Consecutive Irreversible Reactions

This consists of two consecutive irreversible first-order (or pseudo-first-order) reactions. The differential rate equations are... 

Generalization of Scheme X to any number of consecutive irreversible first-order reactions is obviously possible, although the equations quickly become very cumbersome. However, Eqs. (3-42) and (3-44) reveal patterns in their form, and West-man and DeLury have developed a systematic symbolism that allows the equations to be written down without integration. 

Strictly speaking, the flow analogy is valid only for consecutive irreversible reactions, and it can be misleading if reverse reactions are significant. Even for irreversible reactions the rds concept has meaning only if one of the reactions is much slower than the others. For reversible reactions the free energy reaction coordinate diagram is a useful aid. In Fig. 5-10, for example, the intermediate 1 is unstable with respect to R and P, and its formation (the kf step) is the rds of the overall reaction. 

The example of consecutive, irreversible heterogeneous catalytic reaction of the type A —> B — C has been solved in a more general way by Thomas et al. (16). The authors considered scheme (III) with the listed values of the rate constants of surface reactions along with the constants of adsorption and desorption of the reactant A and of the product C. 

A procedure similar to that used in the investigation of the hydro-demethylation of xylenes was also employed in a study of the consecutive hydrogenation of phenol via cyclohexanone to cyclohexanol in gaseous phase on a platinum on silica gel catalyst (p. 27) at 150°C [scheme (VI)] at this temperature both reactions were irreversible under the excess hydrogen used. 

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. 

Cryokinetic studies of the plastocyanin-ferricyanide redox reactions in 50 50 v/v MeOH + H2O, pH = 7.0, p = 0.1 M reveal an Eyring plot shown for the second-order rate constant k from 25 °C to -35°C. The reaction is irreversible over the whole temperature range and there is no evidence for a change in the Cu(I) active site. Recalling that these reactions may involve consecutive steps, explain the deviation from a linear Eyring plot. F. A. Armstrong, P. C. Driscoll, H. G. Ellul, S. E. Jackson and A. M. Lannon, J. Chem. Soc. Chem. Communs. 234 (1988). 

The net result of a photochemical redox reaction often gives very little information on the quantum yield of the primary electron transfer reaction since this is in many cases compensated by reverse electron transfer between the primary reaction products. This is equally so in homogeneous as well as in heterogeneous reactions. While the reverse process in homogeneous reactions can only by suppressed by consecutive irreversible chemical steps, one has a chance of preventing the reverse reaction in heterogeneous electron transfer processes by applying suitable electric fields. We shall see that this can best be done with semiconductor or insulator electrodes and that there it is possible to study photochemical primary processes with the help of such electrochemical techniques 5-G>7>. 

For the general case of trialkoxysilanes, although the hydrolysis reaction is reversible, under the conditions employed it may be considered as three consecutive, irreversible pseudo-first-order reactions shown in the following equations ... 

Figure 8 shows a plot of the concentration of methanol produced by the hydrolysis of SiQAC at pH 4.07 in water and the nonlinear regression curve of equation (18) assuming three consecutive, irreversible first-order reactions. A summary of the observed rate constants at each pH studied is shown in Table 4. Regression fits produced R2 values of better than 0.99 for all the pH values investigated. Plots of the observed values of k, k2, and k3 vs. pH are linear in all cases, with R2 values greater than 0.99, and with slopes of -0.997, -0.992 and -0.999, respectively. The ratio of kt k2 k3 is approximately 20 3 1. 

Reactor design becomes more challenging when yield as well as conversion must be considered. One common situation in which this arises is when there are consecutive irreversible reactions such as the following ... 

Let us apply these general first-order solutions to two specific reactions irreversible consecutive and simple reversible reactions. Consecutive reactions (A —> B —> C) do not have reverse reactions. This leads to ... 

Figure 16. Product distribution for a consecutive irreversible first order reaction A -> R -> S as a function of the space time.

Figure 2.9. Consecutive irreversible reactions. Rate constants for the three elementary reactions are the same (k = 2 = 3 = 0.1 day" ) and [B]o = ICJo = [D]o = 0.

The consecutive-irreversible z-state process. In this process, encountered in chemical engineering reactions, the system undergoes the following succession of transitions ... 

Let us now apply the above birth model to a well-known process, i.e., a consecutive-irreversible z-stage first order chemical reaction, with a single initial substance, the "first member of the family". The various states are Sj s Aj (i = 0,... 

Parallel reactions single and consecutive-irreversible reaction steps. 

PARALLEL REACTIONS SINGLE AND CONSECUTIVE IRREVERSIBLE REACTION STEPS... 

I Inure lb. Consecutive irreversible reactions. The rate constant for the first reaction in series in small n lutive to the other three (fc, =0.02 day-1,k2 = fc3 =0.1 day-1). The bottleneck caused by the rate-limiling step restrains reaction rates for subsequent steps in the reaction. 

Three reversible reactions in series are presented in Figure 5. In contrast to the case of consecutive irreversible reactions presented earlier (Fig. 1), all four species coexist at the final equilibrium position. The product concentrations [B], [C], and [D] grow as the reaction progresses without overshooting their final equilibrium position. 

Reactions of Thiazolium Salts. - Base-induced attack of thiazolium salts and rearrangement of subsequent 2-hydroxy-A -thiazoline was studied by u.v. kinetic spectroscopy (two consecutive irreversible steps).The first step was the nucleophilic attack of OH on C-2 of (103 R = H or Me), affording the thiazoline (104), with measured third-order rate constants. The second step was the nucleophilic cyclization of the thiolate (105) to form the thietans (106) (Scheme 9). 

Extensions of the simple network of consecutive irreversible reactions can easily be expanded to include multiple steps and products, formed by reversible and irreversible elementary reactions. In all complex processes the writing of a reaction network produces the most general description of the kinetic process. Fortunately, in many cases the network is such that the steady state assumptions can be invoked. When this is possible, the kinetic rate expressions for the elementary processes of the reaction mechanism can often be solved analytically, as in the example above, to yield a simpler rate expression for the overall process. The identification of such a mechanistic rate expression, using experimental rate data from a kinetic study, can serve to identify the likely mechanism of that reaction. 

The desired product B is formed by a reversible reaction from 4, and consumed by a consecutive irreversible reaction to C, and is also in competition with the by-product D. Hence, only the species 4 and B are of interest. 

For the situation in which each of the series reactions is irreversible and obeys a first-order rate law, eqnations (5.3.4), (5.3.6), (5.3.9), and (5.3.10) describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For consecutive reactions in which all of the reactions do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time at which the concentration of a particular intermediate passes through a maximum. If interested in designing a continuous-flow process for producing this species, the chemical engineer must make appropriate allowance for the flow conditions that will prevail within the reactor. That disparities in reactor configurations can bring about wide variations in desired product yields for series reactions is evident from the examples considered in Illustrations 9.2 and 9.3. 

If the intrinsic reaction rate is fast compared to the internal and/or external mass transfer processes, the reactant concentration within the porous catalyst and on its outer surface is smaller compared to the bulk concentration, whereas the concentration of the intermediate will be higher. Consequently, the consecutive reaction is promoted and the yield diminishes. The degree of yield losses depends on the ratio between transfer time and the intrinsic rate of the consecutive reaction, which is characterized by the corresponding Thiele moduli and Damkohler numbers referred to the consecutive reaction. For irreversible first-order reactions, the equations are as follows ... 

Gas (or gas with homogeneous catalyst) heat of reaction endothermic reaction rate, fast capacity 0.001-200 L/s good selectivity for consecutive reactions and irreversible first order volume of reactor 1-10000 L OK for high pressures or vacuum. For temperatures < 500 °C. For temperatures > 500 °C use fire tube. For example, used for such homogeneous reactions as acetic acid cracked to ketene. Liquid (or liquid with homogeneous catalyst) heat of reaction endothermic reaction rate, fast or slow capacity 0.001-200 L/s good selectivity for consecutive reactions volume of reactor 1-10000 L OK for high pressures. For temperatures... 

Under anaerobic conditions, Gossett and Zinder showed that the reductive dehalogenation of the chlorinated ethenes occurs as a series of consecutive irreversible reactions mediated by the addition of 1 mole of hydrogen gas for every mole of chloride removed. Thus, the theoretical minimum hydrogen requirement for dechlorination can be calculated on a mass basis as shown below ... 

In order to understand the complexity in oscillatory reactions, it would be worthwhile to examine their relationship with different types of chemical reactions [10], which have been summarized in Fig. 9.8 in increasing order of complexity viz., irreversible reactions -> reversible reactions parallel reaction consecutive reaction -> autocatalytic reactions damped oscillations aperiodic oscillations spatio-temporal oscillations chaotic oscillations. Further, Fig. 9.8 shows the concentration... 

The set of two consecutive irreversible reactions just considered is a subset of the more general case in which both reactions are reversible A B C. The equations for this problem have been solved exactly for two limiting cases (i) [A]o = 1.00 and both [B]o and [C]o = 0, and (ii) A is present as a saturated solution so that the concentration does not change with time. For details, see Lowry, T. M. John, W. T. /, Chem. Sac. 1910, 97, 2634 and references therein. 

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