Relative rate constant

Table 1.2. Relative rate constants of some selected Diels-Alder reactions in water compared to organic solvents of different hydrogen bond donor capacities.

The relative basicities of aromatic hydrocarbons, as represented by the equilibrium constants for their protonation in mixtures of hydrogen fluoride and boron trifluoride, have been measured. The effects of substituents upon these basicities resemble their effects upon the rates of electrophilic substitutions a linear relationship exists between the logarithms of the relative basicities and the logarithms of the relative rate constants for various substitutions, such as chlorination and... 

Table 3 Heteroatom and Benzo-fusion Effects on Relative Rate Constants for N-Methylation (rs.-VHCizziri)...

Fig. 10. Plots of the relative rate constants of the hydrolysis of dextrin vs. the mole ratio of vinylalcohol unit to vinylsulfonic acid unit, o PVS VA, Polyvinylalcohol + HPVS (Ref.

An interesting method, which also makes use of the concentration data of reaction components measured in the course of a complex reaction and which yields the values of relative rate constants, was worked out by Wei and Prater (28). It is an elegant procedure for solving the kinetics of systems with an arbitrary number of reversible first-order reactions the cases with some irreversible steps can be solved as well (28-30). Despite its sophisticated mathematical procedure, it does not require excessive experimental measurements. The use of this method in heterogeneous catalysis is restricted to the cases which can be transformed to a system of first-order reactions, e.g. when from the rate equations it is possible to factor out a function which is common to all the equations, so that first-order kinetics results. 

Tabic 1.2 Relative Rate Constants and Regiospecificities for Addition of Radicals... 

Relative rate constants for reaction of methyl, trifluoromethyl, trichloromethyl,13 and t-butoxy radicals22,23 with the fluoro-olcfins arc summarized in Table 1.2. Note the following points ... 

Tabic 1.3 Relative Rate Constants for Reactions of Radicals with Alkyl-Substituted Acrylate Esters CHR CFEcOaCHs"... 

Figure 1.3 Relative rate constants for addition of alkyl radicals to fumarodinitrilc (k ) and methyl a-chloroacrylate (kz) as a function of temperature (Scheme 1.6).65...

Figure 3.6 Relative rate constants for (3-seission of /-alkoxy radicals at 60 C,4 1...

Labeled initiators have been used in evaluating the relative reactivity of a wide range of monomers towards initiating radicals.159 The method involves determination of the relative concentrations of the end groups fanned by addition to two monomers (e.g. 119 and 120) in a binary copolymer formed with use of a labeled initiator. For example, when AlBMe-a-13C is used to initiate copolymerization of MMA and VAc (Scheme 3.99),157 the simple relationship (eq. 14) gives the relative rate constants for addition to the two monomers. Copolymerizations studied in this way arc summarized in Tabic 3.13. 

A mode] study has demonstrated the pathways shown in Scheme 4,17. The first cyclization step gave predominantly five-membered rings, the second a mixture of six- and seven-membered rings.155 Relative rate constants for the individual steps were measured. The first cyclization step was found to be some five-fold faster than for the parent 5-hexenyl system. Although originally put forward as evidence for hyperconjugation in 1,6-dienes, further work showed the rate acceleration to be sterie in origin.113-I3j... 

In summary, the order of reactivity for the most commonly used ruthenium-based metathesis catalysts was found to be 56d>56c>9=7. This order of reactivity is based on IR thermography [39], determination of relative rate constants for the test reaction 58—>59 (Eq. 8) [40], and determination of turnover numbers for the self metathesis of methyl-10-undecenoate [43]. 

Elucidation of Relative Rate Constants Using GPC Data.125... 

While the effect of monomer concentration [M] on Mv of PIB has been studied by a number of workers using a ariety of initiator systems11-13, such studies have not yet been carried out using M . The objective of this phase of research was to determine the effect of [M] on M and thus to calculate relative rate constants of isobutylene polymerization from GPC data. 

This section concerns studies directed toward an elucidation of relative rate constants, k,./kp and kt/kp, and a mechanistic interpretation of these parameters. The data for the HMWF of PIB samples prepared with 7-BuCl and f-BuBr/Et2AlCl/MeCl systems shown in Table 7 were calculated from Mayo plots (see also p. 56 for Mayo Equation) using M data given in Tables 4 and 5. The data of LMWF of PIB prepared with f-BuBr/Et2AlCl/MeCl system at —50 °C shown in Table 7 were calculated from Mayo plots using M data given in Table 5. 

Mayo plot provides relative rate constants of the molecular weight controlling events22. Transfer and/or termination with solvent, polymer and impurities are assumed to be negligible. Although the Mayo equation is strictly valid only for data obtained at low conversion, Plesch23 has shown that the plot provides remarkably reliable information even with data obtained at relatively high conversions. 

Comparisons of relative rate constants obtained with Mv s of the total polymer and M s of the HMWF for the same samples show similar trends negligible transfer and termination control of molecular weights for the f-BuCl/Et2AlCl/MeCl system in the —40° to —60 °C range and also for the f-BuBr/Et2AlCl/MeCl at —50 °C (Table 7). For the samples prepared with the f-BuCl/Et AlCl system Mayo plots based on Mv s show zero intercept while that based on Mn s of the HMWF shows a small but finite intercept, z., ktr/kp = 1.91 x 10-5 and 2.14 x 10-s at —50° and -60 °C. Similarly, for the samples prepared with the t-BuBr/Et2AlCl system the Mayo plot based on Mn s of HMWF shows zero intercept while the Mayo plot based on Mv s show a very small intercept, ie., ktr/kp = 5.0 x 10-s at —50 °C. The reasons for this small discrepancy are not known. 

Table 4.16 Micellar catalysis of Diels-Alder reactions of cyclopentadiene (1) with 3-(p-substituted phenyl)- -(2-propen-1-one (113) in water at 25 °C. Relative rate constants ( rei) to the reactions performed in sole water...

All products were identified and followed by GC/MS. The lateral positions (C-2, C-3) of 1,2,3,4-TBDD are slightly more reactive compared to the peri positions (C-1, C-4) the two Br3Cl-isomers appear in a ratio of approximately 1 1,5. The relative rate constants of 5 aromatic bromine compounds were determined (Table 3). 

Table 3. Relative rate constants (Kfgi) and half lifes (tj/2> for a mixture of aromatic bromine compounds calculated from the concentrations of educts after reaction with 3.5 g fly ash containing chlorine. 

TABLE 6.1 Relative Rate Constants at 50°C (Eight-Membered Ring = 1) for the Reaction... 

---