Representative initial rate data reactants

Table 1. Representative initial rate data used to determine the order of reaction for the reactants in eq. 3.

For SK-500 the rate at 573°K and 400 sec after the initiation of reactant flow is independent of reactant mole ratio for Ce C2 = 0.7 to 10. Under these conditions the 400-sec point is just beyond the maximum in the rate curve. Similar behavior was observed at one other condition. Initial rate of reaction estimated by extrapolating the decay portion of the rate curves for this data to zero time (see below) indicates a maximum in the rate at C6 C2 == 3.5 (Figure 2). Error bars represent estimated 95% confidence limits. The observed activity for HY is about twice that of SK-500, that for LaY is about two-thirds that of SK-500 (Figure 2). This is consistent with the trend expected (7) since all catalysts were activated to the same temperature. The temperature dependence of the observed rate is large for all systems studied indicating the absence of external mass transfer limitations. 

However, it is often the case that not all the concentrations which are required for the calculation of the reaction stoichiometry are available. It may be that experimentally it is only practicable to measure the concentration of, say, the reactant A at a series of times subsequent to the reaction being started. In this situation, our only help comes from the initial rate. As before, if the initial rate of disappearance of A is affected by the presence of product and/or is less than the rate observed somewhat later in the reaction, we know immediately that the more complicated expressions are required. The converse observations, however, do not necessarily imply that the rate can be represented by the simple equation, (1). In those cases where the preliminary examination of the data indicates that the maximum rate occurs at zero time and is unaffected by the presence of product, the data are examined on the basis of eqn. (1) first if inconsistent rate coefficients are found together with non-simple orders, the data are then re-examined on the basis of the more complicated expressions. This same procedure is adopted when the data consist of a series of concentrations and times but where, for experimental reasons, the early concentration-time values are either unobtainable or sufficiently unreliable as to preclude any reasonable estimates of the initial rate being made the data are examined on the basis of the simple expression first and in the event of inconsistencies re-examined on the basis of the more complicated expressions. It should be clear that improvements in the experimental technique designed to reduce the uncertainties in the initial rates can more than repay the effort involved. 

The information required here is not concentration versus time, but rate of reaction versus concentration. As will be seen later, some types of chemical reactors give this information directly, but the constant-volume, batch systems discussed here do not [ What does it profit you, anyway —F. Villon], In this case it is necessary to determine rates from conversion-time data by graphical or numerical methods, as indicated for the case of initial rates in Figure 1.25. In Figure 1.27 a curve is shown representing the concentration of a reactant A as a function of time, and we identify the two points Cai and Ca2 for the concentration at times q and t2- The mean value for the rate of reaction we can approximate algebraically by... 

To determine the order of reaction for all the reactants in eq. 3, we used the initial rates of reaction calculated for the first 10 % loss of [Mn02] but after the precursor complex had formed. The rates were calculated as previously described (24,26-28) and representative data are in Table 1. 

This term represents a measure of the reactant concentration at any time r or, more correctly, of the dimensionless rate at which P is being converted to A. Using the data in Table 2.1 we have p0 — 5. Because the exponential term involves e, the decay of p is slow for r = 0.693 e 1 ( = 693 for our example data) p = hPo and so the reactant concentration and the rate have fallen to half their initial values. We will make use of this slow variation in p when we... 

We continue to rely extensively on the two-step (initiation - propagation or autocatalytic) model 4) to evaluate data on coking rates. Two rate constants are involved fc for the deposition of coke on a "clean" surface, i.e., with no coke around and k2 when coke is deposited adjacent to another coke deposit. The former rate constant is for an initiation step (or "non-catalytic" coking), while the latter is for the propagation step (or coking catalyzed by the presence of the coke "product") hence, typically, k2 > ki. A third parameter used in the model is M, which represents the maximum amount of coke which can be deposited on the catalyst. In terms of these three parameters, the coke level expected in a pulse reactor after the passage of R amount of reactant is given by ... 

Similarly, the conversion (fraction of reactant transformed or converted) calculated from thermodynamic data would be the end point on a curve of conversion vs time such as that shown in Fig. 1-2. Again, curve A represents the case where the time required to reach equilibrium conditions is great, while in case B the equilibrium conversion is approached more rapidly and is attained essentially at a finite time. Curves A and B could apply to the same reaction the difference between them reflects the fact that in case B the rate has beeAjncreased, for example, by use of a catalyst. The rate of the reaction is initially increased over that for the uncatalyzed reaction, but the equilibrium conversion as shown in Fig. 1-2 is the same for both cases. 

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