Heterogeneous data analysis rate laws

Because reactions in solids tend to be heterogeneous, they are generally described by rate laws that are quite different from those encountered in solution chemistry. Concentration has no meaning in a heterogeneous system. Consequently, rate laws for solid-phase reactions are described in terms of a, the fraction of reaction (a = quantity reacted -r- original quantity in sample). The most commonly encountered rate laws are given in Table 1. These rate laws and their application to solid-phase reactions are described elsewhere. 1 4 10-12 Unfortunately, it is often merely assumed that solid-phase reactions are first order. This uncritical analysis of kinetic data produces results that must be accepted only with great caution. 

Equation (25) is general in that it does not depend on the electrochemical method employed to obtain the i-E data. Moreover, unlike conventional electrochemical methods such as cyclic or linear scan voltammetry, all of the experimental i-E data are used in kinetic analysis (as opposed to using limited information such as the peak potentials and half-widths when using cyclic voltammetry). Finally, and of particular importance, the convolution analysis has the great advantage that the heterogeneous ET kinetics can be analyzed without the need of defining a priori the ET rate law. By contrast, in conventional voltammetric analyses, a specific ET rate law (as a rule, the Butler-Volmer rate law) must be used to extract the relevant kinetic information. 

Attempts to conduct an LSV mechanism analysis of the reduction of Fl=Nj in DMF were inconclusive due to the irreproducibility of the response. However, the system was found to be well behaved in CH3CN and quantitative data, reproduced in Table 9, were obtained (Parker and Bethell, 1980). It was necessary to restrict v to 1.0 V or less because of the interference of the rate of heterogeneous charge transfer with the response. Use of analog differentiation of the response resulted in precision of 0.2 mV in the peak potentials and the LSV slopes were observed to be 20.7 1.7 and 19.4 1.4 mV decade-, for d /dlogv and df /dlogCA, respectively. The application of (60) and (61) provides the basis for assigning rate law (97) for the reactions... 

We could use the rate low as gi en by Equation (E5-5.12) as is, but there are only six data points, and u e should be concerned about extrapolating the rate law over a wider range of partial pressure.s. We could take more data, and/or w e could carry out a theoretical analysis of the type dLscussed in Chapter 1(1 for heterogeneous reactions. If we assume hydrogen undergoes dissociative udsorpiion on the catalyst... 

Total pressure analysis of the initial reactant product conversion rate can distinguish between these two mechanisms, provided that rates of conversion can be measured at sufficiently high pressure. The rate expressions given by equations (14-188) and (14-191) have units of mol/area-time for surface-catalyzed chemical reactions. However, rate data obtained from heterogeneous catalytic reactors are typically reported in units of mol/time per mass of catalyst. One obtains these units simply by multiplying the kinetic rate law (i.e., mol/area-time) by the internal surface area per mass of catalyst (i.e., S ), which is usually on the order of 100 m /g. If the feed stream to a packed catalytic reactor contains pure ethanol, then the initial reactant product conversion rate for the four-step mechanism is... 

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