Langmuir-Hinshelwood formalism

Figure 1.6 Langmuir-Hinshelwood formalism for a bimolecular reaction dependence of rate on pressure of reactant A (see text).

The kinetics of alkane hydrogenolysis, that is, the dependence of rate on reactant concentration, have been the subject of numerous studies, and much effort has been devoted to devising rate expressions based on the Langmuir-Hinshelwood formalism to interpret them. Reactions of ethane, propane, and n-butane with H2 on EUROPT-3 and -4 have been carefully studied, with the surfaces in either as clean a state as possible, or deliberately carbided [21, 22] kinetic measurements at different temperature permitted adsorption heats and true activation energies to be obtained. There were two surprises (but like all surprises they were obvious afterwards) ... 

Reaction Mechanisms. Many reactions over zeolites can be described using the Langmuir-Hinshelwood formalism, which involves describing adsorption, desorption, and reaction over active sites as a series of elementary steps. Consider as an example the hydrogenation of 1-butene ... 

Notwithstanding these difficulties, a number of detailed mechanistic schemes have been proposed and evaluated quantitively " " they contain up to eleven unit steps, and provide varying degrees of harmony with experiment. Alternatively, rate expressions based purely on Langmuir-Hinshelwood formalism... 

In kinetic studies of the hydrogenation of aromatic hydrocarbons, the dependence of rate upon reactant pressures has usually been expressed in Power Rate Law formulations, that is, by orders of reaction that are simple exponents of the pressures. These as we have seen (Section 5.2) are at best approximations to more fundamental expressions based on concentrations of adsorbed species," " although they may well represent results over the limited range in which measurements were made. The Langmuir-Hinshelwood formalism has however sometimes been used, and heats of adsorption of the reactants in their reactive states derived from the temperature-dependence of their adsorption coefflcients. ... 

Detailed microkinetic models are available for CO, H2 and HC oxidation on noble metal(s) (NM)/y-Al203-based catalysts (cf., e.g. Chatterjee et al., 2001 Harmsen et al., 2000, 2001 Nibbelke et al., 1998). The model for CO oxidation on Pt sites includes both Langmuir-Hinshelwood and Eley-Rideal pathways (cf., e.g., Froment and Bischoff, 1990). Microkinetic description of the hydrocarbons oxidation is more complicated, particularly due to a large number of different reaction intermediates formed on the catalytic surface. Simplified mechanisms, using just one or two formal surface reaction steps,... 

For a formal kinetic description of vapour phase esterifications on inorganic catalysts (Table 21), Langmuir—Hinshelwood-type rate equations were applied in the majority of cases [405—408,410—412,414,415]. In some work, purely empirical equations [413] or second-order power law-type equations [401,409] were used. In the latter cases, the authors found that transport phenomena were important either pore diffusion [401] or diffusion of reactants through the gaseous film, as well as through the condensed liquid on the surface [409], were rate-controlling. 

A following stage of chemisorption process on the solid surface is a chemical reaction of the reactant immediately from the gas phase (Eley-Rideal mechanism) or between the intrinsic precursor and active sites (Langmuir-Hinshelwood mechajiism). Possible mechanisms of these reactions and formal kinetic equations have been discussed previously. 

Based on the previous assumptions, we can rigorously and explicitly determine an analytical expression of the apparent kinetic constants, between all the lumped families (Fx -> Fy) according to intrinsic elementary kinetic constants as specified in the Single-Events theory (Cochegrue, 2001 Schweitzer, 1998 Valery, 2002). The same applies for the denominator DEN (see next Fig. 26), in which the sum of the terms expresses the competitive chemisorption of all secondary and tertiary carbocations on the acid sites. The apparent kinetics so obtained formally return Langmuir-Hinshelwood expressions, traditional... 

As pointed out by Levenspid (2000), the usual procedure to study the kinetics of surface-catalyzed reactions is to propose a mechanism based on the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model, derive the corresponding equation, and then fit it to the data at hand. If the fit is good, researchers often claim that thqr have found the actual mechanism. This procedure is questionable, as shown by Topic 4.5.4. It would be better to state that our experimental results are formally described (within the range of the investigated reaction conditions) by the selected kinetic equation (probably out of several possible others). 

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