Surface Reactions with Rate-Controlling Steps

2 Surface Reactions with Rate-Controlling Steps 

At the beginning of this chapter it was stated that reaction sequences involving surface steps [such as (XXV)], could be visualized as a type of chain reaction. This is indeed so, and we shall have more to say concerning the analysis of surface reactions via the pssh a little later on. However, also associated with the development of the theory of surface reaction kinetics has been the concept of the rate-limiting or rate-controlling step. This presents a rather different view of sequential steps than does pure chain reaction theory, since if a single step controls the rate of reaction then all other steps must be at equilibrium. This is a result that is not a consequence of the general pssh. 

In fact, pursuing the example of (XXV) a bit further in this regard, if the surface reaction is rate-limiting, we can express the net rate of reaction directly in terms of the surface species concentrations, Cp and CbT 

Substitution of equations (3-13) and (3-56) into (3-55) gives the rate of reaction in terms of the partial pressures of the reacting species. 

In fact, the value of may be a somewhat elusive quantity, so that in practice this is often absorbed into the rate constant as, say, k s — 

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Irreversible Unimolecular Reactions. Consider the irreversible catalytic reaction A P of Example 10.1. There are three kinetic steps adsorption of A, the surface reaction, and desorption of P. All three of these steps must occur at exactly the same rate, but the relative magnitudes of the three rate constants, ka, and kd, determine the concentration of surface species. Suppose that ka is much smaller than the other two rate constants. Then the surface sites will be mostly unoccupied so that [S] Sq. Adsorption is the rate-controlling step. As soon as a molecule of A is absorbed it reacts to P, which is then quickly desorbed. If, on the other hand, the reaction step is slow, the entire surface wiU be saturated with A waiting to react, [ASJ Sq, and the surface reaction is rate-controlling. Finally, it may be that k is small. Then the surface will be saturated with P waiting to desorb, [PS] Sq, and desorption is rate-controlling. The corresponding forms for the overall rate are ... 

The various steps in the removal of a gas from air by a porous adsorbent may be confined broadly to the following processes (a) mass transfer or diffusion of the gas to the gross surface (b) diffusion of the gas into or along the surface of the pores of granular adsorbent (c) adsorption on the interior surface of the granules (d) chemical reaction between the adsorbed gas and adsorbent (e) desorption of the product and (/) transfer of the products from the surface to the gas phase. Whether surface reaction or diffusion (mass transfer) to the surface becomes the rate-controlling step will become evident in the analysis of the experimental data with respect to the rate constant. 

In mechanistic studies, this form of equation appears whenever the rate-controlling step of a reaction is viewed to involve the association of reactant with some quantity that is present in limited but fixed amounts for example, the association of reactant with enzyme to form a complex, or the association of gaseous reactant with an active site on the catalyst surface. 

The ammoxidation of isobutene has not received much attention. The only contribution in this field is by Onsan and Trimm [2.44] for a rather unusual catalyst, a mixture of the oxides of Sn, V and P (ratio 1/9/3) supported on silica. At 520 C, a maximum selectivity to methacrylonitrile + methacrolein of 80% was reached with a Sn—V—P oxide catalyst (ratio 1/9/3), an isobutene/ammonia/oxygen ratio of 1/1.2/2.5 and a contact time of 120 g sec l ]. The kinetics are very similar to those for the pro-pene ammoxidation. Again, the data are initially analysed by means of (parallel) power rate equations, for which the parameters were calculated, while a more detailed analysis proves that a Langmuir—Hinshelwood model with surface reaction as the rate-controlling step provides the best fit with regard to the two main products. At 520° C, the equation which applies for the production of methacrolein plus methacrylonitrile is... 

Figure 7.1. Rate-limiting steps in mineral dissolution (a) transport-control, (b) surface reaction-control, and (c) mixed transport and surface reaction control. Concentration C versus distance r from a crystal surface for three rate-controlling processes and where Ceq is the saturation concentration and Cs is the concentration out in solution. [From Berner (1980), with permission.]...

The rate-controlling step in reductive dissolution of oxides is surface chemical reaction control. The dissolution process involves a series of ligand-substitution and electron-transfer reactions. Two general mechanisms for electron transfer between metal ion complexes and organic compounds have been proposed (Stone, 1986) inner-sphere and outer-sphere. Both mechanisms involve the formation of a precursor complex, electron transfer with the complex, and subsequent breakdown of the successor complex (Stone, 1986). In the inner-sphere mechanism, the reductant... 

Between 45 and 90°C, the reaction of cubanite with acidic ferric sulfate solutions followed linear kinetics, indicating that the rate-controlling step was some reaction occurring on the surface of the cubanite. The dissolution rate increased with ferric ion concentration and decreased with increasing concentration of sulfuric acid and ferrous sulfate. The naturally slow reaction was accelerated with the addition of NaCl or HCl. The addition of salt in a dump leaching operation would be a relatively easy and cheap procedure to attain increased reaction rates. 

First, SO2 is adsorbed onto the active sites on the surface of ACF, and oxidized with oxygen in flue gas into SO3. Sulfuric acid is formed by hydrating the SO3 with water in flue gas immediately, then finally the sulfuric acid is absorbed in water and desorbed from the sur ce of ACF. In the avobe-mentioned reaction proces, the desorption of sulfric acid from the ACF surface is considered to be a rate controlling step, and therefore it is most important to increase the desorption rate. The ftict that condensation of water in flue gas onto ACF doesn t inhibit adsorption of SO2 but accelerates the reaction is the confinnation-frnished by the different experiment. 

The apparent dependence of PO4-promoted dissolution on solution PO4 rather than adsorbed P contrasts with the results of Stumm et al. (1985) for organic ligands. Stumm et al. (1985), however, studied the reaction rates at higher pH values (3-6). As with proton-promoted dissolution, the reaction mechanism at higher pH may be different from mechanisms occurring at low pH. The rate-controlling step for phosphate- and possibly fluoride-mediated dissolution may not be the detachment of the complex from the surface. If surface detachment is sufficiently rapid, surface complex formation may be rate limiting. 

Iwamoto et al. (54) studied the activity of a series of metalion exchanged zeolites for the water-gas shift reaction. The lower water-gas shift activity of the acidic cations was explained in terms of hard-soft acid/base properties. In this model, carbon monoxide, which is a soft base, interacts more strongly with soft acid sites. The adsorption of CO is generally considered to be the rate controlling step in the water-gas shift reaction. Cations of lower acidity are generally softer acids and as such adsorb CO more readily. This would lead to higher surface concentrations of CO, thereby increasing the water-gas shift acitivity of the sample. 

The kinetics of the disproportionation of NbClj have been investigated, as have those of the reaction between NbCl3 and NbCls. Thermodynamic functions have been calculated for MX5 (M = Nb or Ta X = Cl or Br)/ The rate-controlling step in the formation of NbClj from Nb and CI2 is the adsorption of CI2 on the metal surface/ In the analogous reaction with Ta, TaC is produced/ ... 

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