Pseudo-order rate constants determination

Worked Example 8.17 The following kinetic data were obtained for the second-order reaction between osmium tetroxide and an alkene, to yield a 1,2-diol. Values of k are pseudo-order rate constants because the 0s04 was always in a tiny minority. Determine the second-order rate constant k2 from the data in the following table ... 

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... 

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),... 

Table 5.6 provides information taken from the kinetic reaction profile for Br" in Figure 5.7b. Use this information to determine a value for the pseudo-order rate constant in Equation 5.22. 

To siimmorize The initial rale method is essentially an isolation technique but it does not require that any reactants have to be in large excess. In general for a reaction involving two or more reactants, one of these is isolated by arranging that the initial concentrations of the others are held at fixed values during a series of experiments. The main application of the method is for the determination of partial order. Values of pseudo-order rate constants can be determined but with an accuracy that, in turn, depends on how accurately initial rates of reaction can be measured. 

Given the form of an experimental rate equation which has a particular order, determine the units in which the experimental rate constant, or pseudo-order rate constant, would typically be expressed. (Questions 4.2, 5.2, 5.3 and Exercise 5.2)... 

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

The value for the pseudo-first-order rate constant is determined by solving equation 13.6 for k and making appropriate substitutions thus... 

The initial anhydride concentration was about 3 x 10 M, and the amine concentration was much larger than this. The reaction was followed spectrophoto-metrically, and good first-order kinetics were observed hence, the reaction is first-order with respect to cinnamic anhydride. It was not convenient analytically to use the isolation technique to determine the order with respect to allylamine, because it is easier to observe the cinnamoyl group spectrophotometrically than to follow the loss of amine. Therefore, the preceding experiment was repeated at several amine concentrations, and from the first-order plots the pseudo-first-order rate constants were determined. These data are shown in Table 2-1. Letting A represent... 

Table 2-1. Determination of Reaction Order from Pseudo-First-Order Rate Constants ...

Reactions catalyzed by hydrogen ion or hydroxide ion, when studied at controlled pH, are often described by pseudo-first-order rate constants that include the catalyst concentration or activity. Activation energies determined from Arrhenius plots using the pseudo-first-order rate constants may include contributions other than the activation energy intrinsic to the reaction of interest. This problem was analyzed for a special case by Higuchi et al. the following treatment is drawn from a more general analysis. ... 

Kennedy and co-workers10 studied model cationic polymerization initiation and termination. They determined the effect of halogens in f-BuX and MeX on the rate of reaction between f-BuX and Me3Al. The pseudo second order rate constant decreased (Table 1) as ... 

To determine the rate constant one uses the same methods as mentioned under the first-order reaction, i.e. a plot of log[A] versus time. The product k[B]o assumes the role of a pseudo-first order rate constant, from which the true second-order rate constant is easily obtained. 

The successive equilibria are characterized by K12 and K23, respectively, and when Kl2 (often denoted K0) cannot be directly determined, it may be estimated from the Fuoss equation (3), where R is the distance of closest approach of M2+ and 1/ (considered as spherical species) in M OH2 Um x) +, e is the solvent dielectric constant, and zM and zL are the charges of Mm+ and Lx, respectively (20). Frequently, it is only possible to characterize kinetically the second equilibrium of Eq. (2), and the overall equilibrium is then expressed as in Eq. (4) (which is a general expression irrespective of mechanism). Here, the pseudo first-order rate constant for the approach to equilibrium, koba, is given by Eq. (5), in which the first and second terms equate to k( and kh, respectively, when [Lx ] is in great excess over [Mm+]. When K0[LX ] <11, koba - k,K0[Lx ] + k.it and when K0[LX ] > 1, fc0bs + k l. Analogous expressions apply when [Mm+] is in excess. 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

Pseudo-first-order rate constants (k0t,s) determined from the linear relationship of In (Am-At) with time, were calculated for different concentrations of catalyst. A pseudo-first-order rate constant was also calculated for the uncatalyzed hydrolysis at pH 8.5, and was substracted from the values found for the catalyzed hydrolysis. 

In the experiments carried out, the rate of hydrogenation was first order with respect to [C=C] from 30 to 90% conversion. Pseudo first order rate constants (k ) were determined for experiments over a range of conditions in order to measure the effect of different reaction parameters. The maximum hydrogenation rate constant recorded in this study was an order of magnitude less than the rate of H2 mass transfer10 and so gas uptake measurement reflected the inherent chemically controlled kinetics of the system. 

Use Guggenheim s method to determine the pseudo first-order rate constant. 

Under the conditions of the experiment, it is known that the reaction may be considered as irreversible. From the data below determine the order of the reaction with respect to benzoyl chloride and the pseudo reaction rate constant under these conditions. 

In aqueous solution the water concentration may be considered constant, so the reverse reaction follows pseudo first-order kinetics. The data below on this reaction have been taken from Emanuel and Knorre. Use them to determine the values of both first-order rate constants. 

The experimentally observed pseudo-first order rate constant k is increased in the presence of DNA (18,19). This enhanced reactivity is a result of the formation of physical BaPDE-DNA complexes the dependence of k on DNA concentration coincides with the binding isotherm for the formation of site I physical intercalative complexes (20). Typically, over 90% of the BaPDE molecules are converted to tetraols, while only a minor fraction bind covalently to the DNA bases (18,21-23). The dependence of k on temperature (21,24), pH (21,23-25), salt concentration (16,20,21,25), and concentration of different buffers (23) has been investigated. In 5 mM sodium cacodylate buffer solutions the formation of tetraols and covalent adducts appear to be parallel pseudo-first order reactions characterized by the same rate constant k, but different ratios of products (21,24). Similar results are obtained with other buffers (23). The formation of carbonium ions by specific and general acid catalysis has been assumed to be the rate-determining step for both tetraol and covalent adduct formation (21,24). 

Strategy. (1) We ascertain the order of reaction, (2) we determine the pseudo rate constant k , (3) from k , we determine the value of the second-order rate constant k2. 

Thus the value of pseudo-first order rate constant is k [Q]Totai 0/(1 + 0)-The value of 0 may be independently determined by analyzing organic phase for X and Nu ions. 

Specificity constant Defined as kcJKm. It is a pseudo-second-order rate constant which, in theory, would be the actual rate constant if formation of the enzyme-substrate complex were the rate-determining step. 

Figure 1. Competition kinetics for the Ru(NH2)62y reduction of Co([14 aneNk)-(0H,)0 Reactions at 25°C, pH 2, and n = 0.1(NaClO,). Individual pseudo-first-order rate constants were determined from the exponential (to four half-lives) decay of Co([14]aneN,)(OH2)022 absorbance at 360 nm. Reactions were performed by mixing a solution containing Ru(NH2)62 and Co([14]aneNh)(OHt) -(1 X I 3 M) with a solution saturated in 02(1.2 X 10 3 in an Aminco stopped-...

LFP-Probe Method. In cases where the radicals of interest do not contain a useful chromophore, the LFP technique can be modified by incorporation of a probe radical reaction that gives a product with a chromophore. The probe reaction can be unimolecular or bimolecular, a constant concentration of probe reagent is employed in the latter case. Formation of the detectable species occurs with an observed first-order or pseudo-first-order rate constant equal to k0. In the presence of another reagent X that reacts with the original radical, the rate constant for formation of detectable species is kohs = k0 + kx [X], and the bimolecular rate constant is determined (as before) by conducting the reaction at varying concentrations of X. Note that the LFP-probe technique is a direct method even though the reactant or product of interest is not monitored. 

To understand the pharmacokinetic relevance of the proxibarbal-valofan equilibrium, the kinetics and thermodynamics of the reaction were carefully examined in aqueous and biphasic media. The various pseudo-first-order rate constants shown in Fig. 11.19 were determined in the pH range of 6.7 - 8.0... 

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