Second-order rate constant of reaction

Relative second-order rate constants of reactions performed in water in the presence and absence of CD. 

Analysis of the variation of the overall rate constant of reaction with [surfactant] was discussed in Section 3 (p. 222) and the treatment allows calculation of the second-order rate constants of reaction in the micellar pseudophase. These rate constants can be compared with second-order rate constants in water provided that both constants are expressed in the same dimensions and typically the units are M-1 s-1. Inevitably the comparison... 

Worked Example 8.16 The reaction of the ester ethyl methanoate and sodium hydroxide in water is performed with NaOH in great excess ([NaOH]o = 0.23 mol dm-3). The reaction has a half-life that is independent of the initial concentration of ester present. 13.2 per cent of the ester remains after 14 min and 12 s. What is the second-order rate constant of reaction k2l... 

Table 11.2 Influence of additives on the second-order rate constants of reaction (11.7) at 25°C in water, (from Lubineau et al. 1994) (reproduced with kind permission from Gauthier-Villars, 1994)...

Table 3.1 summarises the influence of the diamine ligands on the equilibrium constant for binding of 3.8c to the ligand-metal ion complex (K ) and the second-order rate constant for reaction of the ternary complex (ICjat) (Scheme 3.5) with diene 3.9. 

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%. 

Studies of micellar catalysis of himolecular reactions of uncharged substrates have not been frequent" ". Dougherty and Berg performed a detailed analysis of the kinetics of the reaction of 1-fluoro-2,4-dinitrobenzene with aniline in the presence of anionic and nonionic surfactants. Micelles induce increases in the apparent rate constant of this reaction. In contrast, the second-order rate constant for reaction in the micellar pseudophase was observed to be roughly equal to, or even lower than the rate constant in water. 

The effect of micelles of SDS, CTAB and C12E7 on the apparent second-order rate constants of the Diels-Alder reaction between nonionic 5.1a, anionic 5.1 f and cationic 5.1g with 5.2 is reported in Table 5.1. These apparent rate constants are calculated from the observed pseudo-first-order rate constants by dividing the latter by the overall concentration of 5.2. 

When the dienophile does not bind to the micelle, reaction will take place exclusively in the aqueous phase so that the second-order rate constant of the reaction in the this phase (k,) is directly related to the ratio of the observed pseudo-first-order rate constant and the concentration of diene that is left in this phase. 

TABLE 8. Second-order rate constants for reactions of 9-R-fluorenyl carbanions with a-halosulfones and sulfoxides in Me2SO solution at 25 °c63a-87... 

TABLE 7.6 Second-Order Rate Constants for Reaction of Phenolic Monomers with Formaldehyde"... 

In contrast to the reactions shown in Scheme 3, the complex OsHCl(CO)(P Pr3)2 reacts with cyclohexylacetylene at room temperature to give the hydride-vinylidene derivative OsHCl(C=CHCy)(CO)(P Pr3)2 in 70% yield (Scheme 8).37 Kinetic measurements yield a second-order rate constant of (6.0 0.2) x 10 3 at... 

These investigators report that the second-order rate constant for reaction B is equal to 1.15 x 10 3 m3/mole-ksec at 20 °C. Determine the volume of plug flow reactor that would be necessary to achieve 40% conversion of the input butadiene assuming isothermal operating conditions and a liquid feed rate of 0.500 m3/ksec. The feed composition is as follows. 

The rate constant for the exponential relaxation of the latter system to the starting system was calculated to be 1.4 x 10 s . From this value, an approximate second order rate constant of 1.0 x 10 L mol" -s"l was calculated for the reaction between IV and CO. Given the above determination of the limiting rate constant for CO dissociation... 

The basicity constants in water and micelles then have the same units (M 1), and values of K and Kb are not very different for arenimidazoles and nitroindoles under a variety of conditions (Table 10). The comparisons suggest that inherent basicities are not very different in water and cationic micelles, but, as with second-order rate constants of bimolecular reactions (Section 5), there is a limited degree of specificity because K /Kb is slightly larger for the nitroindoles than for the arenimidazoles, almost certainly because of interactions between the cationic micellar head groups and the indicator anions. 

The Bransted plots for the (La3 + ( OCH3))2 and 9 Zn2 + ( OCH3)-catalyzed methanolyses of 20 and 21 shown in Figs 7 and 8 exhibit gradients that are much steeper than the corresponding Bra ns ted plots for the methoxide reactions. This is easily visualized in the log/log plot of the second-order rate constants of the metal-catalyzed reactions vs. the methoxide reaction which is shown in Fig. 12 where the gradient of the La3+ plot is 1.94 + 0.10 while that for the 9 Zn2+( OMe) plot is 1.49 + 0.11. The situation for the phosphorothioates is not nearly so pronounced since the similar plots for series 21 (not shown) has a gradient for the La3+ plot of 1.15 + 0.10 while that for the 9 Zn2 + ( OMe) plot is 0.99 0.06.17c... 

Most importantly, the direct reaction of anisole cation radical with N02 (64) is established by the pseudo-first-order kinetics observed for the disappearance of AN+- in the presence of added N02 (see Fig. 16A). The magnitude of the second-order rate constant of k2 = 1.5x109m i s evaluated in this way is thus consistent with the spectral decay of the freely diffusing aromatic cation radical (AN+<) in Fig. 15. 

The reverse reaction of lactonization of pilocarpic acid is proton-catalyzed and, hence, favored at low pH. Thus, the pilocarpine/pilocarpic acid ratio was 1.0, 1.6, 2.7, 4.0, 5.1, and 6.7 at pH values of 6.0, 5.6, 5.2, 4.8, 4.4, and 4.0, respectively [161]. Interestingly, the lactonization of isopilocarpic acid is ca. 17-fold faster than the lactonization of pilocarpic acid, since the second-order rate constants of proton-catalyzed lactonization at 25° were 0.96 and 0.055 M-1 min-1 for isopilocarpine and pilocarpine, respectively [162], A lack of planarity in the lactone ring of pilocarpine, and a more lac-tone-like planarity in isopilocarpine, appear to account for this difference in reactivity between the two epimers. 

The second-order rate constants for reaction of Co(NH3)jL" (A ) and Co(ND3)jL" (Atd) with and Cr " have been measured. Explain the results shown... 

The second-order decay of the three-coordinate transient (to form a dimer, k = 2 X lO M s ) can be accelerated in the presence of substrates, Ph3P, CO etc. The second-order rate constant for reaction with CO, 1.0 x 10 M s is consistent with an early... 

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