Heterogeneous collision frequency

Collision frequency (homogeneous) Anodic faradaic impedance Cathodic faradaic impedance Collision frequency (heterogeneous)... 

Transport of the gas to the surface and the initial interaction. The first step in heterogeneous reactions involving the uptake and reaction of gases into the liquid phase is diffusion of the gas to the interface. At the interface, the gas molecule either bounces off or is taken up at the surface. These steps involve, then, gaseous diffusion, which is determined by the gas-phase diffusion coefficient (Dg) and the gas-surface collision frequency given by kinetic molecular theory. 

The analysis of the curvature of the experimental parabola led to very reasonable determinations of the intrinsic barrier. The measured values are relatively large, ca. 10-13 kcal moP, i.e. larger than usually found in stepwise dissociative processes but still not as large as found with other dissociative-type acceptors, such as halides. On the other hand, if the intrinsic barriers are calculated by the Eyring equation (equation 4) the values are larger by a few kcal mol (using the collision frequency factor Z). This is because the heterogeneous ET is actually non-adiabatic (which means that the actual pre-exponential factor is smaller). This is a very important aspect, which will be covered below. 

The one-dimensional velocity distribution function will be used in Section 10.1.2 to calculate the frequency of collisions between gas molecules and a container wall. This collision frequency is important, for example, in determining heterogeneous reaction rates, discussed in Chapter 11. It is derived via a change of variables, as above. Equating the translational energy expression 8.9 with the kinetic energy, we have... 

The experimental quantity used to characterize heterogeneous reaction rates is the "reaction probablity", y, which is defined as the fractional collision frequency that leads to reactive loss. Kinetic data for the generally irreversible reactive uptake of trace gas species on condensed surfaces are expressed in terms of uptake experiments, where the disappearance of the species under consideration and/or the appearance of one or more reaction products has been observed. Such processes may not be rate limited by Henry s law constraints, however the fate of the uptake reaction products may be subject to saturation limitations. 

Parsons (1975) used the concept of particle surfaces as electrodes to compare homogeneous and heterogeneous reactions in the marine environment. Two factors are important in this comparison (1) the change in geometry affects collision frequencies, steric interactions, and so on and (2) adsorbed species may... 

It was recognized early in the history of heterogeneous catalysis that, in many instances, only a relatively small proportion of the surface was catalytically active. The pre-exponential rate factor was seen to be very small in relation to likely collision frequencies of molecules adsorbed on the surface, taking into account steric requirements, while poisoning (inhibition of the catalysed reaction) could result from surprisingly low levels of specific impurities (see below). Hence the term active sites was coined to describe those localities on the surface which would induce the desired chemical reaction. 

Summary.—The mechanism of the activation process in gaseous systems has been investigated from the point of view of (1) activation by radiation (2) activation by collision. An increase in the radiation density of possible activating frequencies has resulted in no increased reaction velocity. The study of the bimolecular decomposition of nitrous oxide at low pressures has led to the conclusion that the reaction is entirely heterogeneous at these pressures. A study of the unimolecular decomposition of nitrogen pentoxide between pressures of 7io mm. Hg and 2 X 10 3 mm. Hg shows no alteration in the rate of reaction such as was found by Hirst and Rideal but follows exactly the rate determined by Daniels and Johnson at high pressures. No diminution of the reaction velocity as might be ex-expected from Lindemann s theory was observed. 

One of the most useful theories of activation is the collision theory of reactions. This theory assumes that the activated molecules are formed from collisions with other normal reactant species. Such thermally activated molecules decompose to or react with other molecules. The number and frequencies of collisions indicate that not all collisions are effective in producing an activated molecule. As it was shown before [13], the key point is the effective collision factor in the theory. In the case of a heterogeneous reaction, if the surface catalyst concentration is relatively small compared with the bulk concentration of the reactants, the number of active sites for the catalytic reaction will suffice for the reaction to occur. Therefore, the catalytic reaction has one more advantage only a small quantity of the additive is enough for the reaction. 

The effects of gas distributor design and its extent depend on the superficial gas velocity and fiow regime in which the BC operates. In the case of heterogeneous flow, the sparger has a negligible influence on the bubble size and gas-liquid mass transfer because the bubble dynamics are determined by the rate of coalescence and breakup, which are controlled by the liquid properties and the nature and frequency of bubble collisions (Chaumat et al., 2005). Hence, the sparger effect is more pronounced at lower superficial gas velocities (Uq < 0.15m/s) while it is much less important at Uq > 0.20 m/s and nonexistent at Uq > 0.30m/s (Han and Al-Dahhan, 2007). Viscous liquids are also not affected by the gas distributor design if the column is sufficiently tall (Zahradnik et al., 1997). 

The preexponential or the frequency factor A is catalyst dependent, that is, it varies with the extent of surface and has the same units as the rate constant k. On the basis of the collision theory, it can be estimated that the frequency factor of a unimo-lecular heterogeneous reaction is smaller than that of its homogeneous counterpart by a factor of 10. It follows that, for efficient catalysis, the activation energy ,4 of the catalyzed reaction should be at least 80 kj/mol lower than that of the uncatalyzed one at 298 K. At higher reaction temperatures, the difference in must also be higher in order to keep the advan-... 

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