Coverage, intermediate

FIG. 4 Phase diagram of Langmuir monolayers at low and intermediate surface coverage (schematic). Not shown are the various phases on the condensed side at high surface coverage. 

In connection with the adsorption of organic molecules at the surface of an electrode it is possible to distinguish two types (a) adsorption of undissociated molecules and (b) adsorption of intermediates formed by dissociation of the original molecule. The variation of coverage of the surface of a... 

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. 

Scriver CR et al (editors) The Metabolic and Molecular Bases of Inherited Disease, 8th ed. McGraw-Hill, 2001. (This comprehensive four-volume text contains coverage of malignant hyperthermia [Chapter 9], channelopathies [Chapter 204], hypertrophic cardiomyopathy [Chapter 213]> the muscular dystrophies [Chapter 216], and disorders of intermediate filaments and their associated proteins [Chapter 221].)... 

By utilizing this we can now express the coverages of all the relevant intermediates and the overall rate in terms of equilibrium constants of the steps in quasi-equilibrium, the pressures of the reactants and the products, and the rate constant of the rate-determining step. 

Figure 6.38. Potential energy diagram for the hydrogenation of ethylene to the ethyl (C2H5) intermediate on a palladium(m) surface. The zero of energy has been set at that of an adsorbed H atom, (a) Situation at low coverage ethylene adsorbed in the relatively stable di-cr bonded mode, in which the two carbon atoms bind to two metal atoms. In the three-centered transition state, hydrogen and carbon bind to the same metal atom, which leads to a considerable increase in the energy...

We will list the elementary steps and decide which is rate-limiting and which are in quasi-equilibrium. For ammonia synthesis a consensus exists that the dissociation of N2 is the rate-limiting step, and we shall make this assumption here. With quasi-equilibrium steps the differential equation, together with equilibrium condition, leads to an expression for the coverage of species involved in terms of the partial pressures of reactants, equilibrium constants and the coverage of other intermediates. 

For ammonia synthesis, we still need to determine the coverages of the intermediates and the fraction of unoccupied sites. This requires a detailed knowledge of the individual equilibrium constants. Again, some of these may be accessible via experiments, while the others will have to be determined from their respective partition functions. In doing so, several partition functions will again cancel in the expressions for the coverage of intermediates. 

The micro-kinetic model also predicts the coverages of the various intermediates on the surface. As shown in Tab. 8.2, the approximation of the surface being dean is quite reasonable. The highest coverages are observed for hydrogen and formate, but the majority of sites are free, even at 50 bar. 

Table 8.2. Coverages of the various intermediates in the methanol synthesis for a stoichiometric gas mixture at 500 K at 85 % equilibrium note that the surface is almost empty at low pressures, while H atoms and formate coverages become significant at high pressure.

Figure 8.18. Surface coverages ofthe various intermediates on a copper surface during the water-gas shift reaction at 200 °C in a gas mixture of33% HjO, 52% Hj, 13%C02, and 1 % CO. Note the high coverage of formate at...

Interestingly, the PEMFC may also operate directly on methanol. Naturally, the problems associated with high coverage of various intermediates will be present, as mentioned above, as well as additional problems such as loss of methanol over the membrane. Nevertheless, it is possible to operate a methanol fuel cell with a voltage around 0.4 V and a reasonable current, to power small mobile devices such as portable computers and cell phones and make them independent of connection to the conventional power net. For more details on fuel cells we refer the reader to L. Carr-ette, K.A. Friedrich and U. Stimming, Fuel Cells 1(1) (2001) 5-39. 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

Effects of Sulfur Coverage. The kinetic results reported in the previous section are from reactions performed on surfaces that are initially clean. The surfaces after reaction were examined by AES and shown to be covered with carbon and sulfur at coverages close to a monolayer. It is interesting to note that although this is the case even after reaction times on the order of minutes the reaction rate is constant for a period of approximately one hour. Either the reaction is occurring on top of this oarbon/sulfur layer or these species are present as sulfur containing hydrocarbon fragments that are intermediates in the desulfurization process. 

H2S adsorption on the (2x2)-S covered Pt(lll) surface at IlOK contrasts with adsorption on the clean surface. On the (2x2)-S surface no complete dissociation Is observed at low temperature Instead, H2S partially dissociates to form an adsorbed SH Intermediate with a characteristic bend vibration at 585 cm . Heating adsorbed SH on the (2x2)-S covered surface leads to a SH+H recombination reaction not observed on clean Ft. The recombination process removes the excess SH so that the stable, high coverage (/3 X /3)R30 -S lattice can be formed. 

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