Rate constant determination for

A simpler phenomenological form of Eq. 13 or 12 is useful. This may be approached by using Eq. 4 or its equivalent, Eq. 9, with the rate constants determined for Na+ transport. Solving for the AG using Eqn. (3) and taking AG to equal AHf, that is the AS = 0, the temperature dependence of ix can be calculated as shown in Fig. 16A. In spite of the complex series of barriers and states of the channel, a plot of log ix vs the inverse temperature (°K) is linear. Accordingly, the series of barriers can be expressed as a simple rate process with a mean enthalpy of activation AH even though the transport requires ten rate constants to describe it mechanistically. This... 

Figure 4. Arrhenius plot of rate constants determined for 600K MW polystyrene samples.

Figure 6. Reservoir sizes, residence times, and 5 Fe values for aqueous Fe(II), as calculated for DIR assuming first-order rate laws. Timescale arbitrarily set to 100 days. Calculations based on rate constant determined for a 23 day DIR experiment involving hydrous ferric oxide (HFO) by S. algae (Beard et al. 1999). The percent total reduction at 100 days is shown in the grey box on the lower right side of the lower diagrams, based on the value of k. Parts A-C assume a 2/ 1 ratio of 10, whereas parts D-F assume Bikjki ratio of 1000. As constrained by first-order rate laws, the proportion of the intermediate products Fe(III)-L, followed by Fe(II)-L, increase before substantial accumulation of the final Fe(II)aq product (Parts A and D). Tlie fraction of Fe(III)-L in the exchangeable pool of Fe (Fe(III)-L + Fe(II)-L + Fe(II)aq) decreases with time, primarily due to accumulation of the Fe(II)aq end product, where the rate of change is a function of the kjk ratio.

The observed rate constants determined for the exchange of C-MeOAc with C-Mel at 180 °C in AC2O/ACOH over a range of concentrations of Lil, Nal, and [QASjl are shown in Figure 5.10 [29], It can be seen that the rate increases progressively with concentration for all the salts, and while the effect of Nal or [QAS]I is very similar, Lil is up to twice as effective on a molar basis. 

Initial yields for conversion to the trans-vinylene isomer can be derived by adding to the apparent yield the rate of destruction calculated from the initial concentration of trans-vinylene groups and the first-order rate constants determined for the amorphous trans polymer. The initial yield of trans-vinylene groups is 6.8 for gamma radiation and 4.4 for the reactor. The value for gamma radiation is similar to Golub s value of 7.2 for both gamma and electrons. 

A completely contrasting situation is shown in Fig. 14.1CW. Here, krel represents the ratio of apparent zero-order rate constants determined for the reduction of the model... 

Hence, these Qc values are a quantitative measure for the relative affinities of the various NACs to the reactive sites. Figs. 14.10e and/show plots of log Qc versus h(AtN02)/0.059 V of the 10 monosubstituted benzenes. A virtually identical picture was obtained for the log Qc values derived from an aquifer solid column and from a column containing FeOOH-coated sand and a culture of the iron-reducing bacterium, Geobacter metallireducens (GS15). Furthermore, a similar pattern (Fig. 14.10c) was found when correlating relative initial pseudo-first-order rate constants determined for NAC reduction by Fe(II) species adsorbed to iron oxide surfaces (Fig. 14.12) or pseudo-first-order reaction constants for reaction with an iron porphyrin (data not shown see Schwarzenbach et al., 1990). Fig. 14.12 shows that Fe(II) species adsorbed to iron oxide surfaces are very potent reductants, at least for NACs tv2 of a few minutes in the experimental system considered). 

Results of a study of electrostatic acceleration of enolization in cationic ketones have implications for enzymatic catalysis of enolization.136 Rate constants determined for water-, acetate- and hydroxide ion-catalysed enolizations of cationic ketones (79) (pK 11.13) and (80) (pK 11.90) have been compared with those for (81). It has been estimated that the inductive effects of the charged lings lower the p/y,s of (81) and (79) by 4.2 and 1.2 log units, respectively, whereas for (79) the electrostatic effect lowers the pAa by 6.3 log units, and enhances oh by 330-fold relative to a typical methyl ketone. The rate of enolization of (81) is enhanced 2.3 x 104-fold by the through-space electrostatic effect. 

Mezyk SP (1995) Rate constant determination for the reaction of sulfhydryl species with the hydrated electron in aqueous solution. J Phys Chem 99 13970-13975 Mezyk SP, Bartels DM (1995) Direct EPR measurement of Arrhenius parameters for the reactions of H atoms with H2O2 and D atoms with D2O2 in aqueous solution. J Chem Soc Faraday Trans 91 3127-3132... 

We have found that sulfite and bisulfite undergo one-electron oxidation by many free radicals to produce S03. Rate constants determined for selected radicals are given in Table 1. Measurement of the rate constant over a wide range of pH has, in some cases, allowed the separate determination of rate constants for the oxidation of sulfite and bisulfite. The very strong oxidant OH reacts very rapidly and oxidizes bisulfite faster than sulfite, possibly due to a contribution from hydrogen atom abstraction. For radicals which are relatively weaker oxidants, the reaction with sulfite is the faster. For example, with Br2 the ratio of rate constants for sulfite to bisulfite is about 4 for the even weaker... 

Maldotti A, Chiorboli C, Bignozzi CA, et al. 1980. Photooxidation of 1,3-butadiene containing systems rate constant determination for the reaction of acrolein with hydroxyl radicals. Int J Chem Kinet 12 905-913. 

A second example is illustrated by the V-Tricine system (25). Its EXSY spectrum, revealing intramolecular exchange, is shown in Figure 10. The V-Tricine complex differs from the V-TEA complex in that the two-pendent hydroxymethyl arms are inequivalent (an ABC system) (46). The rate constants determined for the coordinated arm exchanging with each pendent arm [fc(C4b - C5f) and fc(C4b - C6f)] are very similar (25). Assuming the chemical event is the formation of a single species from which the two pendent arms and the chelated arm is derived, each rate represents only one-third of the exchange rate as shown in equation 6 ... 

When the carbocations are generated by Laser flash photolysis, the ion pair collapse with the nucleophilic counterion Cl- is so fast [136] that the decay cannot be followed with the instrumentation used for these experiments, i.e., only those carbocations which manage to escape from the [Aryl2CH + Cl ] ion pair can be observed. Consequently, all rate constants determined for the Laser photolytically produced carbocations refer to the reactions of the nonpaired entities. 

The consistency of the rate constants determined for the reaction of methylene-cyclopentane with stable carbocation salts in CH2C12 and with... 

Mezyk SP. (1995) Rate constant determination for the reaction of sulfliydryl species with the hydrated electron in aqueous solution. J Phys Chem 99 13970-13975. 

It is of interest to compare the rate constants determined for intramolecular ET in Ps-NiR (23 s at 298 K, pH 7.0) with the corresponding ones reported for Pa- and Pp-NiRs (cf. Table V). An early stopped-flow study of the reduction kinetics of Pa-NiR by an excess of reduced azurin yielded a rate constant of... 

A second important lesson from the radical clock experiments relates to the extremely large rate constants determined for the radical recombination step with substrate 22. The rate constant of 1.5 x 10 s is on the time-scale of a bond... 

Rate constant determined for OH + CO at room temperature and low pressure (89). 

Additional experiments were carried out (264) for the reaction of OH radicals with toluene to verify the observed behavior. An increase In the total pressure (argon diluent) from 100 + 2 torr to 200 + 2 torr at 325.3, 378.4, and 424.4 K had no effect on the rate constants within the experimental errors (+5-10%) and, furthermore, the addition of 2.0 torr O2 at 397.4 K and 2.3 torr O2 at 352.6 K had no effect (within +10-15%) on the rate constants. Less extensive rate data for the reaction of OH radicals with toluene-dg (264) showed similar behavior. Thus the rate constant at 298 K was within 5% of that for toluene (Table 9), while the rate constant determined for toluene-dg at 432 K was a factor of 2.5 lower than that for toluene at 424 K. 

Relative rate constant data placed on an absolute basis using the absolute room-temperature rate constant determined for the reaction of S( P) atoms with (290). 

Also included on Fig. 8 is the rate constant determination for reaction (2) in a flame by Fenimore and Jones (9). The line drawn in this region for the temperature dependence of the direct reaction (2) corresponds to an Arrhenius form. It has a frequency factor 2 x 10" cm sec and activation energy of 9 kcal/mole, estimated respectively by the OH + CH A-factor and an estimate of AH for reaction (2) coupled with a 2 kcal/mole barrier. While this forms a reasonable description of the two experimental results, it would be desirable to measure points intermediate in temperature. 

Table 2. Second order rate constants determined for the reactions between chromate and some thiols, dithiols and ascorbate.

Summary of Experimental and Simulated Rate Constants Determined for All Kinetic Experiments at 20 C in Which Both the H2O2 and Cysteine Concentrations Were Varied ... 

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