Consecutive with reversible steps

CONSECUTIVE-PARALLEL REACTIONS WITH REVERSIBLE STEPS... 

There are a number of possible schemes which may explain the rate behavior associated with (1.98). A single step can be ruled out. At least two consecutive or competitive reactions including one reversible step must be invoked. 

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>. 

Horiuti quotes the American chemist Daniels "Despite Eyring and Arrhenius, chemical kinetics is all-in-all confusion. But through all the confusion of complications some promising perspective can be seen. Numerous consecutive, competing and reverse reactions by themselves are simple mono- or bimolecular reactions that in principle obey simple laws. Hence we are fighting not so much with primary steps as with the problem of their mutual coordination to interpret the observed facts and to make practical predictions [13]. Such considerations had been made a very long time ago. 

Industrial chemical reactions are often more complex than the earlier types of reaction kinetics. Complex reactions can be a combination of consecutive and parallel reactions, sometimes with individual steps being reversible. An example is the chlorination of a mixture of benzene and toluene. An example of consecutive reactions is the chlorination of methane to methyl chloride and subsequent chlorination to yield carbon tetrachloride. A further example involves the chlorination of benzene to monochlorobenzene, and subsequent chlorination... 

Although the equation reflects the overall reaction, the reaction usually consists of a series of consecutive reversible steps. The sequence of steps is triglyceride to diglyceride to monoglyceride with 1 mole of methyl ester formed at each cleavage (14). 

Two consecutive reversible steps of oxidation for all studied manganese-capped tris-dimethylglyoximates and tris-nioximates with Ei/2 from 650 to 740 and 430 - 470 mV were attributed to the following electrochemical processes ... 

The electrochemical oxidation of TTF was studied in [C2mim][BF4] [20]. The two-electron oxidation of TTF was reversible and proceeded through two consecutive one-electron steps, which is consistent with the sequential oxidation of TTF to TTF" and TTF ". During slow scans, a dark orange precipitate was observed on the electrode surface. If the electrode was not cleaned between experiments, a decrease in the oxidation wave of TTF" to TTF " was observed [20]. Similar precipitation phenomena have been reported in chloroaluminate melts in which TTF" and TTP are also produced through two consecutive one-electron oxidation of TTF [21]. 

For example, suppose a kinetic scheme of a consecutive-competitive reaction with a reversible step... 

The consecutive two-step reaction with both steps being reversible... 

The consecutive-competitive reaction with a reversible step... 

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. 

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. 

Two one-electron transfers with different extents of reversibility. In the case where not all the processes of a consecutive electron transfer sequence are reversible, the irreversibility of a particular step becomes evident by the absence of the reverse peak in its pertinent response. For all other aspects the preceding considerations remain valid. 

As expected on the basis of the presence of an Fe3S4 and an Fe4S4 cluster the response displays multiple redox processes. As a matter of fact there are three consecutive reduction processes, namely A, B and C, with characteristics of chemical reversibility. The processes A and B involve one-electron additions, whereas process C is a two-electron step. Processes A and C are assigned to the Fe3S4-centred reductions [3Fe-4S]+/0 and [3Fe-4S]0/2-, whereas the central system B is assigned to the Fe4S4-centred reduction [4Fe-4S]2+/+. The redox potentials (vs. NHE) for these processes are ... 

The schemes considered are only a few of the variety of combinations of consecutive first-order and second-order reactions possible including reversible and irreversible steps. Exact integrated rate expressions for systems of linked equilibria may be solved with computer programs. Examples other than those we have considered are rarely encountered however except in specific areas such as oscillating reactions or enzyme chemistry, and such complexity is to be avoided if at all possible. 

For complexes formed between hard acceptors and donors, the expected decrease of ASn for each consecutive step obviously occurs (Table 1). Even if the acceptor coordinated to the hard donor is a borderline case, like Cu2+, or even mildly soft, like Cd2+, the same rule applies. The only exceptions are the In + fluoride and Zn + acetate systems where mild reversals are observed on the formation of the third and second complexes, respectively. These are possibly connected with a change of the coordination figure which causes an especially large number of water molecules to be set free at these particular steps. More marked reversals are shown by the same acceptors at the same steps in connexion with soft ligands (Table 2). The phenomenon will therefore be further discussed together with the material presented in Table 2. 

The student should be aware that in kinetic equations rate constants are usually numbered consecutively via subscripts and that the subscripts do not imply anything about the molecularity. The system which is used here employs odd-numbered constants for steps in the forward direction and even-numbered constants for steps in the reverse direction. However, many authors number the steps in the forward direction consecutively and those in the reverse direction with corresponding negative subscripts. 

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