Kinetics, surface-reaction controlling

Students of professor R. G. Anthony at College Station, TX used a mechanism identical (by chance) to that in UCKRON for derivation of the kinetics. Yet they assumed a model in which the surface reaction controls, and had two temperature dependent terms in the denominator as 13,723 and 18,3 16 cal/mol. Multiplying both the numerator and the denominator with exp(-15,000) would come close to the Ea,/R about 15,000 cal/mol, with a negative sign, and a denominator similar to that in the previously discussed models. 

Kinetic Term The designation kinetic term is something of a misnomer in that it contains both rate constants and adsorption equilibrium constants. For thfe cases where surface reaction controls the overall conversion rate it is the product of the surface reaction rate constant for the forward reaction and the adsorption equilibrium constants for the reactant surface species participating in the reaction. When adsorption or desorption of a reactant or product species is the rate limiting step, it will involve other factors. 

A situation, intermediate between a) and b) - a mixed transport-surface reaction controlled kinetics -may develop. 

Based on Langmuir-Hinshelwood kinetics the rate expression for a first order reaction (A —> R) that is surface reaction-controlled becomes equal to the following expression [2] ... 

Table 13.9 Monomolecular kinetics for alkane cracking when surface reaction controls the rate.

Fig. 2.3 Rate-limiting steps in mineral dissolution (a) transport-controlled, (b) surface reaction-controlled, and (c) mixed transport and surface reaction control. Concentration (C) versus distance (r) from a crystal surface for three rate-controUing processes, where is the saturation concentration and is the concentration in an infinitely diluted solution. Reprinted from Sparks DL (1988) Kinetics of soil chemical processes. Academic Press New York 210 pp. Copyright 2005 with permission of Elsevier...

To derive the corresponding kinetic expressions for a bimolecular-unimolecular reversible reaction proceeding via an Eley-Rideal mechanism (adsorbed A reacts with gaseous or physically adsorbed B), the term K Pt should be omitted from the adsorption term. When the surface reaction controls the rate the adsorption term is not squared and the term KgKg is omitted. 

With surface reaction-controlled kinetics, ion detachment is slow and ion accumulation at the crystal surface cannot keep up with advection and diffusion. In this type of phenomenon, the concentration level next to the crystal surface is tantamount to the surrounding solution concentration. Increased flow rate and stirring have no effect on the rate of surface reaction-controlled rate processes (Berner, 1978, 1983). 

The third type of rate-limiting mechanism for mineral dissolution— mixed or partial surface reaction-controlled kinetics—exists when the surface detachment is fast enough that the surface concentration builds up to levels greater than the surrounding solution concentration but lower than that expected for saturation (Berner, 1978). 

Dissolution occurring by a surface reaction is often slower than by transport-controlled kinetics because the latter results from more rapid surface detachment. There appears to be a good correlation between the solubility of a mineral and the rate-controlling mechanism for dissolution. Table 7.1 lists dissolution rate-controlling mechanisms for a number of substances. The less soluble minerals all dissolve by surface reaction-controlled kinetics. Silver chloride is an exception, but its dissolution... 

The relationship of the stirring rate in these experiments to the rates of hydrolysis reactions of basalt phases is indicative of surface-reaction controlled dissolution (21). First order kinetics are not inconsistent with certain rate-determining surface processes (22). Approximate first order kinetics with respect to dissolved oxygen concentration have been reported for the oxidation of aqueous ferrous iron (23) and sulfide (24), and in oxygen consumption studies with roll-type uranium deposits(25). 

SrTi03 may serve as a well-investigated material for such a bulk conductivity sensor. Its defect thermodynamics and also the relevant kinetic parameters have been discussed in detail in Part I.2 In particular at low temperatures and at small sample thicknesses L, the kinetics of oxygen incorporation becomes surface reaction controlled, and ks the decisive kinetic parameter. 

Powders vary dramatically in particle size on the basis of their origin. It is common for catalyst manufacturers to classify powders in order to assure users of consistency from batch to batch since suspension, settling rates, filtration, and performance in slurry-phase reactions are all dependent on particle size. The effect on suspension, settling rates, and filtration is obvious. However, factors that favor these are unfavorable for kinetics. For reactions controlled by transport rates from the bulk fluid to the surface of the catalyst, the overall reaction rate is a strong function of geometric surface area and thus is favored by small particles. Pore diffusion resistance is also minimized by smaller particles since reaction paths to active sites are smaller. The only mode of reaction control not influenced by particle size is for those reactions in which rate is controlled by reaction at active sites. Therefore, a compromise for optimum filtration and maximum reaction rates must be made. 

Figure 13.5. Transport vs surface controlled dissolution. Schematic representation of concentration in solution, C, as a function of distance from the surface of the dissolving mineral. In the lower part of the figure, the change in concentration (e.g., in a batch dissolution experiment) is given as a function of time, (a) Transport controlled dissolution. The concentration immediately adjacent to the mineral reflects the solubility equilibrium. Dissolution is then limited by the rate at which dissolved dissolution products are transported (diffusion, advection) to the bulk of the solution. Faster dissolution results from increased flow velocities or increased stirring. The supply of a reactant to the surface may also control the dissolution rate, (b) Pure surface controlled dissolution results when detachment from the mineral surface via surface reactions is so slow that concentrations adjacent to the surface build up to values essentially the same as in the surrounding bulk solution. Dissolution is not affected by increased flow velocities or stirring. A situation, intermediate between (a) and (b)—a mixed transport-surface reaction controlled kinetics—may develop.

Equation (10-3) represents the case when diffusion controls the overall process. The rate is determined by k the kinetics of the chemical step at the catalyst surface are unimportant. Equation (10-4) gives the rate when the mass-transfer resistance is negligible with respect to that of the surface step i.e., the kinetics of the surface reaction control the rate. -. 

CQ. It is found that the data of CN is fitted nicely into a straight line. For other "less than ideal" catalysts, such as low Ru-content catalyst Cl and high Ru-content catalyst CQ, the linearity of the fits is much worse [12]. As the current study serves only as an initial exploratory work on this catalyst system, further detailed investigation on the reaction mechanisms using other kinetic models such as surface reaction control and Oj desorption control [35] will not be carried out here. 

Wagner was well aware that these processes also may affect or even control the kinetics of oxidation, sulfidation, and so on, and he initiated research on the phase boundary reaction kinetics [10-18]. Some cases of surface reaction control are described in Sect. 6.2.3.2. The surface reactions generally have no electrochemical character, but as shown, electron transfer steps are involved [10-12]. Least is known about the reactions at the inner interface, but studies on sulfidation [13-18] have proven its role. 

The transition between linear surface reaction controlled kinetics and parabolic bulk diffusion-controlled kinetics certainly must be gradual. This transition could be observed very well for the case of the oxidation of iron in CO2—CO mixtures to wustite [10,11] and was described by Wagner. For this special case, the mathematical description was derived from the fact that the flux of oxygen transfer to the FeO surface must be always equal to the flux of Fe transported to the surface by diffusion needed for the formation of the nonstoi-chiometric Fei ),0 ... 

The growth kinetics of this process are reported to be second order and surface reaction controlled. The precipitation of silver iodide in ethanol by the reaction... 

Mixed Control In the previous two sections we have examined the kinetics of active gas corrosion from the standpoint of two limiting scenarios (1) surface reaction control and (2) diffusion control. Under many conditions, it is quite likely that one of these two processes will limit the overall rate of corrosion, and hence one of these two limiting models can be used to calculate the corrosion rate. Under certain conditions, however, the surface reaction and diffusion rates may be comparable, in which case both will influence the overall rate of corrosion. When two series processes both affect the overall rate, they essentially act as two series resistances. Like electronic resistors, these two kinetic resistances will add in series. However, it is important to keep in mind one key point the resistance of each process is effectively given by the inverse of its rate thus. 

FIGURE 5.5 Summary of the key kinetic concepts associated with active gas corrosion under the surface reaction, diffusion, and mixed-control regimes, (a) Schematic iUusIration and corrosion rate equation for active gas corrosion under surface reaction control, (b) Schematic illustration and corrosion rate equation for active gas corrosion under reactant diffusion control. (c) Schematic illustration and corrosion rate equation for active gas corrosion under mixed control, (d) Illustration of the crossover from surface-reaction-conlrolled behavior to diffusion-controlled behavior with increasing temperature. The surface reaction rate constant (k ) is exponentially temperature activated, and hence the surface reaction rate tends to increase rapidly with temperature. On the other hand, the diffusion rate inereases only weakly with temperature. The slowest process determines the overall rate. 

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