Quasi-equilibrium model

It is important to realize that the assumption of a rate-determining step limits the scope of our description. As with the steady state approximation, it is not possible to describe transients in the quasi-equilibrium model. In addition, the rate-determining step in the mechanism might shift to a different step if the reaction conditions change, e.g. if the partial pressure of a gas changes markedly. For a surface science study of the reaction A -i- B in an ultrahigh vacuum chamber with a single crystal as the catalyst, the partial pressures of A and B may be so small that the rates of adsorption become smaller than the rate of the surface reaction. 

For convenience, these qualitative and quantitative absorption models have been classified into three categories based on their dependence on spatial and temporal variables [2], The first category is referred to as quasi-equilibrium models. The quasi-equilibrium model, including the pH-partition hypothesis... 

Kcrsien S.R.A, Prins W, van Swaaij W.P.M, quasi -equilibrium models for biomass gasification, to be published... 

The dynamic surface tensions for four / -LG concentrations are shown again in Figure 6 together with the curves calculated for the quasi-equilibrium and kinetic regime model. For all concentrations there is better agreement with the experimental points for the kinetic model rather than for the quasi-equilibrium model. 

First models have been derived by Dukhin et al. [27, 28, 30, 101], and Borwankar and Wasan [102]. They used a quasi-equilibrium model by assuming that the characteristic diffusion time is much greater than the relaxation time of the electrical double layer, and thus, the complicated electro-diffusion problem is reduced to a simply transport problem. Datwani and Stebe [103] analysed this model and performed extensive numerical calculations, however, they did not include the electro-migration term into the diffusion equation so that the results are not relevant for further discussions. 

Fig. 4.30 Dynamic surface tension for water solutions of CioEOj at the hexane boundary for a concentration of c =410 mol/cm (O) theoretical calculations reorientation quasi-equilibrium model (1-4) Langmuir model (dotted line) the parameters used were to = 5.8-10 mVmol, (o i = 4.8-10 mVmol, max = 1.410 mVmol, D = 510 cmVs, K = 1.5, and a = 4 (1), a = 5 (2), a = 6 (3), a = 7 (4).

Fig. 4.39. Experimental data and theoretically calculated dynamic surface tension of P-lactoglobulin solutions for the concentrations 10" and 210 mol/l solid lines - quasi-equilibrium model, dotted lines -kinetic model calculated for a rate constant k = 10 s, according to [77]...

Transition-state theory arose from statistical mechanics and describes the distribution of energy among molecules using partition functions. This means that a firm grasp of the theoretical imderpinnings of transition-state theory requires an understanding of statistical mechanics. Houston (2001) describes many of the concepts discussed here from a statistical mechanics point of view and Fueno (1999) explains partition functions. However, the quasi-equilibrium model presented here is a simpler approach that illustrates... 

The quasi-equilibrium model considers a simple reaction where atom A reacts with molecule BC and displaces atom C to produce molecule AB. 

The quasi-equilibrium model assumes that the transition-state cluster is in equilibrium with the A and BC species so that their activities are related by an equilibrium constant. 

The quasi-equilibrium model can be further developed to show how temperature affects rates. The first step is to relate the free energy of activation (AG, ) toln.fi . ... 

The quasi-equilibrium model provides a simple way to account for the effect of ionic strength on the rates of aqueous reactions. In this model the ions A and B combine to form an activated complex that breaks down to... 

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