Absolute rate

Rosenstock H M, Wallenstein M B, Wahrhaftig A L and Frying H 1952 Absolute rate theory for isolated systems and the mass spectra of polyatomic molecules Proc. Natl Acad. Sci. USA 38 667-78... 

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

Quack M 1979 Quantitative comparison between detailed (state selected) relative rate data and averaged (thermal) absolute rate data for complex forming reactions J. Phys. Chem. 83 150-8... 

Tominaga K, Kliner D A V, Johnson A E, Levinger N E and Barbara P F 1993 Femtosecond experiments and absolute rate calculations on intervalence electron transfer of mixed-valence compounds J. Chem. Rhys. 98 1228—43... 

Finally, exchange is a kinetic process and governed by absolute rate theory. Therefore, study of the rate as a fiinction of temperature can provide thennodynamic data on the transition state, according to equation (B2.4.1)). This equation, in which Ids Boltzmaim s constant and h is Planck s constant, relates tlie observed rate to the Gibbs free energy of activation, AG. ... 

These experiments yield T2 which, in the case of fast exchange, gives the ratio (Aoi) /k. However, since the experiments themselves have an implicit timescale, absolute rates can be obtained in favourable circumstances. For the CPMG experiment, the timescale is the repetition time of the refocusing pulse for the Tjp experiment, it is the rate of precession around the effective RF field. If this timescale is fast witli respect to the exchange rate, then the experiment effectively measures T2 in the absence of exchange. If the timescale is slow, the apparent T2 contains the effects of exchange. Therefore, the apparent T2 shows a dispersion as the... 

Quack M, Sutcliffe E, Hackett P A and Rayner D M 1986 Molecular photofragmentation with many infrared photons. Absolute rate parameters from quantum dynamics, statistical mechanics, and direct measurement Faraday Discuss. Chem. Soc. 82 229-40... 

Bonanno R, Boulmer J and Weiner J 1983 Determination of the absolute rate oonstant for assooiative ionization in... 

There are a few cases where the rate of one reaction relative to another is needed, but the absolute rate is not required. One such example is predicting the regioselectivity of reactions. Relative rates can be predicted from a ratio of Arrhenius equations if the relative activation energies are known. Reasonably accurate relative activation energies can often be computed with HF wave functions using moderate-size basis sets. 

Olah and Overchuk also attempted to discover evidence of slow mixing by carrying out reactions in high-speed flow systems. Evidence, including the isolation of dinitro compounds (> i %), was indeed found, but held to show that the effect of imperfect mixing was only minor. The reactions were, unfortunately, too fast to permit determinations of absolute rates (half-lives of about io s). 

Most of the reactions with which organic chemists are concerned involve poly-atomic molecules, and occur in solution at temperatures not far removed from the ambient. There is not at present the faintest possibility of chemical theory predicting the absolute rates of such processes. 

Admitting the impossibility of calculating absolute rates, we can concern ourselves with the effect of a structural modification to a particular reactant which we take as a point of reference if the rate constant for the reaction involving the modified compound is k, and that for the... 

Fig. 1-24. Absolute rate of H/D exchange (mole liter min ) in 1.8 N NaOD at 60°C of thiazole (Concentration, 3.2 mole liter" ) (430).

The terms favored and disfavored imply just that. Other factors will determine the absolute rate of a given ring closure, but these relationships point out the need to recognize the specific stereoelectronic requirements which may be imposed on the transition state in ring-closure reactions. 

Absolute rate data for Friedel-Crafts reactions are difficult to obtain. The reaction is complicated by sensitivity to moisture and heterogeneity. For this reason, most of the structure-reactivity trends have been developed using competitive methods, rather than by direct measurements. Relative rates are established by allowing the electrophile to compete for an excess of the two reagents. The product ratio establishes the relative reactivity. These studies reveal low substrate and position selectivity. 

Recent development of techniques for measuring the rates of very fast reactions has permitted absolute rates to be measured for some fundamental types of free-radical reactions. Some examples of absolute rates and values are given in Table 12.2. 

Table 12.2. Absolute Rates of Some Free-Radical Reactions "...

Table 12.9. Absolute Rates of Addition Reactions of Methyl, Cyanomethyl, and Hydrosymethyl Radicals toward Substituted Aikenes, CHi=CHX...

It has been possible to measure absolute rates and activation energies for rearrangement of the substituents in a series of 2-substituted 2,2-dimethylethyl radicals. The rates at 25°C and the E for several substituents are indicated below. 

The absolute rate of dissociation of the radical anion of /i-nitrobenzyl chloride has been measured as 4 x 10 s . The w-nitro isomer does not undergo a corresponding reaction. This is because the meta nitro group provides no resonance stabilization of the benzylic radical. 

The observation of condensation products at 30°C may seem to contradict statements made earlier regarding our ability to separate the methylolation and condensation reactions by holding reaction temperatures below 70°C. Flowever, there is no conflict. The differences in the situations are primarily matters of absolute rate. The relative rates are still similar for methylolation and condensation. No... 

In order to obtain the absolute rate constant Atq, tq must be known. This is a much more difficult measurement, requiring specialized techniques. For singlet-singlet transitions tq is often of the order 10 s. 

A prediction of AE /AEq to within 0.1 kcal/mol may produce a AG /AGq accurate to maybe 0.2 kcal/mol. This corresponds to a factor of 1.4 error (at T = 300 K) in the rate/equilibrium constant, which is poor compared to what is routinely obtained by experimental techniques. Calculating AG /AGq to within 1 kcal/mol is still only possible for fairly small systems. This corresponds to predicting the absolute rate constant, or the equilibrium distribution, to within a factor of... 

The absolute rate constants for the reaction of a variety of electrophilic free radicals with 4-(dimethylamino)-l,5-dimethyl-2-phenyl-l,2-dihydro-3//-pyrazol-3-one (aminopyrine) and l,5-dimefliyl-2-phenyl-l,2-dihydro-3//-pyrazol-3-one... 

Acetylenes have hijh synthetic utility, and hydrogenation of the triple bond occurs in many reaction sequences (7). Often the goal of this reduction is formation of the cis olefin, which usually can be achieved in very high yields (for an exception, see Ref. 10). Continued reduction gives the paraffin. Experimentally, both the relative and absolute rates of acetylene and olefin hydrogenation have been found to depend on the catalyst, substrate, solvent, reaction conditions, and hydrogen availability at the catalyst surface. Despite these complexities, high yields of desired product usually can be obtained without difficulty. 

Note (a) Design ilions for both nominal and absolute ratings are based on the measure of a particle size, not a pore size, (b) Ratings are based on arbitrary laboratory tests by the filter manufacturer and can vary in actual plant conditions as preiaously discussed. 

Nominal Rating Microns Equivalent Standard Absolute Rating Microns... 

The radicals formed by imimolecular rearrangement or fragmentation of the primary radicals arc often termed secondary radicals. Often the absolute rate constants for secondary radical formation are known or can be accurately determined. These reactions may then be used as radical clocks",R2° lo calibrate the absolute rate constants for the bimolecular reactions of the primary radicals (e.g. addition to monomers - see 3.4). However, care must be taken since the rate constants of some clock reactions (e.g. f-butoxy [3-scission21) are medium dependent (see 3.4.2.1.1). 

The electron transfer step is typically fast and efficient. Griller et a/.292 measured absolute rate constants for decay of benzophenone triplet in the presence of aliphatic tertiary amines in benzene as solvent. Values lie in die range 3-4x109 M 1 s 1 and quantum yields are close to unity. 

Rate constants tor reactions of carbon-centered radicals tor the period through 1982 have been compiled by Lorand340 and Asmus and Bonifacio- 50 and for 1982-1992 by Roduner and Crocket.3 1 The recent review of Fischer and Radom should also be consulted.j41 Absolute rate constants for reaction with most monomers lie in the range 105-106 M"1 s"1. Rate data for reaction of representative primary, secondary, and tertiary alkyl radicals with various monomers are summarized in Table 3.6. 

Absolute rate constants for addition reactions of cyanoalkyl radicals are significantly lower than for unsubstituted alkyl radicals falling in the range 103-104 M V1.341 The relative reactivity data demonstrate that they possess some electrophilic character. The more electron-rich VAc is very much less reactive than the electron-deficient AN or MA. The relative reactivity of styrene and acrylonitrile towards cyanoisopropyl radicals would seem to show a remarkable temperature dependence that must, from the data shown (Table 3.6), be attributed to a variation in the reactivity of acrylonitrile with temperature and/or other conditions. 

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