Stepping rate

In the Fe2+-Tl3+ reaction, the limiting form attained when [Fe2+] < A [Fe3+] showed an inverse dependence on [Fe3+], In other words, [Fe3+] was so high that the first step produced so low a [Tl2+] as to make the second step rate-controlling. Under these conditions, the first step is a rapid prior equilibrium. 

If mechanism (a) were correct, the rate law would be rate = [N02 [C0]. But this expression does not agree with the experimental result and can be eliminated as a possibility. Mechanism (b) has rate = NO,]2 from the slow step. Step 2 does not influence the overall rate, but it is necessary to achieve the correct overall reaction thus this mechanism agrees with the experimental data. Mechanism (c) is not correct, which can be seen from the rate expression for the slow step, rate = [NO ][CO]. [COJ cannot be eliminated from this expression to yield the experimental result, which does not contain [CO. ... 

To see if the proposed mechanism predicts the correct rate law, we start with the rate-determining step. The second step in this mechanism is rate-determining, so the overall rate of the reaction is governed by the rate of this step Rate — 2[Br ][H2 ] This rate law describes the rate behavior predicted by the proposed mechanism accurately, but the law cannot be tested against experiments because it contains the concentration of Br atoms, which are intermediates in the reaction. As mentioned earlier, an intermediate has a short lifetime and is hard to detect, so it is difficult to make accurate measurements of its concentration. Furthermore, it is not possible to adjust the experimental conditions in a way that changes the concentration of an intermediate by a known amount. Therefore, if this proposed rate law is to be tested against experimental behavior, the concentration of the intermediate must be expressed in terms of the concentrations of reactants and products. 

From Step 3 (the slow step), rate = 3[F] where F is an intermediate... 

From the slow step, rate = 2[0][03], However, O is an intermediate and its concentration must be expressed in terms of the reactant, 03. 

In order to test the validity of these qualitative expectations, CASPT2/6-31G calculations on the ring expansion reactions of ortho, meta, and para-cyano-phenylnitrene (12a-c) were performed.96 Fig. 15 summarizes the results. In all three cases, the ring expansions were computed to be nearly thermoneutral, with the first step rate-determining. 

The interpretation of k as a step rate constant (see equations 1.4-8 and 4.1-3) was used by Denbigh and Turner (197 1, p. 123). The interpretation of k as the species rate constant kM was used subsequently by Denbigh and Turner (1984, p. 125). Details of the consequences of the model, both here and in Chapter 18, differ according to which interpretation is made. In any case, we focus on the use of the model in a general sense, and not on the correctness of the interpretation of k... 

This network is a series-parallel network series with respect to HCHO in steps (1) and (2), parallel with respect to CH4 in steps (1) and (3), and parallel with respect to 02 and H20 in all steps. The rate constants kl, k2, and are step rate constants (like k in equation... 

This reaction takes place in two stages, the rate-determining step (rate constant kr) being the alkylation of the aromatic compound this is followed by a fast proton transfer to monomer [100]. The reaction is in fact a Friedel-Crafts alkylation of all the transfer... 

We first consider the case where the rate-determining step is the forward homogeneous electron transfer step (rate constant ke). The governing equations are... 

In complex reacting systems, such as those in combustion processes, a simple one-step rate expression will not suffice. Generally, one finds simultaneous, interdependent reactions or chain reactions. 

Fig. 14 Reduction of PhjCSPh by electrochemically generated aromatic anion radicals (in DMF at 25°C). Variation of the rate-determining step rate constant, A , with the standard potential of the aromatic anion radical, p,g (from left to right azobenzene, benzo[c]cinnoline, 4-dimethylaminoazobenzene, terephthalonitrile, naphthacene, phlhalonitrile, perylene, fluoranthene, 9,10-diphenylanthracene). The dotted lines are the theoretical limiting behaviours corresponding to the concerted (right) and stepwise (left) pathways. (Adapted from Severin et al 1988.)...

Rarely is the third step rate-limiting but appears to occur with Ag(I) ... 

The oxidation of glycolaldehyde by tetrachloroaurate was carried out in acetic acid-sodium acetate buffer and found to be first order in [Au(III)] and [glycolaldehyde]. H+ and Cr both retarded the reaction. A compatible mechanism was proposed, which involves a one-step, rate-determining, two-electron transfer and the involvement of three gold species, AuCH, AuClsCOHa), and AuClsCOH), the last being the most active. 

His treatment puts the values for the first-step rate constants as... 

Figure 2. The catalytic reaction cycle of the Tetrahymena ribozyme (E), showing the binding and docking reactions (leading to the formation of E-S complex), followed by a bond cleavage breaking step (the rate constant for which is kchem) and release of the 5 -fragment in the multiturnover steps (rate constant equals k t).

FRACTAL REACTION KINETICS RATE CONSTANT CHEMICAL KINETICS RATE-CONTRIBUTING STEP RATE-CONTROLLING STEP... 

RATE-DETERMINING STEP or RATE-LIMITING STEP Rate enhancement,... 

Rate-determining step (rate-limiting step) (2007) "These terms are best regarded as synonymous with rate-controlling step". 

Quasi-equilibrium treatments, on the other hand, assume that all elementary steps prior to the rds are almost in equilibrium, i.e. they can occur sufficiently fast not to alter significantly their equilibrium conditions under net charge flow at the interface. For this assumption to be valid, the elementary step rate coefficients must be at least ten times larger than that of the rds. 

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