Kinetics mass transport influences

In the former case, the rate is independent of the diffusion coefficient and is determined by the intrinsic chemical kinetics in the latter case, the rate is independent of the rate constant k and depends on the diffusion coefficient the reaction is then diffusion controlled. This is a different kind of mass transport influence than that characteristic of a reactant from a gas to ahquid phase. 

In this chapter, we revisit the subject of reaction/transport interactions in heterogeneous catalysts, this time from a quantitative standpoint. The topic must be examined from two perspectives. First, a researcher that is studying the kinetics of a heterogeneous catalytic reaction (or reactions) must ensure that his or her experiments are free of transport effects. In other words, the experiments must be conducted under conditions where intrinsic chemical kinetics determines the reaction rate(s). The researcher may have to make calculations to estimate the magnitude of heat and mass transport influence. He or she may also have to carry out diagnostic experiments in order to define a region of operation where transport does not affect the reaction rate and selectivity. 

Schuck P 1996 Kinetics of iigand binding to receptors immobiiized in a poiymer matrix, as detected with an evanescent wave biosensor, i. A computer simuiation of the influence of mass transport Biophys. J. 70 1230-49... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

The published values for the activation energies and pre-exponential factors of transesterification and glycolysis vary significantly. Catalysts and stabilizers influence the overall reaction rate markedly, and investigations using different additives cannot be compared directly. Most investigations are affected by mass transport and without knowledge of the respective mass transport parameters, kinetic results cannot be transferred to other systems. 

Additional experiments in a loop reactor where a significant mass transport limitation was observed allowed us to investigate the interplay between hydrodynamics and mass transport rates as a function of mixer geometry, the ratio of the volume hold-up of the phases and the flow rate of the catalyst phase. From further kinetic studies on the influence of substrate and catalyst concentrations on the overall reaction rate, the Hatta number was estimated to be 0.3-3, based on film theory. 

Intrinsic kinetic data can only be measured provided that the overall reaction rate is not limited by mass transport. Only then reahstic parameters can be calculated concerning the influence of catalyst and substrate concentrations (reaction order) as well as the temperature dependency (activation... 

Another point that can be evidenced by the Ha number is the location of reaction. Since the Ha numbers are very small regarding mass transport at the G/L- as well as at the L/L-interphase, the reaction takes place predominantly in the bulk of the catalyst phase. Experimental work on the influence of the stirring rate on the overall reaction rate also underhnes the results obtained by theoretical calculations. There were no detectable changes in the reaction rate as long as stirring rates > 1000 rpm were apphed. Therefore, kinetic experiments were typically performed at 2000 rpm. 

Since the overall reaction rate in the loop reactor is limited by mass transport at the phase boundary, one would expect that the Ru concentration has a weaker influence on the rate of reaction than in the batch reactor. We have carried out experiments at a Ru concentration of 0.005 M as well as at 0.01 M and observed nearly a doubling of the overall reaction rate, giving rise to a reaction order of 0.96 with regard to Ru. The result is somehow surprising, since it can be explained only in terms of a kinetic control of the reaction, like in the batch reactor. On the other hand, previous experiments clearly indicate a mass transport limitation at the L/L-interphase. So the question which arises is how it can be possible that a multiphase reaction system is limited by both mass transport and kinetics ... 

In this chapter we derive the Butler-Vohner equation for the current-potential relationship, describe techniques for the study of electrode processes, discuss the influence of mass transport on electrode kinetics, and present atomistic aspects of electrodeposition of metals. 

Formal kinetic investigations (performed only with acidic ion exchange catalysts) revealed, in most cases, the first-order rate law with respect to the alkene oxide [285,310,312] or that reaction order was assumed [309,311]. Strong influence of mass transport (mainly internal diffusion in the polymer mass) was indicated in several cases [285,309, 310,312,314]. The first-order kinetics with respect to alkene oxide is in agreement with the mechanism proposed for the same reaction in homogeneous acidic medium [309,315—317], viz. 

In FPTRMS, transport of the reactive species of interest from the reactor to the detector can make a contribution to the observed time dependence such that the chemical kinetics becomes convoluted with mass transport rates. This will have to be accounted for in data analysis if reliable rate coefficients are to be obtained. If the physical rate processes are sufficiently fast they will make a negligible contribution to the kinetics. In this section we examine the above four factors to see when they influence the chemical kinetics. The first, third, and fourth items put an upper limit on the rate at which decays and growths can be reliably determined, and the second one sets a lower limit on the decay rate. 

The eight reaction steps in the sensor model include a variety of chemical and physical processes, all of which are influenced by the system components shown in Fig. 1. The sensor is usually designed so that the kinetics of the physical processes (i.e., mass transport by diffusion) are limiting, but it is possible to construct sensors that exhibit performance characteristics limited by the kinetics of the chemical/electrochemical processes. 

The analysis of the kinetics of the charge transfer is presented in Sect. 1.7 for the Butler-Volmer and Marcus-Hush formalisms, and in the latter, the extension to the Marcus-Hush-Chidsey model and a discussion on the adiabatic character of the charge transfer process are also included. The presence of mass transport and its influence on the current-potential response are discussed in Sect. 1.8. 

It will be assumed in this section that the mass transport is much more rapid than the redox kinetics, such that the activities or concentrations of species O and R at the electrode-solution interface can be considered as identical to their bulk values (i.e., a = a °l and c = c 1 with i = O, R). The influence of the mass transport on the current-potential response is treated in Sect. 1.8. 

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