Vacant surface site

Figure 7-22 Catalytic cycle in which reactant A adsorbs on a vacant surface site S to form the adsorbate AS,...

It can be shown that through appropriate substitution of Eqs. (3.108) through (3.110) and use of the fractional area balance (/ - - foeCh + /n = where / is the fraction of vacant surface sites), the deposition rate can be expressed in terms of the partial pressures (concentrations) of the reactants as... 

Steady-state conditions require the combination of Eqs. (9.168) and (9.170) giving Eq. (9.171). It also indicates the formation of vacant surface sites ( ) capable of further oxygen adsorption. If certain further assumptions hold, Eq. (9.171) determines a limiting selectivity of 6/7 or 85.7% ... 

The replacement of the variables in (B.5) is symmetrical relative to the values of the quantities Xh but leads to cumbersome expressions. The asymmetry of the replacement in (B.6) yields unnormalized values of the functions Y, but leads to simpler equations. Its use is preferable if it is known that the concentration of the component 5 (vacant surface sites or a solvent in a solution) is not very small. As a result, the system of equations with the dimension s(s+l)/2 is reduced to the system of equations of the dimension (j-l). 

S is a vacant surface site because the adsorbate cannot be adsorbed on a site AS that is already occupied. The activities of vacant and occupied surface sites are proportional to the fraction of the sites that are vacant, )r, and occupied by one adsorbate molecule, ),. Because in the Langmuir isotherm, only monolayer adsorption is allowed ),- + ), = 1 and... 

The second-best case to consider is two reactions of the same order differing by one reactant only, for example, Cs + Hs CHS versus CHS + Hs CH2,s. Finally, if a vacant surface site S is treated as a reactant, one can compare dissociation reactions with recombination reactions, e.g., S + COs Cs + Os versus Hs + COs HCOs + S. Here, however, the conclusions based on AE will be the least definitive, because the differences in the nature of surface sites (on-top, bridge, or hollow) and in the effective number of the sites involved in the reaction may strongly affect the value of A. 

So that we will be able to consider the controversy concerning the atomisation of hydrogen by gold [111], we now develop relations for the kinetics of atomisation when s2 is not constant, but depends on temperature. The discussion will also be relevant to our later development of the kinetics of recombination. We assume that the adsorption of a molecule requires the presence of two adjacent vacant surface sites and that the probability that adsorption occurs when a molecule strikes such a pair of sites is k2,1 so we write... 

Consider a surface catalysing the hydrogenation of an alkene and let per volume of reactor ST be the total number of surface sites Sv be the number of vacant surface sites... 

Assuming a zero-order dependence of the rate on methanol surface concentration and 0( ), = 0( ), o- (CH ) it follows that 0(CH ), = 0( ), = 0 (1 - with ki being the rate constant of CFl formation and 0( ) 0 the initial concentration of vacant surface sites. The dashed line in Fig. 50d represents the calculated rate (amount) of CFl formation and fits the data reasonably well. This comparison... 

Schematic depiction of a square lattice populated by A atoms. Empty squares represent vacant surface sites.

Here kl is a surface intermediate formed by adsorption of A onto a vacant surface site 1. The total concentration of active sites on the catalytic surface, in moles per unit amount of catalyst, is... 

Here, represents a vacant surface site or an adsorbed species. The adsorbed intermediate then reacts to form C02 that readily desorbs ... 

This equation is based on the aigument that each gas molecule colliding with a vacant surface site has a finite and fixed probability of sticking on this site, while... 

In this equation a is the condensation coefficient the probability that a molecule is adsorbed provided it has the necessary activation energy E and collides with a vacant surface site. / O) is the function of surface coverage and represents the probability that a collision will take place at a vacant site. 

A+0B+0( .+0v= (8.126) Inserting an expression for the fraction of vacant surface sites gives after rearrangement ... 

Cv concentration of vacant surface sites fj fugacity of species j... 

In the derivations which follow, we will use k to denote a rate constant, K to denote an equilibrium constant, and 6, to denote the concentration of vacant surface sites. Let us do part (b) first. We shall make the following assumptions ... 

In category 1, the order of the autocatalytic species in the cycle reaction is equal to one (and equal to the order of X in the exit reaction). Category 2 oscillators include mechanisms with autocatalytic reaction of a higher (effective) order in X than the order of X in the removal reaction, and the type X species need not necessarily be chemical species. Rather, they may include vacant surface sites in heterogeneous catalysis, or temperature in thermokinetic oscillation. 

There is evidence that certain chemical adsorption processes involve dissociation of the adsorbate to form two bonds with the adsorbent surface. On many metals, hydrogen is adsorbed in atomic form. For such situations the kinetic approach to the derivation of the Langmuir equation requires that the process be regarded as a reaction between the gas molecule and two vacant surface sites. Thus, the adsorption rate is written as... 

For processes in which an adsorbed intermediate [see Eq. (15) and below] is formed as a result of electron transfer, the rate equation for a discharge must take into account the fraction of unit surface occupied in the steady state. Since discharge can only occur at a vacant surface site, in the simplest case the current is then... 

The autocatalytic elementary reaction step for CO oxidation is the removal reaction of CO from the catalyst surface. The presence of adsorbed CO suppresses the dissociative adsorption of O2, because vacant surface sites are required to accommodate the oxygen atoms that are generated by dissociated molecular oxygen. The CO2 removal reaction, on the other hand, is actually autocatalytic in vacant sites since a molecule of oxygen can ultimately remove two adsorbed CO molecules, thus freeing up two additional sites. 

We derive the Langmuir isotherm by treating the adsorption process like any other chemical equilibrium, except that it is established between gas molecules (species A), vacant surface sites of number Uvacam. and species adsorbed on the surface (number Ha). For a non-dissociative adsorption of species A, adsorption is represented by the following chemical equation ... 

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