Adsorption maximum rate

Sulphur Trioxide (SO2 -I- O2) Linear reaction rates are observed due to phase boundary control by adsorption of the reactant, SO3. Maximum rates of reaction occur at a SO2/O2 ratio of 2 1 where the SO3 partial pressure is also at a maximum. With increasing 02 S02 ratio the kinetics change from linear to parabolic and ultimately, of course, approach the behaviour of the Ni/NiO system. At constant gas composition and pressure, the reaction also reaches a maximum with increasing temperature due to the decreasing SO3 partial pressure with increasing temperature, so that NiS04 formation is no longer possible and the reaction rate falls. 

Figure 1.2 Volcano plot illustrating the Sabatier principle. Catalytic rate is maximum at optimum adsorption strength. On the left of the Sabatier maximum, rate has a positive order in reactant concentration, and on the right of Sabatier maximum the rate has a negative order.

This approach is based on the assumption that polymer adsorption is fast ("instantaneous") compared with flocculation. In other words the surface coverage is taken to be constant during the flocculation process. Equation (1) states that the flocculation rate tends to zero when 0 tends to 0 or 1. The maximum rate occurs at 0 = 0.5, i.e., at 50% surface coverage. 

The flocculation rate dependency on the fractional surface coverage 0 in Equation (1) has been qualitatively confirmed (13, 14), although the maximum rate appears to occur for a surface coverage of less than 50%. The adsorption rate is also a function of 0, and it has been shown (15) for adsorption onto a smooth solid surface that the rate is proportional to the fraction of polymer-free surface area, 1-0. This approach has not... 

In the biomedical literature (e.g. solute = enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf) or a finite concentration (determination of kT) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to (cf. equation (16)), then... 

If r0 and m are known quantities, the activation energy for desorption may be simply determined from the temperature, Tp, at which the maximum rate of desorption occurs (117). For associatively adsorbed CO the reaction order for desorption may be safely assumed to be one and frequently vo = 1013 sec-1 is assumed to be a reasonable value. If the resulting data for d are compared with values for the isosteric heats of adsorption a (these should be equal since the kinetics of adsorption is nonactivated), very often deviations by several kcal/mol occur (91) that indicate the weakness of this assumption. More sophisticated techniques for analyzing thermal desorption spectra (118-121) allow the independent determination of both parameters, v and d. The results demonstrate that vQ may deviate considerably from 1013 sec-1. For example, for the system CO/Ru(001) Menzel et al. (122) came to the conclusion that v0 may reach values up to 1018 sec-1, whereas a rather small number of 1011 sec-1 was derived by Weinberg et at. (76) for CO desorption from an oxidized Ir(l 10) surface. An additional complication arises from the fact that analysis of thermal desorption spectra on the basis of (4) may yield misleading results if desorption takes place via transition to a precursor state (102). which may be the case for adsorbed CO. 

The steady-state rate of C02 formation increases continuously with increasing temperature up to a maximum as shown in Fig. 35. In this range the CO coverage under reaction conditions decreases continuously due to progressive desorption and becomes practically zero at the maximum rate, max (774). As a consequence the rate of oxygen adsorption increases continuously. The rate law is approximately given by... 

If a particular type of particle is to be removed from a suspension by adsorption onto the grains of a packed bed, then clearly the maximum rate will be achieved by choosing grains having a charge opposite to the particles so that no energy barrier exists. However, such grains... 

The best performance (maximum rate) has been observed at medium coverage of Pt by promoters, as expected. Note that this type of active role of Bi promoter could be excluded in the oxidation of a-tetralol, as the catalyst potential was below the limit of detectable OH adsorption (< 0.5 V) up to 95 % conversion. 

If the partial pressure of one of the components A is increased, the reaction rate does not necessarily have to increase for a certain value of PA the maximum rate is obtained above this pressure the rate decreases with increasing PA. The explanation is that for high PA values, adsorption of A is so strong that it hampers adsorption of reactant B and thus retards the surface reaction. Consequently, negative reaction orders can also be found for both components the reaction order is between -1 and 1. 

The hydroxylation of n-hexane on TS-1, in contrast to the epoxidation of propene, reached its maximum rate in the least polar solvent, t-butanol (Table 18.13). Acetonitrile behaved quite similarly to methanol and water [24, 25, 169]. On the assumption that t-butanol was comparable to i-propanol for the effects on adsorption, a clear relationship between rates and partition coefficients was lacking. Considering that hydroxylation and epoxidation involve different active species and mechanisms, a diverse role of the solvent in the two active species could contribute to the differences, whereas the partition coefficients alone could not... 

One notes immediately that the dependence of the rate v on [S] is similar to the Langmuir adsorption term dependence as shown in Fig. 3.3. The maximum rate Vm is obtained when all enzyme sites are occupied, leading to ... 

Figure 8.4. Arsenic elution from abiotic and biotic. S. putrefaciens, an Fe(IIl)-reducing bacterium] columns initially containing As(in)-ferrihydrite-quartz sand. The initial surface coverage (ca. 800 mg Kg ferrihydrite-sand) is approximately 50% of the adsorption maximum. A flow rate of 1 pore volume per day was maintained with an artificial ground water medium. See Herbel and Fendorf (2006) for a detailed description of the medium.

Table 3 and Figure 5 show the results obtained in presence of quinoline, EtsN and thiourea. As seen in Figure 5, small amounts of additives have a strong influence on rate and e.e.. Thiourea and the amines show a different behavior. With the amines, e.e.mm is almost unchanged and the maximum rate is somewhat higher. However, more HCd is necessary to reach to maximum values. Tentative Explanation Competitive, reversible adsorption of EtsN and quinoline and HCd on the modifiable sites. Using k , K, and s of the unmodified system, Kadd can be calculated (Scheme 2, results in Table 3). 

We see again, as we did in Figure 12.9, that the surface is well covered and that adsorbed CO dominates in both catalysts under initial reaction conditions. One can manipulate either term by changing one or both the reactor pressure and/or adsorption equilibrium constants of the catalyst. Note that the disparity between these two numbers on each catalyst is the reason for the low initial rates that would be observed for this feed ratio before a maximum rate is achieved at partial conversion. 

The heat of adsorption is measured more frequently by desorption, by breaking the adsorbate-surface bond. For each molecule-substrate combination, there is an optimum temperature at which the adsorbed molecules are removed at a maximum rate. By rapidly heating the surface (at rates of a few degrees per second) to this optimum temperature, the adsorbed molecules are removed at a maximum rate before their surface concentration is depleted. Working from this optimum tempera-... 

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