at a much slower rate, thus becoming the rate-limiting steps. When integrating heterogeneous kinetics into the modeling, it is instructive to incorporate these effects into conversion models. A simple approach for spherical particles has been widely used in hterature [5] It imifies the bulk surface diffusion and chemical reaction control, as given in Equation (5.19). 

The physical chemist is very interested in kinetics—in the mechanisms of chemical reactions, the rates of adsorption, dissolution or evaporation, and generally, in time as a variable. As may be imagined, there is a wide spectrum of rate phenomena and in the sophistication achieved in dealing wifli them. In some cases changes in area or in amounts of phases are involved, as in rates of evaporation, condensation, dissolution, precipitation, flocculation, and adsorption and desorption. In other cases surface composition is changing as with reaction in monolayers. The field of catalysis is focused largely on the study of surface reaction mechanisms. Thus, throughout this book, the kinetic aspects of interfacial phenomena are discussed in concert with the associated thermodynamic properties. 

Intrinsic Kinetics. Chemisorption may be regarded as a chemical reaction between the sorbate and the soHd surface, and, as such, it is an activated process for which the rate constant (/ ) follows the familiar Arrhenius rate law ... 

Model Reactions. Independent measurements of interfacial areas are difficult to obtain in Hquid—gas, Hquid—Hquid, and Hquid—soHd—gas systems. Correlations developed from studies of nonreacting systems maybe satisfactory. Comparisons of reaction rates in reactors of known small interfacial areas, such as falling-film reactors, with the reaction rates in reactors of large but undefined areas can provide an effective measure of such surface areas. Another method is substitution of a model reaction whose kinetics are well estabUshed and where the physical and chemical properties of reactants are similar and limiting mechanisms are comparable. The main advantage of employing a model reaction is the use of easily processed reactants, less severe operating conditions, and simpler equipment. 

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