Surface reactions rate-limiting

The assumption that the rate-limiting surface reaction is the formation of the half-hydrogenated state [reaction (3)] provides the condition that 1 and, consequently, leads to the approximate expres-... 

Transport during late diagenetic reactions is not rate limiting (surface-reaction controls are rate... 

To illustrate the use of initial rate data, consider the bimolecular reaction A -b B C -I- D. The rate equation for a rate-limiting surface reaction in the sequence is... 

Chemical/Physical. Matheson and Tratnyek (1994) studied the reaction of fine-grained iron metal in an anaerobic aqueous solution (15 °C) containing chloroform (107 pM). Initially, chloroform underwent rapid dehydrochlorination forming methylene chloride and chloride ions. As the concentration of methylene chloride increased, the rate of reaction appeared to decrease. After 140 h, no additional products were identified. The authors reported that reductive dehalogenation of chloroform and other chlorinated hydrocarbons used in this study appears to take place in conjunction with the oxidative dissolution or corrosion of the iron metal through a diffusion-limited surface reaction. 

In general, the rate-limiting surface area, in the overall rate equation, (10), is determined by the mineral with the slowest surface reaction kinetics and the lowest surface area in contact with fluid. 

The rate of surface reaction is equal to mass flux to the surface. Taking the surface concentration equal to zero for mass transfer-limited reactions gives... 

The influence of diffusional limitations in gas phase reactions has been extensively treated by Wheeler and from a chemical engineering viewpoint by Hougen and Watson More recently a monograph by Satterfield and Sherwood has appeared. The problem of diffusion can be separated into two parts, the first is diffusion or mass transfer to the external surface of the catalyst and second, for those catalysts which are porous, diffusion within the catalyst pores. When diffusion is the rate limiting process, reaction rate, selectivity and activation energy are affected. 

An excellent illustration of the LHHW theory is catalytic cracking of n-alkanes over ZSM-5 [8]. For this reaction, the observed activation energy decreases from 140 to -50 ( ) kj/mol when the carbon number increases from 3 to 20. The decrease appeared to linearly depend on the carbon number as shown in Fig. 3.11. This dependence can be interpreted from a kinetic analysis that showed that the hydrocarbons (A) are adsorbed weakly under the experimental conditions. The initial rate expression for a rate-determining surface reaction applies (3.30), which in the limiting case of weak adsorption of A reduces to Eqn. (3.52). The activation energy is then represented by equation (3.53). 

Only when diffusion is fast compared to rate limiting elementary reaction stepS/ these surface composition inhomogeneities may not have kinetic consequences and the adsorbate layer may be considered ideally mixed. 

At high-groundwater flow rates (kf k+), these expressions reduce to C = k CJkf, and R = k+Q, so that a maximum solution rate is reached, independent of flow rate. At the opposite extreme of slow groundwater flow kf 0), C = C, and R = kfC,. Saturation is attained and the rate of dissolution is controlled by the groundwater flow rate. In other words, at high flow the dissolution rate is surface-reaction controlled. The slower process is rate limiting. 

In fact the EADA is the limiting case of the SSA when the rates of adsorption and desorption are much faster than the rate of surface reaction. The use of SSA for the simple case of unimolecular irreversible reaction does not cause significant added complexity, however for more complex reactions the SSA causes considerable complexity and most CSD kinetic models are based on the EADA. 

If the rate of transport of gases along the crack were sufficiently fast, then crack growth would be controlled (rate limited) by the rate of surface reactions with the newly created crack surface. Assuming, for simplicity, that the reactions follow first-order kinetics, the rate of increase in the fractional surface coverage 6 is given by Eqn. (8.15) ... 

Reaction limitation obtains if the rate coefficients of the surface reactions [(4), (5), (6)] are very low compared to the transport steps. Chemical reactions are thermally activated and rates of simple reactions follow Arrhenius behavior. Thus a plot of the logarithm of the deposition rate vs. 1/T is a straight line in the temperature range corresponding to the reaction-limited regime. The slope of this line is determined by the adsorption heats of the reactants and the activation energy of the rate-determining surface reaction step. 

Is the Suriace Reaction Rate-Limiting The rate of surface reaction is... 

The surface reaction between adsorbed molecular hydrogen and germanium dichloride is believed to be rate-limiting. The reaction follows an elementary rate law with the rate being proportional to the fraction of the surface covered by GeCU times the square of the fraction of the surface covered by molecular hydrogen. 

This assumes no reverse reaction, which is the case if the reaction products are rapidly removed from the surface and swept away in the gas phase. Surface coverage dependent terms may also enter into this equation if the reaction rate is limited by available adsorption sites. If a reverse reaction can occur one must also consider the law of mass action behavior as in Equation 4.14, while if there are multiple critical steps one may need to account for this in the reaction rate, as in Equation 4.16. When kf hg the rate is surface reaction rate limited, while hg kf implies a gas phase transport limitation. 

Process 2, the adsorption of the reactant(s), is often quite rapid for nonporous adsorbents, but not necessarily so it appears to be the rate-limiting step for the water-gas reaction, CO + HjO = CO2 + H2, on Cu(lll) [200]. On the other hand, process 4, the desorption of products, must always be activated at least by Q, the heat of adsorption, and is much more apt to be slow. In fact, because of this expectation, certain seemingly paradoxical situations have arisen. For example, the catalyzed exchange between hydrogen and deuterium on metal surfaces may be quite rapid at temperatures well below room temperature and under circumstances such that the rate of desorption of the product HD appeared to be so slow that the observed reaction should not have been able to occur To be more specific, the originally proposed mechanism, due to Bonhoeffer and Farkas [201], was that of Eq. XVIII-32. That is. 

The apparent activation energy is then less than the actual one for the surface reaction per se by the heat of adsorption. Most of the algebraic forms cited are complicated by having a composite denominator, itself temperature dependent, which must be allowed for in obtaining k from the experimental data. However, Eq. XVIII-47 would apply directly to the low-pressure limiting form of Eq. XVIII-38. Another limiting form of interest results if one product dominates the adsorption so that the rate law becomes... 

As with the other surface reactions discussed above, the steps m a catalytic reaction (neglecting diffiision) are as follows the adsorption of reactant molecules or atoms to fomi bound surface species, the reaction of these surface species with gas phase species or other surface species and subsequent product desorption. The global reaction rate is governed by the slowest of these elementary steps, called the rate-detemiming or rate-limiting step. In many cases, it has been found that either the adsorption or desorption steps are rate detemiining. It is not surprising, then, that the surface stmcture of the catalyst, which is a variable that can influence adsorption and desorption rates, can sometimes affect the overall conversion and selectivity. 

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