Substitution kinetics

Where solvent exchange controls the formation kinetics, substitution of a ligand for a solvent molecule in a solvated metal ion has commonly been considered to reflect the two-step process illustrated by [7.1]. A mechanism of this type has been termed a dissociative interchange or 7d process. Initially, complexation involves rapid formation of an outer-sphere complex (of ion-ion or ion-dipole nature) which is characterized by the equilibrium constant Kos. In some cases, the value of Kos may be determined experimentally alternatively, it may be estimated from first principles (Margerum, Cayley, Weatherburn Pagenkopf, 1978). The second step is then the conversion of the outer-sphere complex to an inner-sphere one, the formation of which is controlled by the natural rate of solvent exchange on the metal. Solvent exchange may be defined in terms of its characteristic first-order rate constant, kex, whose value varies widely from one metal to the next. 

This radioactive decay process follows first-order kinetics. Substitute the value of k into the appropriate equation ... 

Analogous to the above ordinary Michaelis-Menten kinetics, substitution of Equation (11.56) in Equation (11.21) yields a formula which allows straightforward calculation of the residence time required for a specific conversion ... 

Since the function j/, only depends on the catalyst geometry, the geometry factor r will only depend on the catalyst geometry and not on the pellet size or reaction kinetics. Substitution of Equation A.22 in A.21 yields... 

J/m. In turn these values of F produce substantial predicted differences in craze growth kinetics. Substituting these values into Eq. (7) the craze tip velocity at constant S, = 100 MPa is predicted to decrease by a factor of 10 from PTBS to PC (values for h of 10 nm and for n, the power law exponent, of 17 are assumed for both) or equivalently the value of Sj to give the same craze tip growth rate increases by a factor of 2.8. Since the measured stress S at the craze tip in PTBS is 27 MPa, the craze tip stress in PC is predicted to be 74 MPa, well above its... 

Pastore, H.O., Ozin, G.A., Poe, and A.J. 1993. Intrazeolite metal carbonyl kinetics Substitution reactions of molybdenum carbonyl (Moj2(CO)6) in sodium zeolite Y. Journal of the American Chemical Society 115, 1215-1230. 

For active substances that have a narrow therapeutic window or non-linear kinetics substitution is not advised since even the smallest variations in the... 

Reaction kinetics, substitution effects, stracture-reactivity reiationships... 

These reactions follow first-order kinetics and proceed with racemisalion if the reaction site is an optically active centre. For alkyl halides nucleophilic substitution proceeds easily primary halides favour Sn2 mechanisms and tertiary halides favour S 1 mechanisms. Aryl halides undergo nucleophilic substitution with difficulty and sometimes involve aryne intermediates. 

The full equation for I is obtained by substituting into Eq. IX-8 the expression for AGmax and the gas kinetic expression for Z ... 

When a molecule is isolated from external fields, the Hamiltonian contains only kinetic energy operators for all of the electrons and nuclei as well as temis that account for repulsion and attraction between all distinct pairs of like and unlike charges, respectively. In such a case, the Hamiltonian is constant in time. Wlien this condition is satisfied, the representation of the time-dependent wavefiinction as a superposition of Hamiltonian eigenfiinctions can be used to detemiine the time dependence of the expansion coefficients. If equation (Al.1.39) is substituted into the tune-dependent Sclirodinger equation... 

Cheng Y-W and Dunbar R C 1995 Radiative association kinetics of methyl-substituted benzene ions J. Rhys. Chem. 99 10 802-7... 

I the sum of the kinetic and potential energy of an electron in the orbital lUg in the electro-atic field of the two bare nuclei. This integral can in turn be expanded by substituting the... 

In Chapter 2 the Diels-Alder reaction between substituted 3-phenyl-l-(2-pyridyl)-2-propene-l-ones (3.8a-g) and cyclopentadiene (3.9) was described. It was demonstrated that Lewis-acid catalysis of this reaction can lead to impressive accelerations, particularly in aqueous media. In this chapter the effects of ligands attached to the catalyst are described. Ligand effects on the kinetics of the Diels-Alder reaction can be separated into influences on the equilibrium constant for binding of the dienoplule to the catalyst (K ) as well as influences on the rate constant for reaction of the complex with cyclopentadiene (kc-ad (Scheme 3.5). Also the influence of ligands on the endo-exo selectivity are examined. Finally, and perhaps most interestingly, studies aimed at enantioselective catalysis are presented, resulting in the first example of enantioselective Lewis-acid catalysis of an organic transformation in water. 

Substituting T = 298 K and the gas constant gives a ratio of about 81. Thus, we expect there will be 80 times as much para product as ortho product, assuming that the kinetic product is obtained. 

Nitration can be effected under a wide variety of conditions, as already indicated. The characteristics and kinetics exhibited by the reactions depend on the reagents used, but, as the mechanisms have been elucidated, the surprising fact has emerged that the nitronium ion is preeminently effective as the electrophilic species. The evidence for the operation of other electrophiles will be discussed, but it can be said that the supremacy of one electrophile is uncharacteristic of electrophilic substitutions, and bestows on nitration great utility as a model reaction. 

We have seen ( 6.2.3) hat there is a close relationship between the rates of electrophilic substitutions and the stabilities of tr-complexes, and facts already quoted above suggest that no such relationship exists between those rates and the stabilities of the 7r-complexes of the kind discussed here. These two contrasting situations are further illustrated by the data given in table 6.2. As noted earlier, the parallelism of rate data for substitutions with stability data for o"-complexes is not limited to chlorination ( 6.2.4). Clearly, rr-complexes have no general mechanistic or kinetic significance in electrophilic substitutions. 

Kinetic data are available for the nitration of a series of p-alkylphenyl trimethylammonium ions over a range of acidities in sulphuric acid. - The following table shows how p-methyl and p-tert-h xty augment the reactivity of the position ortho to them. Comparison with table 9.1 shows how very much more powerfully both the methyl and the tert-butyl group assist substitution into these strongly deactivated cations than they do at the o-positions in toluene and ferf-butylbenzene. Analysis of these results, and comparison with those for chlorination and bromination, shows that even in these highly deactivated cations, as in the nitration of alkylbenzenes ( 9.1.1), the alkyl groups still release electrons in the inductive order. In view of the comparisons just... 

In an intramolecular aldol condensation of a diketone many products are conceivable, since four different ends can be made. Five- and six-membered rings, however, wUl be formed preferentially. Kinetic or thermodynamic control or different acid-base catalysts may also induce selectivity. In the Lewis acid-catalyzed aldol condensation given below, the more substituted enol is formed preferentially (E.J. Corey, 1963 B, 1965B). 

Charge diagrams suggest that the 2-amino-5-halothiazoles are less sensitive to nucleophilic attack on 5-position than their thiazole counterpart. Recent kinetic data on this reactivity however, show, that this expectation is not fulfilled (67) the ratio fc.. bron.c.-2-am.noih.azoie/ -biomoth.azoie O"" (reaction with sodium methoxide) emphasizes the very unusual amino activation to nucleophilic substitution. The reason of this activation could lie in the protomeric equilibrium, the reactive species being either under protomeric form 2 or 3 (General Introduction to Protomeric Thiazoles). The reactivity of halothiazoles should, however, be reinvestigated under the point of view of the mechanism (1690). 

Nucleophilic reactivity of the sulfur atom has received most attention. When neutral or very acidic medium is used, the nucleophilic reactivity occurs through the exocyclic sulfur atom. Kinetic studies (110) measure this nucleophilicity- towards methyl iodide for various 3-methyl-A-4-thiazoline-2-thiones. Rate constants are 200 times greater for these compounds than for the isomeric 2-(methylthio)thiazole. Thus 3-(2-pyridyl)-A-4-thiazoline-2-thione reacts at sulfur with methyl iodide (111). Methyl substitution on the ring doubles the rate constant. This high reactivity at sulfur means that, even when an amino (112, 113) or imino group (114) occupies the 5-position of the ring, alkylation takes place on sulfiu. For the same reason, 2-acetonyi derivatives are sometimes observed as by-products in the heterocyclization reaction of dithiocarba-mates with a-haloketones (115, 116). 

From these results it appears that the 5-position of thiazole is two to three more reactive than the 4-position, that methylation in the 2-position enhances the rate of nitration by a factor of 15 in the 5-position and of 8 in the 4-position, that this last factor is 10 and 14 for 2-Et and 2-t-Bu groups, respectively. Asato (374) and Dou (375) arrived at the same figure for the orientation of the nitration of 2-methyl and 2-propylthiazole Asato used nitronium fluoroborate and the dinitrogen tetroxide-boron trifluoride complex at room temperature, and Dou used sulfonitric acid at 70°C (Table T54). About the same proportion of 4-and 5-isomers was obtained in the nitration of 2-methoxythiazole by Friedmann (376). Recently, Katritzky et al. (377) presented the first kinetic studies of electrophilic substitution in thiazoles the nitration of thiazoles and thiazolones (Table 1-55). The reaction was followed spec-trophotometrically and performed at different acidities by varying the... 

Hthiated 4-substituted-2-methylthia2oles (171) at -78 C (Scheme 80). Crossover experiments at—78 and 25°C using thiazoles bearing different substituents (R = Me, Ph) proved that at low temperature the lithioderivatives (172 and 173) do not exchange H/Li and that the product ratios (175/176) observed are the result of independent metala-tion of the 2-methyl and the C-5 positions in a kinetically controlled process (444). At elevated temperatures the thermodynamic acidities prevail and the resonance stabilized benzyl-type anion (Scheme 81) becomes more abundant, so that in fine the kinetic lithio derivative is 173, whereas the thermodynamic derivative is 172. 

The steric bulk of the base added to 2-methyl-4-phenylthiazole (171b) is another factor of the orientation for the kinetic metalation of 4-substituted 2-methylthiazoles (Table 1-60). Even though the C-5 proton... 

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