Effect on Rate Constants

Picosecond kinetics, 266 Pre-equilibria, 133-135 Pre-steady-state region, 116 Pressure, effect on rate constants, 166-167... 

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

PEDRIELLI p, PEDULLi G F and SKIBSTED L H (2001a) Antioxidant mechanism of flavonoids. Solvent effect on rate constant for chain-braining reaction of quercetin and epicatechin in autoxidation of methyl linoleate, JAgric Food Chem, 49, 3034-40. 

Methods similar to those discussed in this chapter have been applied to determine free energies of activation in enzyme kinetics and quantum effects on proton transport. They hold promise to be coupled with QM/MM and ab initio simulations to compute accurate estimates of nulcear quantum effects on rate constants in TST and proton transport rates through membranes. 

It is assumed in these experiments that the modification closest to the electron-transfer site will have most effect on rate constants. Rate constants are enhanced for 3+ and retarded for 3- redox partners. With Co(phen)33+ and Fe(CN)53 as oxidants it has been demonstrated that both react at the exposed heme edge of cytochrome c (23). The exposed heme edge is also relevant with PCu(II) as oxidant, Table III. With all three oxidants... 

The Diels-Alder reaction (47t 2ir cycloaddition) is by far the best studied reaction of dienes from both theoretical and experimental viewpoints. Frontier molecular orbital theory predicts three types of Diels-Alder reaction. Structural effects on rate constants show the existence of two types of reaction ... 

Note, from Table 4, that kH for PI1CH2CCI is 6 x 107 s 1, about 3 times greater than kH for PI12CHCCI. This underscores the previously noted nonadditivity of bystander effects on rate constants in going from 10a to 66, the second Ph bystander actually slows the 1,2-H shift. The KGH analysis provides a solution to this conundrum. Steric effects in 66 cause the second Ph to adopt... 

It is important to point out here, in an early chapter, that the Born-Oppenheimer approximation leads to several of the major applications of isotope effect theory. For example the measurement of isotope effects on vapor pressures of isotopomers leads to an understanding of the differences in the isotope independent force fields of liquids (or solids) and the corresponding vapor molecules with which they are in equilibrium through use of statistical mechanical theories which involve vibrational motions on isotope independent potential functions. Similarly, when one goes on to the consideration of isotope effects on rate constants, one can obtain information about the isotope independent force constants which characterize the transition state, and how they compare with those of the reactants. 

In earlier sections of this chapter we learned that the calculation of isotope effects on equilibrium constants of isotope exchange reactions as well as isotope effects on rate constants using transition state theory, TST, requires the evaluation of reduced isotopic partition function ratios, RPFR s, for ordinary molecular species, and for transition states. Since the procedure for transition states is basically the same as that for normal molecular species, it is the former which will be discussed first. 

Choosing a method to determine isotope effects on rate constants, and selecting a particular set of techniques and instrumentation, will very much depend on the rate and kind of reaction to be studied, (i.e. does the reaction occur in the gas, liquid, or solid phase , is it 1st or 2nd order , fast or slow , very fast or very slow , etc.), as well as on the kind and position of the isotopic label, the level of enrichment (which may vary from trace amounts, through natural abundance, to full isotopic substitution). Also, does the isotopic substitution employ stable isotopes or radioactive ones, etc. With such a variety of possibilities it is useless to attempt to generate methods that apply to all reactions. Instead we will resort to discussing a few examples of commonly encountered strategies used to study kinetic isotope effects. 

To calculate the mixed solvent isotope effect on rate constants one applies simple ideas from transition state theory to evaluate the isotope effect on the... 

Structures have been determined for [Fe(gmi)3](BF4)2 (gmi = MeN=CHCF[=NMe), the iron(II) tris-diazabutadiene-cage complex of (79) generated from cyclohexanedione rather than from biacetyl, and [Fe(apmi)3][Fe(CN)5(N0)] 4F[20, where apmi is the Schiff base from 2-acetylpyridine and methylamine. Rate constants for mer fac isomerization of [Fe(apmi)3] " were estimated indirectly from base hydrolysis kinetics, studied for this and other Schiff base complexes in methanol-water mixtures. The attenuation by the —CH2— spacer of substituent effects on rate constants for base hydrolysis of complexes [Fe(sb)3] has been assessed for pairs of Schiff base complexes derived from substituted benzylamines and their aniline analogues. It is generally believed that iron(II) Schiff base complexes are formed by a template mechanism on the Fe " ", but isolation of a precursor in which two molecules of Schiff base and one molecule of 2-acetylpyridine are coordinated to Fe + suggests that Schiff base formation in the presence of this ion probably occurs by attack of the amine at coordinated, and thereby activated, ketone rather than by a true template reaction. ... 

Reports on solvent effects on rate constants for aquation of diimine complexes include those on [Fe(5Brphen)3] + and [Fe(4,7-Me2phen)3] " " in methanol- and ethanol-water, [Fe(bipy)3] +, [Fe(phen)3] +, and [Fe(5N02phen)3] + in aqueous methyl D-glycopyranosides, and... 

Figure 2 Diagrammatic summary of selected structural, substituent, and solvent effects on rate constants (kj, at 298 K) for base hydrolysis of low spin iron(II)-diimine complexes. Ligand abbreviations not appearing in the list at the end of this chapter are apmi = (73) with = Me BOH cage = (78) with X = OH ...

Temperature and pressure effects on rate constants for [Fe(phen)3] +/[Fe(phen)3] + electron transfer in water and in acetonitrile have yielded activation parameters AF was discussed in relation to possible nonadiabaticity and solvation contributions. Solvation effects on AF° for [Fe(diimine)3] " " " " half-cells, related diimine/cyanide ternary systems (diimine = phen, bipy), and also [Fe(CN)6] and Fe aq/Fe aq, have been assessed. Initial state-transition state analyses for base hydrolysis and for peroxodisulfate oxidation for [Fe(diimine)3] +, [Fe(tsb)2] ", [Fe(cage)] " " in DMSO-water mixtures suggest that base hydrolysis is generally controlled by hydroxide (de)hydration, but that in peroxodisulfate oxidation solvation changes for both reactants are significant in determining the overall reactivity pattern. ... 

Chemical reactions at supercritical conditions are good examples of solvation effects on rate constants. While the most compelling reason to carry out reactions at (near) supercritical conditions is the abihty to tune the solvation conditions of the medium (chemical potentials) and attenuate transport limitations by adjustment of the system pressure and/or temperature, there has been considerable speculation on explanations for the unusual behavior (occasionally referred to as anomalies) in reaction kinetics at near and supercritical conditions. True near-critical anomalies in reaction equilibrium, if any, will only appear within an extremely small neighborhood of the system s critical point, which is unattainable for all practical purposes. This is because the near-critical anomaly in the equilibrium extent of the reaction has the same near-critical behavior as the internal energy. However, it is not as clear that the kinetics of reactions should be free of anomalies in the near-critical region. Therefore, a more accurate description of solvent effect on the kinetic rate constant of reactions conducted in or near supercritical media is desirable (Chialvo et al., 1998). 

Fig. 16. Structural effects on rate constants (25°C) for base hydrolysis of some...

Solvatochromic shift data have been obtained for phenol blue in supercritical fluid carbon dioxide both with and without a co-solvent over a wide range in temperature and pressure. At 45°C, SF CO2 must be compressed to a pressure of over 2 kbar in order to obtain a transition energy, E, and likewise a polarizability per unit volume which is comparable to that of liquid n-hexane. The E,j, data can be used to predict that the solvent effect on rate constants of certain reactions is extremely pronounced in the near critical region where the magnitude of the activation volume approaches several liters/mole. 

Solvent effect on rate constants. In this section, the rate constant will be predicted qualitatively in CO2 for the Diels-Alder cycloaddition of isoprene and maleic anhydride, a reaction which has been well-characterized in the liquid state (23,24). In a previous paper, we used E data for phenol blue in ethylene to predict the rate constant of the Menschutkin reaction of tripropylamine and methyliodide (19). The reaction mechanisms are quite different, yet the solvent effect on the rate constant of both reactions can be correlated with E of phenol blue in liquid solvents. The dipole moment increases in the Menschutkin reaction going from the reactant state to the transition state and in phenol blue during electronic excitation, so that the two phenomena are correlated. In the above Diels-Alder reaction, the reaction coordinate is isopolar with a negative activation volume (8,23),... 

Substituent effects on rate constants of base-promoted ionisation of ketones have led to the conclusion that an electron-withdrawing substituent increases the rate of ionisation, in agreement with the anionic character of the transition state. This is based chiefly on studies on halogenation and isotope exchange of aromatic ketones. Data on p-values observed by plotting ionisation rate constants versus Hammett -parameters (Table 3) for substituted... 

It is also important to point out that the direction of the ionic strength effect on rate constants does not always correlate with the protein net charge. Thus, in reactions with FMN [47] and flavodoxin [48], three species of cytochrome C2 having net charges of —7, 0 and -1-2 all show attractive electrostatic interactions during ET with these negatively charged species. The reason for this behavior lies in the fact... 

The final application of solvatochromic solvent strength scales is the correlation of reaction rate and equilibrium constants in SCF solvents. Solvatochromic scales are often quantitative indicators of the solvent effect on rate constants for a variety of reaction mechanismsU) In a SCF, this solvent effect may be achieved conveniently with a single solvent using pressure. Based on solvatochromic data, it was predicted that an activation volume can reach thousands of mL/mol in a SCF(8). This prediction was confirmed for various types of reactionsClSbZl). For example, the solvatochromic parameter Ex for phenol blue... 

The theoretical calculations of the maximum isotopic effects on rate constants summarized in Table I lead one to expect differences in isotopic reaction rates ranging from a few per cent for most elements to orders of magnitude for the isotopes of hydrogen. Two methods can be used to measure the rates of... 

Substituent Effects on Rate Constants for Proton Transfer at Carbon... 

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