Watson model

In addition to the assumptions implicit in the use of the Langmuir isotherm the following assumption is applicable to all Hougen-Watson models the reaction involves at least one species chemisorbed on the catalyst surface. If reaction takes place between two adsorbed species, they must be adsorbed on neighboring sites in order for reaction to occur. The probability of reaction between adsorbed A and adsorbed B is assumed to be proportional to the product of the fractions of the sites occupied by each species (0A9B). Similar considerations apply to termolecular reactions occurring on the surface. 

Hougen-Watson Models for the Case of Equilibrium Adsorption. This section treats Hougen-Watson mathematical models for cases where the rate limiting step is the chemical reaction rate on the surface. In all cases it is assumed that equilibrium is established with respect to adsorption of all species. 

Hougen- Watson Models for Cases where Adsorption and Desorption Processes are the Rate Limiting Steps. When surface reaction processes are very rapid, the overall conversion rate may be limited by the rate at which adsorption of reactants or desorption of products takes place. Usually only one of the many species in a reaction mixture will not be in adsorptive equilibrium. This generalization will be taken as a basis for developing the expressions for overall conversion rates that apply when adsorption or desorption processes are rate limiting. In this treatment we will assume that chemical reaction equilibrium exists between various adsorbed species on the catalyst surface, even though reaction equilibrium will not prevail in the fluid phase. 

It has been suggested that the rate limiting step in the mechanism is the chemisorption of propionaldehyde and that the hydrogen undergoes dissociative adsorption on nickel. Determine if the rate expression predicted by a Hougen-Watson model based on these assumptions is consistent with the experimentally observed rate expression. 

Ender these conditions the Hougen-Watson model is consistent with the experimentally observed rate expression. 

Studies of the influence of total pressure on the initial reaction rate for pure reactants present in stoichiometric proportions provide a means of discriminating between various classes of Hoqgen-Watson models. Isolation of a class of probable models by means of plots of initial reaction rate versus total pressure, feed composition, and temperature constitutes the first step n developing a Hougen-Watson rate model. Hougen (14) has considered the influence of total pressure for unimolecular and bimolecular surface reactions the analysis that follows is adopted from his monograph. 

We should also point out that the adsorption equilibrium constants appearing in the Hougen-Watson models cannot be determined from adsorption equilibrium constants obtained from nonreacting systems if one expects the mathematical expression to yield accurate predictions of the reaction rate. One explanation of this fact is that probably only a small fraction of the catalyst sites are effective in promoting the reaction. 

Is the experimental data consistent with this rate expression If so, what is the value of the rate constant What type of Hougen-Watson model gives rise to this form for the rate expression ... 

Buzzi-Ferraris, G., and Donati, G. 1974. A powerful method for Hougen-Watson model parameter estimation with integral conversion data. Chem. Eng. Sci. 29 1504-9. 

Shabaker (SI), for the hydrogenation of propylene over a platinum alumina catalyst, selected a Hougen-Watson model of the form... 

From a consideration of either Eqs. (113) or (114) (K3), it is evident that a saddle point is predicted from the fitted rate equation. This could eliminate from consideration any kinetic models not capable of exhibiting such a saddle point, such as the generalized power function model of Eq. (1) and the several Hougen-Watson models so denoted in Table XVI. 

THE THOERY OF BRANCHING PROCESSES. Theodore E. Harris. First systematic, comprehensive treatment of branching (i.e. multiplicative) processes and their applications. Gallon-Watson model, Markov branching processes, electron-photon cascade, many other topics. Rigorous proofs. Bibliography. 240pp. 5K x 8b. 65952-6 Pa. 6.95... 

The Chick-Watson model needs to be addressed further. Watson explicitly expressed the constant k in Chick s law in terms of the concentration of disinfectant C as aC", where a is an activation constant and n is another constant termed the constant of dilution. Chick s Law, thus, became dNIdt = -aC"dt, where N is the concentration of microorganisms and t is time. Note that C is a function of time. When this equation was integrated, however, it was assumed constant, thus producing the famous Chick-Watson model,... 

Pichavant M., Montel J.-M., and Richard L. R. (1992) Apatite solubility in peraluminous liquids experimental data and an extension of the Harrison-Watson model. Geochim. Cosmochim. Acta 56, 3855-3861. 

If the pathogens exist in a disperse form, the UV light can directly reach them and hence a complete disinfection can occur. The disinfection rate can then be described by first-order reaction kinetics, which is also called as Chick-Watson model (11) ... 

K. F. Rooney, E. Snoeck, and P. H. Watson, Modeling and simulation in clinical drug development. Drug Discov Today 6 802-806 (2001). 

Pichavant M, Montel J-M, Richard LR (1992) Apatite solubility in peraluminous liquids experimental data and an extension of the Harrison-Watson model. Geoehim Cosmoehim Acta 56 3855-3861 Poitrasson F, Chenery SR, Bland DJ (1996) Contrasted monazite hydrothermal alteration mechanisms and their geochemical implications. Earth Planet Sci Lett 145 79-96 Poitrasson F, Chenery SR, Shepherd TJ (2000) Electron microprobe and LA-ICP-MS study of monazite hydrothermal alteration implications for U-Th-Pb geochronology and nuclear ceramics. Geoehim Cosmoehim Acta 64 3283-3297... 

The Hougen-Watson model, which accounts for the fact that a kinetically stable intermediate occupies surface sites, consists of two possible elementary steps that can be rate limiting. Furthermore, the adsorption terms in the denominator of the rate law must account for fractional surface coverage by the intermediate. If ... 

The final form of the Hougen-Watson model for the six-step mechanism described by (14-71) is... 

Since there are three equilibrium constants (i.e., Ka, Kb, and / eq.Rxi) and one kinetic rate constant that one seeks to determine via linear least-squares analysis, it is necessary to have an independent measurement of either Ka or via adsorption studies on the same high-surface-area catalyst in a pulverized state. For example, if this catalyst is exposed to pure gas A and Ka is determined via linear least-squares analysis of its adsorption isotherm, then some of the other temperature-dependent parameters in the Hougen-Watson model are calcnlated as follows from ao, ai and a2. 

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