Rate constant from cycling experiments

Mumane RJ, Cochran JK, Sarmiento JL (1994) Estimates of particle- and thorium-cycling rates in the northwest Atlantic Ocean. J Geophys Res 99 3373-3392 Mumane RJ, Cocliran JK, Buesseler KO, Bacon MP (1996) Least-squares estimates of thorium, particle and nutrient cycling rate constants from the JGOFS North Atlantic Bloom Experiment. Deep-Sea Res 1 43(2) 239-258... 

Table 3 Rate constants / (adduct+02) derived from cycling experiments.

The reaction rate of Co3+ with benzaldehyde was measured in independent experiments from the consumption of Co3+ in the absence of oxygen. The rate constant of this bimolecular reaction was found to coincide with k. Thus, in this process the limiting step of initiation is the reduction of Co3+ by aldehydes, and the complete cycle of initiation reactions includes the reactions [50,51] ... 

Cyclohexyl xanthate has been used as a model compound for mechanistic studies [43]. From laser flash photolysis experiments the absolute rate constant of the reaction with (TMS)3Si has been measured (see Table 4.3). From a competition experiment between cyclohexyl xanthate and -octyl bromide, xanthate was ca 2 times more reactive than the primary alkyl bromide instead of ca 50 as expected from the rate constants reported in Tables 4.1 and 4.3. This result suggests that the addition of silyl radical to thiocarbonyl moiety is reversible. The mechanism of xanthate reduction is depicted in Scheme 4.3 (TMS)3Si radicals, initially generated by small amounts of AIBN, attack the thiocarbonyl moiety to form in a reversible manner a radical intermediate that undergoes (3-scission to form alkyl radicals. Hydrogen abstraction from the silane gives the alkane and (TMS)3Si radical, thus completing the cycle of this chain reaction. 

Hydrolysis of 4-nitrophenyl acetate (NA) (0.5-2.0 mM) was catalyzed by 11 in 10% volume/volume (v/v) CH3CN aqueous solution under comicellar conditions with 10 mM Triton X-100 at pH 9.2 (20 mM CHES buffer) and 25°C (Scheme 7). The second-order dependence of the rate constant, obsd, on the concentration of NA (10-50 dM) and 11 (0.2-1.0 mM) at pH 10.2 (2 mM CAPS buffer) and 25°C with I = 0.10 (NaN03) fits the kinetic equation (5). No other reaction such as acetate transfer to Triton X-100 was observed, as confirmed by a H NMR experiment with a 10% D20 solution of 2.0 mM NA, 0.2 mM 3, and 10 mM Triton X-100. Since the second-order kinetics held after several catalytic cycles, it was concluded that the NA hydrolysis catalytic. In Equation (5), vobsd is the observed NA hydrolysis rate catalyzed by 3, as derived by subtraction of the buffer-promoted NA hydrolysis rate from total NA hydrolysis rate. 

The catalytic decomposition of N20 is regulated by the cycle Fc"/Fcm. N20 interacts with reduced Fe[[ site (Eq.16.1) to yield an extra-lattice oxygen Fe[[[-0 species, the so-called a-oxygen by Panov et al. (29). Most of studies have concluded that the removal of a-oxygen (Eq. 16.2) exhibits the lowest rate constant. The remarkable behavior of Fe exchanged in some zeolites could be ascribed to the occurrence of easily reduced and completely reversible Fe oxo-cation sites (28). TPR experiments by H2 and CO of N20-treated Fe-MFI (27) and Fe-BEA (33) have shown that such Fem-0 sites are much more reductible than those formed by 02 treatment. The influence of the zeolite on the reductibility of Fe species could be understand from quantum chemical calculations (DFT method) on model clusters of FAU and BEA containing Cu", Co" and Fe" cations (36). The calculations indicate that a charge transfer from zeolite to TM ion occurs of ca. one electron, and that the TM-zeolite system behaves like a supermolecule. Obviously, the addition of a reductant such as hydrocarbons (25, 26, 37, 38), CO (39, 40) or NH3 (41) boosts the N20 decomposition by a faster reduction of Fem-0 species. 

However, the studies on the hinge and Tyrl43 provided no information on the electron transfer from flavin-semiqumone to b 2-heme, the step which rate limits the catalytic cycle. In some elegant experiments, Tegoni et al. (1998) showed that the variation of the rate constant (In et) for this step correlates well with variations in the driving force (AG). Thus, this slow intra-molecular electron transfer is almost certainly controlled by thermodynamics. Tegoni et al. (1998) also provided some evidence that the faster, flavohydroquinone - b 2-heme, electron transfer may also be under thermodynamic control although this remains to be conclusively demonstrated. 

Hysteresis curves the elastic properties are determined by repeated extension and recovery at a constant rate between fixed limits (hysteresis behaviour, for example according to DIN 53835, five cycles to 300% extension). In the literature--- extensive work on the dynamometric properties of elastic fibres and rabber threads has been cited. From their experience with many complaints... 

Fig. 11. Suggested catalytic cycle for active MMOH (J. D. Lipscomb version). The cycle, compiled from 31, 48, 50, 53, 56, 63, 64,127-129,132,136,147-150), represents different compounds that have been characterized and some hypothetical compounds (K, R). The rate constants are from single-turnover experiments at 4°C 147).

In the case where both Ajn and Aout are fast, the ratio of the apparent forward and backward rate constants is identical with the dissociation constant determined by equilibrium methods. A different situation prevails in the range where the ratio Ain/A4 is very small. Under such a regime, the brief protonation-dissociation cycle will not propagate into the core, and the dynamics will be controlled only by the rate of the surface reactions. For such specific cases there will be a marked difference between the pKs, derived from the kinetic experiment, and pKobs obtained by equilibrium measurements. Consequently, it is only the accurate kinetic analysis that can furnish the precise description of the system and yields the information about the events that follow the protonation. 

Determine characteristic rate constants or characteristic times from experiments case 1 mean residence time t), mixing time cycle time (f ), OTR... 

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