Maximum rate

As already shown in Figure 6.3b the system exhibits remarkable electrophilic promotional behaviour with p values up to 20.64 This is also shown in Fig. 8.60 which depicts a galvanostatic transient. Application of a negative current between the Pt catalyst-working electrode and the Au counter electrode causes a sharp increase in all reaction rates. In the new steady state of the catalyst (achieved within lhr of current application) the catalytic rate increase of C02 and N2 production is about 700%, while lesser enhancement (250-400%) is observed in the rates of CO and N20 production. The appearance of rate maxima immediately after current application can be attributed to the reaction of NO with previously deposited carbon.64... 

Bjerrum and coworkers have assigned the three rate maxima shown in Figs. 10.7 and 10.8 to (starting from the negative potential) (a) destruction of vanadium polymeric chains (b) electric double layer effect at gold working electrode (c) stabilization of V (V) vs V (IV). These explanations are very plausible. 

The TPR of this sample shows three rate maxima, indicating the difference in the ease of removal for the different oxygen atoms in MoO by H2. The... 

As seen in Figure 7, the surface concentration attains a maximum, overshooting the steady-state concentration value. It has been shown theoretically [35] that the maximum appears for any combination of parameters values. Experimental evidence of the appearance of transient uptake rate maxima (which might be totally or partially related to the maximum predicted by the present uptake model) has already been reported [36-39]. 

Many polymerizations exhibit a maximum polymerization rate at some ratio of initiator to coinitiator [Biswas and Kabir, 1978, 1978 Colclough and Dainton, 1958 Taninaka and Minoura, 1976]. The polymerization rate increases with increasing [initiator]/[coinitiator], reaches a maximum, and then either decreases or levels off. Figure 5-1 shows this behavior for the polymerization of styrene initiated by tin(IV) chloride-water in carbon tetrachloride. The decrease in rate at higher initiator concentration is usually ascribed to inactivation of the coinitiator by initiator. The inactivation process in a system such as SnCl4-H20 may involve hydrolysis of Sn—Cl bonds to Sn—OH. There is experimental evidence for such reactions when comparable concentrations of coinitiator and initiator are present. However, the rate maxima as in Fig. 5-1 are observed at quite low [initiator]/[coinitiator] ratios where corresponding experimental evidence is lacking. An alternate mechanism for the behavior in Fig. 5-1 is that initiator, above a particular concentration, competes successfully with monomer for the initiator-coinitiator complex (V) to yield the oxonium salt (VI), which... 

The overall transformation rate is shown qualitatively in Figure 3.16. Notice that the maximum nucleation rate occurs at a lower temperature than the maximum growth rate, and that the maximum transformation rate may not be at either of these two rate maxima. Note also that there is some finite transformation rate, even at very low... 

Amides are reasonably strong bases, with pKa s of the order of — 1 to — 3189, and therefore are appreciably protonated in solutions of mineral acids192-194. The rate maxima are obtained in strongly acid conditions and the hydrolysis may be formulated... 

The hypothesis of a protonated amide intermediate is supported by the observation of the pH-rate maxima since once the amide is fully protonated, a further, increase in acid concentration decreases the activity of water in the medium188, the rate-determining step being the attack of a water molecule on the conjugate acid of the amide203-205. If the hydrolysis is of the form,... 

Tphe rate-limiting processes in catalytic reaction over zeolites remain A largely undefined, mainly because of the lack of information on counterdiffusion rates at reaction conditions. Thomas and Barmby (7), Chen et al. (2, 3), and Nace (4) speculate on possible diffusional limitations in catalytic cracking over zeolites, and Katzer (5) has shown that intracrystalline diffusional limitations do not exist in liquid-phase benzene alkylation with propene. Tan and Fuller (6) propose internal mass transfer limitations and rapid fouling in benzene alkylation with cyclohexene over Y zeolite, based on the occurrence of a maximum in the reaction rate at about 100 min in flow reaction studies. Venuto et al (7, 8, 9) report similar rate maxima for vapor- and liquid-phase alkylation of benzene and dehydro-... 

The conversion-time curves appear to be very similar to the shape typical of emulsion polymerization, i.e., an S-shaped curve is attributed to the autoacceleration caused by the gel effect (Smith-Ewart 3 kinetics, n>>l). The rate of polymerization-conversion dependence is described by a curve with two rate maxima. The decrease in the rate after passing through the first maximum is ascribed to the decrease of the monomer concentration in particles. Particle nucleation ends between 40 and 60% conversion, beyond the second rate maximum. This is explained by the presence of coemulsifier which stabilizes the monomer droplets against diffusive degradation. 

The rate maxima of Figure 4 suggest that the substrate can be activated through the formation of a 1 1 complex with metal ion. Unfortunately, it was difficult to determine whether chelation occurs on the P—O group, the S—O group, or both. Another problem was the complicated dependency of this metal ion effect on acid concentration. Furthermore examination of this system under neutral conditions was not successful and failed to give reproducible results, because of the very slow rate even in the presence of Mg2+ ion. 

Senent-Perez et al found second-order kinetics for the oxidation of tartaric acid over the range pH 1-12 with rate maxima at pH 4.5 and pH 7.5. Verma and Grover also found second-order kinetics, but with a single rate maximum... 

H5IO6 or lOJ on the hydroxyl group to form a periodate ester whose rate of decomposition is fast. The same workers also studied the oxidation of p-hy-droxyphenyl phosphate by periodate (aqueous solutions, pH 0-10, 25 C). The kinetics are second-order, and the rate maxima are at pH s 0.7 and 7.5. Bunton and Hellyer accounted for the pH dependence by assuming (a) that both the ester and its monoanion react with H5IO6, and (b) that the ester monoanion and dianion react with a periodate monoanion. The decrease in rate beyond pH 7.5 shows that reactions involving the phenoxide ion or the periodate dianion are unimportant. 

AG. The similar rate maxima occur because the continuum of final proton states provides many opportunities for the quantum transition. This is in contrast to etpt, where both initial and final electron/proton states are bound, and the rate constant values depend quite sensitively on the number and energies of the final bound states. 

Method (ii). Redhead [63] derived equations for desorption rate maxima for various orders of reaction, but the expressions are rather insensitive to order so, again, evaluation of the pre-exponential term does not necessarily provide physically useful information. Because Tp can be obtained accurately, however, the energy term can also be precisely estimated and where the adsorbate—surface interaction dominates the adsorbate—adsorbate interaction, it provides a reliable value for the... 

---