First-order rate constant determination

Fig. 2. Hexane cracking with HZSM-5 (Si/AI = 35) at 538°C. a. First order rate constant determined at different hexane pressures, b. First order plot of conversion (e) at different contact times, hexane pressure = 10 torr.

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. 

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). 

As an example, we consider the oxidation of a series of monosubstituted anilines by Mn02 in batch systems. In this case, quite a good correlation between log kK (expressed relative to R of 4-chloroaniline) and E]/2(ArX ) is obtained (Fig. 14.20). The slope of -0.54 indicates that, similar to what we have postulated for the reduction of NACs by surface-bound Fe(II) (see Fig. 14.10 /), the overall reaction rate is determined not solely by the actual electron transfer but also by other steps such as precursor complex formation. Comparable results (slopes of between-0.5 and -0.6) were obtained for the reaction of Mn02 at pH 4 with a series of substituted anilines (Laha and Luthy, 1990), and with a series of substituted phenols at pH 4.4 (Stone, 1987). In all these cases, only initial pseudo-first-order rate constants determined with clean Mn02 were considered. In the presence of solutes such as Mn2+ that may adsorb to the oxide surface, much slower reaction rates and much... 

The irreversible, first-order reaction of gaseous A lo B occurs in spherical catalyst pellets with a radius of 2 mm. For this problem, the molecular diffusivity of A is 1.2 X 10" cm s and the Knudsen diffusivity is 9 X 10 " cm s. The intrinsic first-order rate constant determined from detailed laboratory measurements was found to be 5.0 s . The concentration of A in the surrounding gas is 0.01 mol L . Assume the porosity and the tortuosity of the pellets are 0.5 and 4, respectively. 

Morpholinopropiophenone proved to be a more suitable system (Carsky et al., 1964). The increase in the more positive phenyl vinyl ketone wave (Fig. 12) at pH < 7 5 followed first-order kinetics. The logarithm of the wave-height was a linear function of time for conversions below 80%. The first-order rate constant, determined from slopes of such plots, was measured at various pH-values. The plot of the rate constants against pH possesses a form of a dissociation curve (Fig. 11) with an inflexion point corresponding to p K mb =... 

As an example, in Table 6, the pseudo-first-order rate constants determined by Jafvert and Wolfe (1987) are given for the disappearance of some polyhalo-genated ethanes in an anaerobic sediment-water mixture. For all compounds, the most important reaction mechanism was found to be vicinal dehalogenation (reaction 8 in Table 1). As can be seen, in this system, an appreciable fraction of all compounds (particularly, the hydrophobic compound hexachloroethane) was present in the sorbed form. We should note, however, that unlike the case of surface complexation of hydrophilic compounds at oxide surfaces, (e.g., ill encountered in the oxidation of phenols by manganese oxides, see Stone, 1987),... 

A great many model systems that have been studied by electroanalytical methods are available for comparison with sono-voltammetric measurements. The reduction of halogenated aromatic compounds is known to cause in many cases the cleavage of the carbon halide bond with a first-order rate constant determined by the properties of the molecule. From the known range of accessible diffusion layer thicknesses in sonovoltammetry, ca. 1-15 xm, unimolecular rate constants ranging from 10 to 10" s are accessible. The reduction of 3-bromobenzophenone and ortho-bromonitrobenzene in DMF [66] may be described by the ECE type mechanism given in Eqs. 7(a-d). 

Consider the thermolysis of compound 58 to 59 (equation 6.41). Experimental temperatures and first-order rate constants determined at those temperatures are shown in the first two columns of Table 6.2. Note that the second column is labeled "k x 10 (s )." This means that the experimental rate constants have units of s and that the numerical values were multiplied by 10 for the convenience of listing in the table. Therefore, the observed rate constant at 324.8°C is 1.27 x 10- s . The third column lists the inverse of the reaction temperature in K. As an example, the inverse of (273.15 -I- 324.8) is 0.001672. The fourth column is the natural logarithm of the rate constant. For example. In 0.00127 is -6.669. Plotting the parameters in the second two columns produces Figure 6.18. The slope of the best-fit line through the data points is —23295, which equals —Eg/R. Multiplying the slope by the value of —R therefore gives an Eg of 46,286 cal/mol = 46.3 kcal/mol. The value of In A is 32.3. Traditionally, chemists report values of... 

Theoretical studies of the gas-phase hydrolysis or methanolysis of methylsul-fonyl chloride indicated a concerted Sn2 process involving a four-membered cyclic transition state. The tertiary amine-catalysed hydrolysis of benzenesul-fonyl chloride was shown to be inhibited by chloride ion and a nucleophilic mechanism of catalysis was favoured. Kinetic studies" of the solvolysis of p-substituted benzenesulfonyl chlorides in aqueous binary mixtures with acetone, methanol, ethanol, acetonitrile and dioxime showed that the reactions were third order processes, with first order rate constants determined mainly by the molar concentrations of the protic solvent, so that the reaction rates appear to be dominated by solvent stoichiometry. The solvolyses in methanol and ethanol yield both an alcoholysis (ap) and a hydrolysis product (hp). Solvolyses of electron-rich arylsulfonyl chlorides, under neutral or acidic conditions, exhibited surprising maxima in solvent-dependent S values as defined by Equation 15. 

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