Insertion rate constant

In pentane, the distribution of 1,3-insertion product 25 to 1,2-Me shift product 26 is 91 9. Upon addition of 2-methyl-1-butene, the yield of 25 smoothly decreases (to 19% with 4 M alkene), but the yield of 26 is unaffected 1 Moreover, correlation of addn/l,3-CH insertion (to 25) for 18 is nicely linear. The simplest interpretation is that 25 comes directly from carbene 18, whereas the 1,2-Me shift product 26 comes from the excited diazirine.27 Interestingly, thermolysis of 24 at 79°C produces 90% of 25 and 10% of 26, but now the yields of both products smoothly decrease in the presence of an alkene. In thermolysis the (electronically) excited diazirine is unavailable, both 25 and 26 stem from the carbene, and their formation is suppressed by the alkene s interception of the carbene. A pyridine ylide kinetic study gave the 1,3-CH insertion rate constant (18 - 25) as 9.3 x 10s s"1.27-47... 

Three distinct propagating species, each having different equilibrium olefin binding constants and insertion rate constants, are present. They are Cp2ZrH(olefin)+, Cp2ZrR (olefin)+ and Cp2ZrR(olefin)+. 

Insertion rate constants for endo-(Cp )2NbH(CH2CHR) complexes... 

From alkyl complex Po, the olefin can be captured to form the rt-complex tto, and inserted via 1,2- or 2,1-insertion route. In the model apphed here we consider the olefin capture and its insertion as one reactive event, i.e., we assume a pre-equihbrium between the alkyl and olefin complexes, described by an equilibrium constant =[Tto]/[Po]=exp (AG ,p ./RT). This corresponds to neglecting the barrier for the monomer capture. Such an approach is valid for the late-transition metal complexes, e.g., the diimine catalysts studied in the present work, where the resting state of the catalyst is a very stable olefin Ti-complex [16] and the olefin capture barrier and the related n-complex dissociation barrier is much lower than the insertion barriers. This assumption allows one to speed up the simulation otherwise many olefin capture/dissocia-tion steps, not important for the final result of the simulation, would be happening before insertion takes place. It follows from the above considerations that the insertion rate is given by Eq. (8), and the equation for the isomerisation vs insertion relative probability (Eq. 4) includes the isomerisation and insertion rate constants, the equilibrium constant, K omph <>nd the olefin pressure, polefin,- Finally, the relative probability for the two alternative insertions is given by Eq. (4) it depends on the two rate constants ratio only. 

As seen, the activation energy for fusion rapidly increases and grows to unfavorable values with increasing P. In comparison, fusion of dissimilar micelles is more probable. The most favored (lowest activation barrier), however, corresponds to the case where one of the fusing entities is a unimer. This corresponds to an insertion of a unimer into a micelle, which will have the following insertion rate constant ... 

Using Fqs. 52-53, one can eliminate one rate constant and express Eq. 50 in terms of the insertion rate constant ... 

For gas-phase reactions, Eq. (5-40) offers a route to the calculation of rate constants from nonkinetic data (such as spectroscopic measurements). There is evidence, from such calculations, that in some reactions not every transition state species proceeds on to product some fraction of transition state molecules may return to the initial state. In such a case the calculated rate will be greater than the observed rate, and it is customaiy to insert a correction factor k, called the transmission coefficient, in the expression. We will not make use of the transmission coefficient. 

Figure 13. Numerically calculated PMC potential curves from transport equations (14)—(17) without simplifications for different interfacial reaction rate constants for minority carriers (holes in n-type semiconductor) (a) PMC peak in depletion region. Bulk lifetime 10" s, combined interfacial rate constants (sr = sr + kr) inserted in drawing. Dark points, calculation from analytical formula (18). (b) PMC peak in accumulation region. Bulk lifetime 10 5s. The combined interfacial charge-transfer and recombination rate ranges from 10 (1), 100 (2), 103 (3), 3 x 103 (4), 104 (5), 3 x 104 (6) to 106 (7) cm s"1. The flatband potential is indicated.

Figure 14. PMC potential dependence, calculated from analytical formula (18) for different interfacial rate constants for minority carriers S = 1 cm, minority carrier flux toward interface I,- 1 cm-2s 1, a= 780enr1, L = 0.01 cm, 0=11.65 cmV, Ld = 2x 0"3cm), (a) sr = 0 and different charge-transfer rates (inserted in the figures in cm s 1), (b) Constant charge-transfer rate and different surface recombination rates (indicated in the figure).

Carbene itself is extremely reactive and gives many side reactions, especially insertion reactions (12-19), which greatly reduce yields. When it is desired to add CH2 for preparative purposes, free carbene is not used, but the Simmons-Smith procedure (p. 1088) or some other method that does not involve free carbenes is employed instead. Halocarbenes are less active than carbenes, and this reaction proceeds quite well, since insertion reactions do not interfere.The absolute rate constant for addition of selected alkoxychlorocarbene to butenes has been measured to range from 330 to 1 x 10 A few of the many ways in... 

The second CSTR has the same rate constant and residence time, but the dimensionless rate constant is now based on (n, )2 = 0.618a rather than on Uin- Inserting A t2(am)2 = = (0-5)(0.618) = 0.309 into Equation... 

More complicated rate expressions are possible. For example, the denominator may be squared or square roots can be inserted here and there based on theoretical considerations. The denominator may include a term k/[I] to account for compounds that are nominally inert and do not appear in Equation (7.1) but that occupy active sites on the catalyst and thus retard the rate. The forward and reverse rate constants will be functions of temperature and are usually modeled using an Arrhenius form. The more complex kinetic models have enough adjustable parameters to fit a stampede of elephants. Careful analysis is needed to avoid being crushed underfoot. 

Figure 2. Inhibition of eel AChE by ANTX-A(S) - the secondary plot. P, the first-order rate constant which was the rate of inhibition at that ANTX-A(S) concentration obtained from the primary plot (insert). The intercept on the 1/P axis is 1/k and the intercept on the 1/[I] axis is -1/K. Figure insert Progressive irreversible inhibition of eel AChE by ANTX-A(S). The inactivation followed first-order kinetics. ANTX-A(S) concentrations, xg/mL (A) 0.083 ( ) 0.166 (o) 0.331 ( ) 0.497 (V) 0.599 ( ) control. Each point represents the mean of 3 or 4 determinations.

Fig. 34. Arrhenius plot of In k versus 1/T for PSS-doped [Fe(6-Mepy)2(py)tren](CI04)2 for the temperature range 50 to 300 K. Here k is the relaxation rate constant, the straight line representing a least squares fit of the 150-300 K data producing AE = 823 cm". The insert shows k versus T between 4.2 and 50 K. According to Ref. [138]...

The theoretical approach involved the derivation of a kinetic model based upon the chiral reaction mechanism proposed by Halpem (3), Brown (4) and Landis (3, 5). Major and minor manifolds were included in this reaction model. The minor manifold produces the desired enantiomer while the major manifold produces the undesired enantiomer. Since the EP in our synthesis was over 99%, the major manifold was neglected to reduce the complexity of the kinetic model. In addition, we made three modifications to the original Halpem-Brown-Landis mechanism. First, precatalyst is used instead of active catalyst in om synthesis. The conversion of precatalyst to the active catalyst is assumed to be irreversible, and a complete conversion of precatalyst to active catalyst is assumed in the kinetic model. Second, the coordination step is considered to be irreversible because the ratio of the forward to the reverse reaction rate constant is high (3). Third, the product release step is assumed to be significantly faster than the solvent insertion step hence, the product release step is not considered in our model. With these modifications the product formation rate was predicted by using the Bodenstein approximation. Three possible cases for reaction rate control were derived and experimental data were used for verification of the model. 

When the hydrogenation insertion is the rate-controlling step, the rate constant k is much smaller than the two other rate constants koi and k2o- Hence, the... 

Like other metal reactions studied previously in our laboratory, H2 elimination is initiated by insertion into one of the C-H bonds forming HMC3H5. The reaction rate constant for Y + cyclopropane was found to be very small at room temperature, 0.7 x 10 12 cm3 s 1, and it was suggested that the reaction most likely involved termolecular stabilization of C-H or C-C insertion complexes, rather than molecular elimination.22 By analogy with other systems studied, the dynamically most favorable route to H2 loss in this case is likely via H atom migration to the Y-H moiety, with concerted... 

Studies have been carried out on the methylated complex [H3C-Niin(17)(H20)]2+, which is obtained from the reaction of methyl radicals (generated by pulse radiolysis) with [Ni(17)]2+. The volumes of activation are consistent with the coherent formation of Ni—C and Ni—OH2 bonds, as expected for the generation of a Ni111 complex from a square planar Ni11 precursor.152 The kinetics of reactions of [H3C-Niin(17)(H20)] + involving homolysis, 02 insertion and methyl transfer to Crn(aq) have been determined, and intermediates have been considered relevant as models for biological systems.153 Comparing different alkyl radicals, rate constants for the... 

Zinc is also used in biological studies to gain information about non-zinc containing systems. It can be a convenient redox inactive replacement for the study of complex systems with multiple redox centers. For example, the mechanism of quenching the triplet state of zinc cytochrome c by iron(II) and iron(III) cytochrome c has been studied. Zinc insertion has been used to get around the difficulty of studying two heme proteins with the same absorption spectra and provides rate constants for iron and iron-free cytochrome c quenching.991... 

The metalloalkyne complex Ru ( )-CH=CH(CH2)4C CH Cl(CO)(P,Pr3)2 exhibits behavior similar to that of cyclohexylacetylene (Scheme 10).40 Thus, it reacts with OsHCl(CO)(P Pr3)2 to give the hydride-vinylidene derivative (P Pr3)2 (CO)ClRu ( )-CH=CH(CH2)4CH=C OsHCl(CO)(P,Pr3)2, which evolves in toluene into the heterodinuclear-pi-bisalkenyl complex (P Pr3)2(CO)ClRu (is)-CH=CH(CH2)4CH=CH-( ) OsCl(CO)(P,Pr3)2. Kinetic measurements between 303 and 343 K yield first-order rate constants, which afford activation parameters ofAH = 22.1 1.5, kcal-mol-1 andAS = -6.1 2.3 cal-K 1-mol 1. The slightly negative value of the activation entropy suggests that the insertion of the vinylidene ligand into the Os—H bond is an intramolecular process, which occurs by a concerted mechanism with a geometrically highly oriented transition state. 

Kinetic studies (31P- and H-NMR) both of the direct reaction of 14 with TMS and of the rearrangement of 24 resulted in rate constants which were inconsistent with our original picture of C-Si activation exclusively via C-H insertion. The separate 1st order rearrangement of 24 occurs so slowly that 24, were it the only intermediate in the reaction of TMS with the [(dtbpm)Pt(O)] fragment, would accumulate and lead to an experimentally observable concentration, which was never observed in the kinetic runs. 

The nature and distribution of the products of an olefin oligomerization reaction will depend, inter alia, on the relative rate constants of the insertion step (ki)vs. the displacement step (fcd) [Eq. (11)] ... 

In general, 1,2-C shifts do not compete effectively with the 1,2-H shifts of acyclic alkyl and alkylhalocarbenes. However, r-butylchlorocarbene (18) lacks the a-H needed for a 1,2-H shift, and so affords 1,3-CH insertion and 1,2-Me migration Eq. 14. Note that only for the thermally generated 18 is the 1,2-Me shift product (26) derived from the carbene. Photolytic generation of 18 from diazirine 24 gives only 1,3-CH insertion to dimethylchlorocyclopropane 25 in this case, the 1,2-Me shift product is formed by RIES of the diazirine.27 Based on the rate constant for the 1,3-CH insertion of t-BuCCl at 25°C (9.3 x 105 s 1), we can estimate A 105 s 1 for the 1,2-Me shift at 78°C. 

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