Surface reactions rate laws

By combining surface-reaction rate laws with the Langmuir expressions for surface coverages, we can obtain Langmuir-Hinshelwood (LH) rate laws for surface-catalyzed reactions. Although we focus on the intrinsic kinetics of the surface-catalyzed reaction, the LH model should be set in the context of a broader kinetics scheme to appreciate the significance of this. 

Blum, A. E., and A. C. Lasaga (1987), "Monte Carlo Simulations of Surface Reaction Rate Laws", in W. Stumm, Ed., Aquatic Surface Chemistry, pp. 255-292. 

Surface reaction rate laws for dislocation-free surfaces. No surface diffusion allowed. Crystal growth for InS > 0, dissolution for InS < 0. Solid line, /kT = 3.5 dashed line, d>/kT = 3.0. 

Combining the equations for CA S, CB S, and Cv with the surface reaction rate law, we obtain... 

Blum A. E. and Lasaga A. C. (1987) Monte Carlo simulations of surface reaction rate laws. In Aquatic Surface Chemistry Chemical Processes at the Particle-water Interface (ed. W. Stumm). Wiley, New York, pp. 255-291. 

Blum, A.E., and A.C lisaga. 11 1988. Monte Carlo simulations of surface reaction rate laws, p. 255-292. In W.E.Sumn Cntn (ed.) Aquatic surface chemistry. John Wiley Sons, New York. 

Because in each step the reaction mechanism is elementary, the surface reaction rate law is... 

If the PBR is less than unity, the oxide will be non-protective and oxidation will follow a linear rate law, governed by surface reaction kinetics. However, if the PBR is greater than unity, then a protective oxide scale may form and oxidation will follow a reaction rate law governed by the speed of transport of metal or environmental species through the scale. Then the degree of conversion of metal to oxide will be dependent upon the time for which the reaction is allowed to proceed. For a diffusion-controlled process, integration of Pick s First Law of Diffusion with respect to time yields the classic Tammann relationship commonly referred to as the Parabolic Rate Law ... 

A rate law that shows some of the peculiarities of reactions in solids arises in the following way. A solid particle having a spherical shape is assumed to react only on the surface. This rate law has been found to model the shrinking of solid particles in aerosols as well as other reactions that take place on the surface of solid particles. 

The active sites from which a reaction in a solid spreads are known as nuclei. It is known that nuclei may grow in one, two, or three dimensions, and each case leads to a different form of the rate law. If the nuclei form in random sites in the solid (or perhaps on the surface), the rate laws are known random nudeation rate laws that have the form... 

We have thus far written unimolecular surface reaction rates as r" = kCAs assuming that rates are simply first order in the reactant concentration. This is the simplest form, and we used it to introduce the complexities of external mass transfer and pore diffusion on surface reactions. In fact there are many situations where surface reactions do not obey simple rate expressions, and they frequently give rate expressions that do not obey simple power-law dependences on concentrations or simple Arrhenius temperatures dependences. 

The particular form for the reaction rate law invoked above has been justified in a number of ways. One interpretation is that a second adsorbed reactant may also be involved in the final step, but that the adsorption and desorption of this species occurs on a much faster timescale than that of P or of the reaction step. Thus, if this second reactant is denoted R, which may be polyatomic and adsorb onto n surface sites, the kinetics become... 

Let us write reaction rates for mechanism (1) in accordance with the law of mass action (for surface reactions this law is known as "the law of surface action )... 

Some prefer to write the surface reaction rate in terms cf the fraction of the surface of sites covered (i.e.,/ ) rather than the number of sites C. s covered, the difference being the multiplication factor of the total site concentration, C, In any event, the final form of the rate law is the same because C, k, and so on, are all lumped... 

Both B and C are adsorbed on the surface. The rate law for a gas-oil cracking reaction on fresh catalyst can be approximated by... 

Reaction Number Dissolution Reactant Surface Complex Rate Law... 

If surface reaction is assumed to be rate limiting and irreversible (and no adsorbed inerts are involved), the overall rate expression for consumption of A becomes -rA = A aCa/(1 + KaCa + KbCb), where k is the surface reaction rate constant and Ka and A b are adsorption equilibrium constants. If the surface is only sparsely covered, i.e., KaCa + KbCb 1, this can be approximated as simply va kKACA = k CA-This illustrates how a simple power law rate expression can apply, under some circumstances, for what is actually a relatively complex mechanism. 

The empirical rate law in Eq. 23 holds only for the initial rates. Tamura et al. (1976) observed an autocatalytic effect of the ferric precipitates produced in the reaction. Sung and Morgan (1980) identified y-FeOOH as the primary oxidation product at neutral pH and confirmed its autocatalytic effect. Adsorbed Fe(II) seems to compete in an additional parallel reaction with the dissolved ferrous species. Fast surface reaction rates resulted from a fit of the kinetic data. Examples of these constants are included in Fig. la for comparison. They represent only estimates of an order of magnitude because Tamura et al. (1976) did not determine the surface concentration of Fe(II). However, Figure 2 shows qualitatively that the ferrous ion is adsorbed specifically to mineral surfaces. 

The surface concentration can be calculated by the formulae s = C (1 -j/joo)-The results of numerical solution of appropriate integral equations for the surface concentration (derived in the diffusion boundary layer approximation) in the case of power-law surface reaction for n = 1 /2 and n = 2 was indicated in [133]. The maximum inaccuracy of formula (5.1.7) in these cases is about 10% for any value of the surface reaction rate constant. 

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