Kinetic irreversibility

Depending on pH, increasing the acidity of the solution either makes the potential required to yield a fixed turnover frequency more oxidizing by 60 mV/pH or does not affect it. This pH dependence is in most cases the same as that of the Fe /n (.Q jpjg jjj jjjg absence of a substrate. These identical pH dependences suggest a pre-equilibrium between the ferric and ferrous forms of the catalyst followed, by a kinetically irreversible step that does not involve proton or electron transfer (e.g., O2 binding). 

I1J2 inputs to the system s substrate pools of Xi and X3, respectively. Simple mass action kinetics. Irreversible reactions. 

Coupled cyclic enzyme system Ii and I2 are inputs to the system s pools of substrate Xi and X3, respectively simple mass action kinetics irreversible reactions. 

SHIFTED BINDING POLYMERIZATION QUASI-EQUIVALENCE ACTIN ASSEMBLY KINETICS ACTIN-BASED MOTILITY MICROTUBULE ASSEMBLY KINETICS IRREVERSIBLE POLYMERIZATION CRITICAL CONCENTRATION BIOCHEMICAL SELE-ASSEMBLY PROCESSIVITY... 

POLYMERIZATION KINETICS (Irreversible) IRREVERSIBLE POLYMERIZATION Polymerization time course,... 

Define and explain the following terms for electrode kinetics irreversible, quasi-reversible, linear region, and reversible. (Bockris)... 

Thus, at Arij > RT, the reaction rate relates only to the direct reaction channel (from i to j) and is independent of the reverse channel (from j to i). In the other words, the inequahty A j > RT is a strict condition of kinetic irreversibility of process ij. 

Let us find the correct thermodynamic criteria of kinetic irreversibility of chemical reactions. It is evident for an elementary reaction ij that the statement... 

Hence, the correct thermodynamic criterion of the kinetic irreversibility at any step in the chemical transformation chain is a considerable (against quantity RT) change in the chemical potential of the reaction groups related to this step—that is, A j > RT. Note that the criterion is valid for both elementary and stepwise reaction, although in the latter case, one must consider the affinity for the stepwise transformation A,2 > RT. 

In kinetic diagrams, the kinetic irreversibility is usually indicated with a single arrow ( ), while the potential kinetic reversibility is shown by a double arrow (t ). In any complex pathway with the known drops of chemical potentials at individual stages, the transformation chain can be broken down into kineticaUy reversible and kineticaUy irreversible steps (Figure 1.6). A priori consideration of some elementary steps of a stepwise reaction as kineticaUy irreversible may cause some serious mistakes in making conclusions via classical kinetic analysis of the scheme of chemical transformations. 

Figure 1.6 Partition of the transformation sequence into groups with the kinetic "irreversibility" between them. When the reaction goes left to right, transformations Y2 Y3, Y3 Y4, Y4 Y5, Y5 —> Ye, Ye Yy, and Yy P can be considered as kinetically irreversible, whereas the kinetic reversibility must be taken into consideration for transformations R Yq, Yq Yy, and Y5 Yg. The differences of stationary chemical potentials of intermediates are greater than RT for the former groups but smaller than RT for the latter groups (the scale is shown at the top right).

An important a priori assumption of the kinetic irreversibility of any step of a stepwise process is that it may result in considerable errors in identifying both the rate limiting and the rate determining steps. Let us illustrate this statement with the preceding sequence of monomolecular reactions. If the kinetic irreversibility of all of the elementary reactions is a priori assumed, then the direct consequence of this statement is the fol lowing relationship ... 

This means that 85 = 8 and, as a result, the first elementary reaction, which is a priori considered kineticaUy irreversible, appears to be the rate determining or even rate limiting step of the entire transformation. This conclusion may differ from the result of analysis obtained without any a priori assumptions on the kinetic irreversibility of individual steps. In conclusion, any a priori assumption on the kinetic irreversibility of, for example, aU steps of the stepwise process is evidently too crude in gen eral cases. In our example, the objective requirement of the rate limiting nature of the first step is the inequality 81 8j at i 7 1. 

The thermodynamic form of kinetic equations aUows us to easily find the apparent activation energy, EaS, for the stationary occurrence of stepwise processes, especiaUy in the case of their kinetic irreversibility. For instance, if stepwise process (1.54) goes from left to right and is kineticaUy irrevers ible in whole—that is, R P—and if Sum is the smaUest quantity of aU 8 in the transformation chain, then... 

While Ars/RT < 1 for both cases, there are no steps that are kinetically irreversible for the stepwise reaction under consideration. 

For example, a specific feature of chemical transformations in a reactive system that is far from thermodynamic equihbrium is the kinetic irre versibility of both the whole stepwise process and its individual steps (see Section 1.4.2). At the same time, we saw in Section 1.4.4 that a priori assumptions on kinetic irreversibility of particular steps of the process often appear inconsistent and, as a result, lead to inaccurate results of the kinetic analysis. 

It is important to emphasize that the condition A2 > 2Aj is identical to the condition A2 Aj—that is, to the kinetic irreversibility of the autocatalytic reaction or (what is the same) the remoteness of the process under consideration from the point of its equilibrium. 

As earlier, R and P are the starting reactant and final product, respectively, of the stepwise transformation (see also Section 3.4.1). External parameter R can be taken here as the controlling parameter. The kinetic irreversibility of the second step means that this step is a priori far from thermodynamic equilibrium. This is the necessary condition of the instability of stationary states. Let us check this. 

Thus, within the range of existence of Y2 that is, at R > 2/81 = Rq the state is stable. It is important that the probable instability of the stationary state Yi = 0 is a consequence of the assumption on kinetic irreversibility of reaction Y P and relates with the position of controlling parameter R around bifurcation point R (see Example 8). 

In the considered example, the last step in the kinetic scheme (3.21) was a priori assumed to be kinetically irreversible. Interestingly, the multiplicity of stationary states in this scheme can arise namely at the kinetic irreversibility of the steps. Let us demonstrate this. 

Unlike Example 7, the kinetic Irreversibility of the second step is not a priori assumed. 

When P 0, this is identical to the solution given in Example 7 for the process where step 2 of the transformation scheme is a priori considered as kinetically irreversible (P 0). Examples 6 and 7 demonstrate that an open system that is nonlinear in respect to intermediates may have multiplicity. The next example considers a system with more than two stationary states. 

Indeed, one can analyze In the same manner the evolution of the system under consideration under conditions of reversibility of all of the elementary reactions in scheme (3.30). Unfortunately, in this situation the analytic solution of the eigenvalue equation in respect to parameter X appears unreasonably awkward. However, if the kinetic irreversibility of both nonlinear steps are a priori assumed, it is easy to find stationary valued (Y, Z ), and we come to the preceding oscillating solution. At the same time, near thermodynamic equilibrium (i.e., at R aa P), there exits only a sole and stable stationary state of the system with (Y Z R). 

In the case under consideration, the rate-determining and rate-limiting steps of the overall catalytic process are identical, since both are steps with minimal ,. Like the case of noncatalytic transformations (see Section 1.4), the apparent activation energy, Eas, of the catalytic stepwise reaction (4.3) is easy to determine when the stepwise process is kinetically irreversible R P. Evidently,... 

When the catalyzed reaction is kinetically irreversible, R 3> P and, therefore,... 

To continue the analysis, we need to inspect potential situations with the occupation of the active center by the reaction intermediates. We shall do that for the case of the kinetic irreversibility of the overall stepwise process at R S> P. At the low occupation of the active center by intermediates Ki and K2, 0k,/0k < 1 and 0k2/0k < 1- When so, A 1 and... 

Let us determine the apparent activation energy of the stepwise process in this case under additional conditions of the kinetic irreversibility of the catalyzed process at... 

We can find the apparent activation energy, Eas, of the process by considering separately the limiting cases of controlling the concentration of complex K2 by the "external reactants either R or P and, as usual, under the condition of the kinetic irreversibility of the stepwise process at R P. 

In the case of the kinetically irreversible "left-to-right" catalytic stepwise reaction,... 

Let us find the rate and apparent activation energy of the stationary process in a particular situation of the kinetically irreversible stepwise reaction of the CO oxidation, step 1 being the rate-limiting stage and intermediate K2 being dominant on the surface. The stationary rate of the overall stepwise process (4.60) is... 

If step 1 is rate-limiting, this is the kinetically irreversible step ... 

The solution of the problem needs ratio K2/K to be expressed via external parameters and R. It follows from (4.62) and from the condition of kinetic irreversibility of step 1 that... 

Let us find the apparent activation energy of the stationary process provided that the overall process is kinetically irreversible, step 2 is rate-limiting, and the catalyst surface is covered predominantly by intermediate K3 Under this statement of the problem, step 2 is kinetically irreversible, while the preceding step 1 being considered partially equilibrium that is, R = N2 K Thus,... 

Many materials are prepared via chemical synthesis in a mother Hquor or mother gas mixture to have synthesis conditions that wiU ensure the quantitative yield of the desired substance—at least with respect to one of the initial reactants. The quantitative yield implies considerable shifting of the equilibrium of the stepwise reaction toward the formation of the required substance modification. This corresponds to the condition of kinetic irreversibility of the process and, as a consequence, to the system going far away from the initial state of the material precursors. 

Moreover, the discipline combines thermodynamics and chemical kinetics and thus may be helpful to researchers who are engaged in study ing complex chemical transformations—in particular, catalytic transforma tions. For example, some of the important concepts in this subject are the conditions of kinetic irreversibility of complex stepwise stoichiometric reactions and rate determining and rate limiting stages. The lecturers in traditional chemical kinetics recognize that these concepts are not simple ones and tend to conceal them in their courses. Fortunately, these con cepts appear to be consistently and properly defined in terms of thermody namics of nonequilibrium processes. 

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