Potentially Rate-Controlling Steps

Another approach to the identification of sites of possible metabolic control is to compare the apparent equilibrium constant (K )— determined in vitro under certain conditions (temperature, pH, and ionic strength) which approximate the in vivo environment—with the 

Despite these reservations, use of either the relative maximal capacity or the equilibrium/nonequilibrium reaction approach identifies the same enzymes as catalyzing potentially rate-controlling reactions. For example, in most mammalian tissues both methods suggest that the potential exists for control of glycolytic flux at the hexokinase, phosphofructokinase, and pyruvate kinase reactions (cf. Newsholme and Start, 1973). 

The above approaches identify reactions in a pathway which might exercise a regulatory function. Proof of the actual site of rate control under specified conditions is, however, only possible when measurements are made on a pathway whose flux has been perturbed by an activator or inhibitor. Such an approach characterizes the crossover theorem of Chance et al. (1958) and was originally applied to studies of electron-transport chain. According to this theorem, one may define the 

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The kinetics of adsorption control the efficiency of the process and equilibrium time. It also describes the rate of adsorbate uptake onto activated palash leaves. In order to identify the potential rate-controlling steps involved in the process of adsorption, two kinetic models were studied and used to fit the experimental data from the adsorption of phenol onto activated palash leaves. These models are the pseudo-first-order and pseudo-second-order models. 

Clearly, the cis-isomer is needed for the coupling to occur in a concerted fashion. The inorganic product of the final reductive elimination step is the initial Pd(0) complex so that the overall process is catalytic in Pd(0). The kinetics of product formation can be complicated because of the multiple potential rate-controlling steps. In addition, the nature of the catalyst may change due to complexation by X as the reaction proceeds, and the strong base may complex with Pd(0) or Pd(II) to further complicate matters. 

It is essential to point out that the mechanism of mass transfer, as will be discussed in this chapter, represents only one of the potential rate controlling steps governing reactor performance in the system. 

In contrast to the equilibrium electrode potential, the mixed potential is given by a non-equilibrium state of two different electrode processes and is accompanied by a spontaneous change in the system. Besides an electrode reaction, the rate-controlling step of one of these processes can be a transport process. For example, in the dissolution of mercury in nitric acid, the cathodic process is the reduction of nitric acid to nitrous acid and the anodic process is the ionization of mercury. The anodic process is controlled by the transport of mercuric ions from the electrode this process is accelerated, for example, by stirring (see Fig. 5.54B), resulting in a shift of the mixed potential to a more negative value, E mix. 

Figure 3.5. Potential energy changes during progress of reaction chlorination of an alkane. Formation of radical is rate-controlling step.

Figure 25.3. Potential energy changes during course of reaction nucleophilic aromatic substitution. Formation of carbanion is rate-controlling step strength of C--X bond docs not affect over-all rate.

This is one of the few electrode reactions that does not follow the Butler-Volmer equation. The reason is that the dual-site dissociatidn of the H2 molecule is the rate-controlling step. But although this is a non-electrochemical step, the reaction rate is still a function of the potential, because the hydrogen oxidation is self-... 

Charge conservation is ensured by the release of protons and/or sodium ions from the mesoporous system to the electrolyte solution. This mechanism is consistent with the observation of two peaks (see Figure 3.7c) at the potentials observed for the noncata-lyzed oxidation of H2Q and NADH in solution. Consistently, chronoamperometric data fyide infra) can be approached to those theoretically predicted for an electron transfer process preceded by a chemical reaction in solution phase, as demanded, roughly, by a process where adduct formation (Equation 3.16) acts as a rate-controlling step. 

In Section 26.2, the rate of an electrochemical reaction was shown to be dependent on the electrode potential, the intrinsic rate constants for the forward and backward reactions at the electrode, and the concentrations of oxidized and reduced species at the electrode surface. When the transport of reactants and/or products to and/or from the electrode surface is the rate-controlling step, and in Equation (26.46) will differ from those in the bulk solution. For uncharged species in solution, transport... 

The kinetic models developed in all cases assumed the existence of a single rate-controlling step with all remaining mechanistic steps being in quasi-equilibrium. The potential term was first assumed to involve a... 

However, Manes and co-workers noted (19, 20) that the potential term could assume a more complicated form in some cases. Horiuti (10, II, 12, 13, 14) introduced the concept of the stoichiometric number of the rate-controlling step and showed how it could be used to develop a more rigorous form for the potential term. The stoichiometric number of each of the elementary steps which make up an over-all reaction is defined as the number of times it occurs for each occurrence of the over-all reaction. 

In case of reactions involving adsorbed intermediates the electrode material affects the rates in a similar way as in the case of catalytic reactions at the gas-solid interface. However, the potential dependence of the rates of reactions producing adsorbed intermediates results in a potential-dependent coverage of the latter. In general, for a reaction sequence with a rate-controlling step involving an adsorbed intermediate, the kinetic equation may be expressed as... 

Because the rate-controlling step in this reaction can be diffusion of the reducing agent into the fibers or the chemical reaction itself, it is important to consider the rate in terms of these two potentially rate-limiting factors. 

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