LHHW kinetics

The LHHW kinetics represent a large oversimplification but, nevertheless, constitute a first step in quantifying catalytic kinetics. 

There are several reasons for deviations from the LHHW kinetics Surface heterogeneity, surface reconstruction, adsorbate island formation and, most important, lateral coadsorbate interactions.18,19 All these factors lead to significant deviations from the fundamental assumption of the Langmuir isotherm, i.e. constancy of AHa (and AHB) with varying coverage. 

This type of isotherm is more realistic for describing chemisorption at intermediate 0a values but quickly leads to mathematically cumbersome or intractable expressions with many unknown parameters when one considers coadsorption of two gases. One needs to know how -AHa is affected both by 0A and by the coverages of all other adsorbates. Thus for all practical purposes the LHHW kinetics represent even today the only viable approach for formulating mathematically tractable, albeit usually highly inaccurate, rate expressions for catalytic kinetics. In Chapter 6 we will see a new, medium field type, approach which generalizes the LHHW kinetics by accounting also for lateral interactions. 

Despite the already discussed oversimplifications built into the Langmuir isotherm and in the resulting LHHW kinetics, it is useful and instructive at this point to examine how a promoter can affect the catalytic kinetics described by the LHHW expressions (2.11) to (2.14). 

The problem posed by Eq. (6.22), without the additional complication of the O dependence, is a classical problem in heterogeneous catalysis. The usual approach it to use Langmuir isotherms to describe reactant (and sometimes product) adsorption. This leads to the well known Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics.3 The advantage of this approach is... 

Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics, 21 Nernst, 95... 

We know from Proposition 1 that the constant term Bq C vanishes at the thermodynamic equilibrium. Some features of Equation (67) similar to the known LHHW-kinetic equation. There is a "potential term" Bq responsible for thermodynamic equilibrium, there is a "denominator" of the polynomial type. However there is also a big difference. Equation (67) includes the term D, which is generated by the non-linear steps. 

For SR of higher hydrocarbons, Rostrup-Nielsen " and Tottrup " postulated a Langmuir-Hinshelwood-Houghen-Watson (LHHW) kinetic model. It was assumed that the hydrocarbon chemisorbs on a dual catalytic site, followed by successive a-scission of the C-C bond. The resulting Ci species react with adsorbed steam to form H2 and CO. The expressions were lit to data for SR of n-Cv on a Ni/MgO catalyst at 500°C the overall rate expression is " " ... 

As discussed in Chapter 1, the LHHW kinetic structure has the form... 

Figure 6.78 shows how the LHHW kinetics are selected. Figure 6.79 gives the Input window for the reactions R-l with the Stoichiometry page tab selected. Figure 6.80... 

Figure 6.80 Methanol reaction LHHW kinetic factor.

Rice Herzfeld Pyrolysis Cycles LHHW Kinetics... 

Table 5.7 Rate constants for LHHW kinetics by the hydrogenation of phenol [20].

Table 5.9 Parameters in LHHW kinetic model for cyclohexanol dehydrogenation.

It should be emphasized that the LHHW kinetic rate expressions are derived with assumptions of energetic uniformity and if this is violated then these constraints should be used with caution. In a transient kinetics study Dckker et al. [21] have shown that an occupancy dependent CO adsorption enthalpy on Pt results in very low values of the reaction activation energy, and might even become negative. 

Recently a rigorous quantitative model was developed in order to describe promotional and, more generally, catalytic kinetics [130,147]. The model can be viewed as an extension of classical Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics. 

An equally important system of reactions is one where the catalyst becomes deactivated either intrinsically or throngh deposition of carbonaceons products. The modeling of such systems becomes involved where deactivation has to be conpled with LHHW kinetics. Another complicated situation can arise where the reaction occnrring on the deactivating catalyst is complex but each step can be represented by power law kinetics. In the present case study, we consider such a reaction to illustrate the application of rigorons statistical methods to complex reacting systems. ... 

FIGURE 5.50 Interphase and intraphase non-isothermai effectiveness factor for LHHW kinetics for the reaction C — P, y = 40. 

An interesting feature of LHHW kinetics is worth noting. Many reactions on surfaces known to be nonideal surprisingly follow the ideal LHHW models, a situation that can only be described as the placebo effect or the paradox of heterogeneous kinetics (Boudart et al., 1967 Boudart, 1986). In the same vein but with less justification, it has also been argued for more than four decades—... 

Figure 7.7 Effectiveness factor plots for LHHW kinetics. Negative values represent desorption of product with = Pas tid = k, a new parameter (adapted from Roberts and Satterfield, 1965).

Regime 2 corresponds to film diffusion control and hence is independent of the kinetics. Thus the developments outlined in the previous sections are equally valid for reactions with LHHW kinetics. 

All of our analyses will be based on the use of Equation 17.1 and a generalized Thiele modulus. We consider both power law and LHHW kinetics. 

Figure 17.3 Overall eflectiveness factor plots for LHHW kinetics (Chaudhari and Ramachandran, 1980). = (I + kA(/l) )/ vk. A in figure = [A]. ...

Typical dependences of the reaction rate on the reactant concentration for LHHW kinetics. 

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