Rate consecutive reaction

For the consecutive reactions 2A B and 2B C, concentrations were measured as functions of residence time in a CSTR. In all experiments, C o = 1 lb moPfF. Volumetric flow rate was constant. The data are tabulated in the first three columns. Check the proposed rate equations,... 

On Figure 6.1.1, the four consecutive reaction steps are indicated on a vertical scale with the forward reaction above the corresponding reverse reaction. The lengths of the horizontal lines give the value of the rate of reaction in mol/m s on a logarithmic scale. In steady-state the net rates of all four steps must be equal. This is given on the left side with 4 mol/m s rate difference, which is 11 mm long. The forward rate of the first step is 4.35 molW s and the reverse of the first reaction is only 0.35 mol/m s, a small fraction of the forward rate. 

The formation of resins, tarry matter by consecutive reaction, is prevalent in organic reactions. Figure 3-13a shows the time variations in the concentrations of A, B, and C as given by these equations. The concentration of A falls exponentially, while B goes through a maximum. Since the formation rate of C is proportional to the concentration of B, this rate is initially zero and is a maximum when B reaches its maximum value. 

Consecutive reactions involving one first-order reaction and one second-order reaction, or two second-order reactions, are very difficult problems. Chien has obtained closed-form integral solutions for many of the possible kinetic schemes, but the results are too complex for straightforward application of the equations. Chien recommends that the kineticist follow the concentration of the initial reactant A, and from this information rate constant k, can be estimated. Then families of curves plotted for the various kinetic schemes, making use of an abscissa scale that is a function of c kit, are compared with concentration-time data for an intermediate or product, seeking a match that will identify the kinetic scheme and possibly lead to additional rate constant estimates. 

Applications have been made to consecutive reactions,with several methods being developed to extract the rate constants. Consider Scheme XIV. 

A kinetic scheme that is fully consistent with experimental observations may yet be ambiguous in the sense that it may not be unique. An example was discussed earlier (Section 3.1, Consecutive Reactions), when it was shown that ki and 2 in Scheme IX may be interchanged without altering some of the rate equations this is the slow-fast ambiguity. Additional examples of kinetically indistinguishable kinetic schemes have been discussed.The following subsection treats one aspect of this problem. 

This argument can be extended to consecutive reactions having a rate-determining step. - P The composition of the transition state of the rds is given by the rate equation. This composition includes reactants prior to the rds, but nothing following the rds. Thus, the rate equation may not correspond to the stoichiometric equation. We will consider several examples. In Scheme IV a fast acid-base equilibrium precedes the slow rds. 

Fig. 4. Dependence of relative concentrationa nj/nt of reaction components A, B, and C on time variable r (arbitrary units) in the case of consecutive (— — ) reactions according to scheme (Ha) or parallel (C ) reactions according to scheme (lib). Ads X, Ads A, Des Y denotes that the rate determining step in the overall transformation is adsorption or desorption of the respective substance Des (B + C) denotes that the overall rate is determined by simultaneous desorption of the substance B and C. Ki/Ki = 0.5 for consecutive, and Ki /Ki — 0.5 for parallel reactions, b nxVn. 0 = 2.5 for consecutive reactions Kt = 0.5, and for parallel reactions Ki/Ki — 0.5. c nxVnA0 = 2.5 fcdesBKi Ky/fcdesoXj Kx = 10 [cf. (53)]. d Ki = 1.75 for consecutive, and Ki/Ki = 1.75 for parallel reactions.

Also from the examples shown in Fig. 5 (the transient case where no step is clearly rate determining) it is evident that the selectivity of the consecutive reaction A —> B —> C, as estimated from the curves, will be in... 

In contrast to consecutive reactions, with parallel competitive reactions it is possible to measure not only the initial rate of isolated reactions, but also the initial rate of reactions in a coupled system. This makes it possible to obtain not only the form of the rate equations and the values of the adsorption coefficients, but also the values of the rate constants in two independent ways. For this reason, the study of mutual influencing of the reactions of this type is centered on the analysis of initial rate data of the single and coupled reactions, rather than on the confrontation of data on single reactions with intergal curves, as is usual with consecutive reactions. 

Analysis of the first-order rate coefficient in terms of the two consecutive reactions which were occurring, yielded values of 5.3 xlO-4 and 2.64 xlO-4 the latter value was confirmed as arising from reaction on the first reaction product, 3,4-dichlorodiphenylmethane, because separate 3,4-dichlorobenzylation of this gave a rate coefficient of 2.98 x 10-4. The first-order (overall) rate coefficients obtained at 15 °C (0.665 x 10-4) and 35 °C (6.1 x 10-4) yielded Ea = 19.6, and log A = 14.3, the rate ratio for the consecutive reactions being the same (0.5) at both temperatures later studies have tended to confirm this order of activation energy. 

Competition reactions ad eosdem, 106 ad eundem, 105 (See also Reactions, trapping) Competitive inhibitor, 92 Complexation equilibria, 145-148 Composite rate constants, 161-164 Concentration-jump method, 52-55 Concurrent reactions, 58-64 Consecutive reactions, 70, 130 Continuous-flow method, 254—255 Control factor, 85 Crossover experiment, 112... 

Radioactive decay provides splendid examples of first-order sequences of this type. The naturally occurring sequence beginning with and ending with ° Pb has 14 consecutive reactions that generate a or /I particles as by-products. The half-lives in Table 2.1—and the corresponding first-order rate constants, see Equation (1.27)—differ by 21 orders of magnitude. 

Consider the consecutive reactions, A B C, with rate constants of... 

The rate constants are given by Equation (6.3), and both reactions are endothermic as per Equation (6.4). The flow diagram is identical to that in Figure 6.1, and all cost factors are the same as for the consecutive reaction examples. Table 6.1 also applies, and there is an interior optimum for any of the ideal reactor t5qjes. 

Consecutive Reactions. The prototypical reaction is A B C, although reactions like Equation (6.2) can be treated in the same fashion. It may be that the first reaction is independent of the second. This is the normal case when the first reaction is irreversible and homogeneous (so that component B does not occupy an active site). A kinetic study can then measure the starting and final concentrations of component A (or of A and A2 as per Equation (6.2)), and these data can be used to fit the rate expression. The kinetics of the second reaction can be measured independently by reacting pure B. Thus, it may be possible to perform completely separate kinetic studies of the reactions in a consecutive sequence. The data are fit using two separate versions of Equation (7.8), one for each reaction. The data will be the experimental values of for one sum-of-squares and b ut for another. 

Example 7.5 Suppose the consecutive reactions 2A B C are elementary. Determine the rate constants from the following experimental data obtained with an isothermal, constant-volume batch reactor ... 

Figure 2.S. Concentrations of reactant, intermediate, and product for a consecutive reaction mechanism for different rate constants.

The result obtained from a Hj (5%)/Ar (95%) - TPR/MS in a soak-ramp mode test is shown in Figure 3 for a sample of DESOX. The onset temperature found for H S release in this case, approximately 580°C, is substantially higher than 450°C, the typical onset temperature found in the propane-TPR/MS test. The result was essentially identical in terms of the onset temperature for H S release even when undiluted was used as the reactant. Unlike the propane-TPR/MS tests, where the reaction products are essentially HjS only with virtually negligible amounts of SOj, Hj-TPR/MS tests always showed both SOj and HjS. These data, notably the pattern of change in the rates of SOj and H2S released with temperature in Figure 3, clearly demonstrate, as expected, that the reduction of S to S in step 3 is a consecutive reaction. 

OS 81] [R 7] [P 61] An increase in residence time by a factor of about 3 was accomplished by changing the flow rate from 3.0 to 0.9-1.1 pi min [19[. By far the main reaction product detected was methane otherwise only traces of methanol were present. Instead, at the shorter residence hme a mixtrue containing 68% ethene, 16% ethane and 15% methane was obtained [19,138[. Hence the presence of methane demonstrates that complete cracking occurred as a consecutive reaction to dehydration. 

Consecutive reactions, isothermal reactor cmi < cw2, otai = asi = 0. The course of reaction is shown in Fig. 5.4-71. Regardless the mode of operation, the final product after infinite time is always the undesired product S. Maximum yields of the desired product exist for non-complete conversion. A batch reactor or a plug-flow reactor performs better than a CSTR Ysbr.wux = 0.63, Ycstriiuix = 0.445 for kt/ki = 4). If continuous operation and intense mixing are needed (e.g. because a large inteifacial surface area or a high rate of heat transfer are required) a cascade of CSTRs is recommended. 

Consecutive reactions, E < Ei. The selectivity of the desired product decreases with temperature. However, a low temperature disfavours the reaction rate. A nonuniform temperature-time profile should be applied to maximize reactor productivity (see Fig. 5.4-72). At the start, no desired product is present in the reaction mixture. The temperature should then be as high as possible to keep the rate of P formation high. During the course of reaction, the amount of P in the reaction mixture increases. Therefore, the temperature should be lowered to minimize the rate of formation of the unwanted product from the desired product. 

The reactor system works nicely and two model systems were studied in detail catalytic hydrogenation of citral to citronellal and citronellol on Ni (application in perfumery industty) and ring opening of decalin on supported Ir and Pt catalysts (application in oil refining to get better diesel oil). Both systems represent very complex parallel-consecutive reaction schemes. Various temperatures, catalyst particle sizes and flow rates were thoroughly screened. 

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