Adsorption steady state

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

Although the continuous-countercurrent type of operation has found limited application in the removal of gaseous pollutants from process streams (Tor example, the removal of carbon dioxide and sulfur compounds such as hydrogen sulfide and carbonyl sulfide), by far the most common type of operation presently in use is the fixed-bed adsorber. The relatively high cost of continuously transporting solid particles as required in steady-state operations makes fixed-bed adsorption an attractive, economical alternative. If intermittent or batch operation is practical, a simple one-bed system, cycling alternately between the adsorption and regeneration phases, 1 suffice. 

In order to study the influence of surface disorder in the MM reaction, Frachenbourg et al. [91] have considered a substratum which has two types of randomly distributed sites with different adsorption rates. It is found that such a kind of disorder can sustain a reactive steady state, in contrast to the standard MM process on homogeneous surfaces. 

To get the equilibrium sticking coefficient we assume that at an ambient pressure Pq the adsorbate is in equilibrium at a temperature T with partial coverages Hq, m, and Iq. We then increase the pressure slightly to p = Pq- - AP and linearize the rate equations in the increase in the precursor coverages Am = (m) —m and Al = (/) — Iq. If adsorption into and desorption from the precursors is much faster than transitions from the precursors into the adsorbed state, we can ignore terms proportional to An = n) -6 on the right-hand side of Eqs. (70-72) and also assume that the precursors will be in a steady state. It has been shown that the sticking... 

Ching C. B., Ruthven D. M. (1985) An Experimental Study of a Simulated Counter-Current Adsorption System - I. Isothermal Steady State Operation, Chem. Eng. Sci. 40 877-885. 

FIGURE 2.23 Schematic diagram showing the routes of possible removal of drug from the receptor compartment. Upon diffusion into the compartment, the drug may be removed by passive adsorption en route. This will cause a constant decrease in the steady-state concentration of the drag at the site of the receptor until the adsorption process is saturated. 

The influence of electronegative additives on the CO hydrogenation reaction corresponds mainly to a reduction in the overall catalyst activity.131 This is shown for example in Fig. 2.42 which compares the steady-state methanation activities of Ni, Co, Fe and Ru catalysts relative to their fresh, unpoisoned activities as a function of gas phase H2S concentration. The distribution of the reaction products is also affected, leading to an increase in the relative amount of higher unsaturated hydrocarbons at the expense of methane formation.6 Model kinetic studies of the effect of sulfur on the methanation reaction on Ni(lOO)132,135 and Ru(OOl)133,134 at near atmospheric pressure attribute this behavior to the inhibition effect of sulfur to the dissociative adsorption rate of hydrogen but also to the drastic decrease in the... 

The inverse of these numbers express roughly the average lifetimes of oxygen at the two adsorption states at steady state, i.e. 

As discussed in Chapter 7, this form can provide a good fit of the data if the reaction is not too close to equilibrium. However, most reaction engineers prefer a mechanistically based rate expression. This section describes how to obtain plausible functional forms for based on simple models of the surface reactions and on the observation that aU the rates in Steps 2 through 8 must be equal at steady state. Thus, the rate of transfer across the film resistance equals the rate of diffusion into a pore equals the rate of adsorption equals the rate of reaction equals the rate of desorption, and so on. This rate is the pseudohomo-geneous rate shown in Steps 1 and 9. 

We present expressions for reaction rates and steady-state concentrations using the simplified assumption that Cads hydrogenation to CH4 occurs in one reaction step. We also assume that Oads removal is fast and that hydrogen adsorption is not influenced by the other adsorbates. 

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. 

The observation of negative apparent activation energy can most simply be interpreted in terms of the competition between the adsorption and desorption of methylacetylene on the surface. This qualitative explanation is illustrated in Figure 3, where the steady-state production of trimethylbenzene is compared with the TPD trace of methylacetylene. The fall off in steady state cyclotrimerization rate matches the tail of the desorption spectrum and illustrates the role of reactant desorption at higher temperatiu-es controlling the availability of alkyne monomers and thus the overall cyclotrimerization rate in this temperatime/pressure regime. 

At low values of the bulk concentration Bcy surface coverage is proportional to this concentration, but at high values it tends toward a limit of unity. This equation was derived by Irving Langmuir in 1918 with four basic assumptions (1) the adsorption is reversible (2) the number of adsorption sites is limited, and the value of adsorption cannot exceed A° (3) the surface is homogeneous aU adsorption sites have the same heat of adsorption and hence, the same coefficient B and (4) no interaction forces exist between the adsorbed particles. The rate of adsorption is proportional to the bulk concentration and to the fraction 1-9 of vacant sites on the surface = kjil - 9), while the rate of desorption is proportional to the fraction of sites occupied Vj = kjd. In the steady state these two rates are equal. With the notation kjk = B, we obtain Eq. (10.14). 

Nal concentration, up to 1 X 10 They also obtained steady-state data using a potential step method. The applied potential was initially set at -0.9 V, where no iodide absorption occurs. The electrode was stepped to various positive potentials and A/(ad) was recorded until equilibrium values were obtained. Similar measurements were done in an electrolyte without Nal, and A/(no-ad) was recorded as a reference. The net change in frequency was determined as IAA/I = A/(ad) -A/(no-ad). Figure 27.22 shows I AA/I vs. E plots for various Nal concentrations. Analysis of the data showed that iodide adsorption occurred in accordance with the Temkin isotherm. 

In the steady state, the rates of adsorption and desorption are equal to each other and to the overall rate of this reaction v, = For the steady-state value of... 

Continuous CO Oxidation on Piatinum The main difference between CO stripping and continuous CO oxidation is the CO (re-)adsorption Reaction (6.3). In contrast to CO stripping, this leads a steady-state CO oxidation current because of the continuous supply of CO. In modeling the continuous CO oxidation, we also need to consider the mass transport of CO from the bulk of the solution to the electrode surface. The temporal change in the CO coverage is now given by... 

Analytic expressions were obtained for the O and OH adsorption isotherms by solving the steady state rate equations. 

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