Relative intrinsic rate constants

Similar conclusions are reached when comparing the reactivity of ben-zylidene-type substrates, IV, with respect to attack by hydroxide ion. If adjustments for the dependence of the equilibrium constants on X and Y are made (18, 19), the relative intrinsic rate constants can be estimated (Table III). As with the amine reactions, the k0 values follow the same order as for... 

Table III. Relative Intrinsic Rate Constants for OH-Addition to H5C6CH=CXY and for Deprotonation of CH2XY Expressed as log [ 0(CN)2/k0XY]...

In addition to the influence of the complexation equilibrium constant K, the observed reaction rate of arenediazonium salts in the presence of guest complexing reagents is influenced by the intrinsic reaction rate of the complexed arenediazonium ion. This system of reactions can be rationalized as in Scheme 11-1. Here we are specifically interested in the numerical value of the intrinsic rate constant k3 of the complexed diazonium ion relative to the rate constant k2 of the free diazonium ion. 

For example, suppose we examine the effects of increasing concentrations of de-naturant, which has two effects the intrinsic rate constants for folding, kf and kc, become lower, and the concentration of U increases relative to C. Initially, the change in concentration is not important while ATc-u is greater than 1, and so both mechanisms slow down because of the intrinsic rate constants decreasing. When [C] = [U] at higher concentrations of denaturant, kobs for scheme 18.13 slows down by a further factor of 2 since Kc /(1 + Kc v) — 0.5 (in equation... 

Steric effects reduce rate and equilibrium constants of nucleophilic additions but the question how the intrinsic barrier is affected does not always have a clear answer. Comparisons of intrinsic rate constants for the addition of secondary alicyclic amines versus primary aliphatic amines suggest that k0 is reduced by the F-strain. This implies that the development of the F-strain at the transition state is quite far advanced relative to bond formation. The effects of other types of steric hindrance on k0 such as prevention of coplanarity of Y in the adduct or even prevention of jt-overlap between Y and the C=C double bond in the alkene have not been thoroughly examined and hence are less well understood. 

The fact that the intrinsic rate constants for nucleophilic addition to Fischer carbene complexes are relatively low, for example, much lower than for most reactions with comparable vinylic substrates or carboxylic esters,188 constitutes strong evidence for the presence of substantial transition state imbalances. However, there have only been a few studies of substituent effects that demonstrate the imbalance directly by showing a uc > p uc or by providing an estimate of its magnitude from the difference a uc - p uc. One such study is the reactions of 76-Cr-Z and 76-W-Z with HC CCII20 and C.F3CH20, 183 It yielded a Llc 0.59 and p ]uc< 0.46 for 76-Cr-Z, and a[juc 0.56 and 0 42 for 76-W-Z, i.e., a ue > p uc as expected. 

Acidity constants and rates of reversible deprotonation of triphenylphosphonium ion (54), (55) and pyridinium ions (56), (57) by amines in water, 50 50 v/v DMSO-water, and 90 10 v/v DMSO-water have been determined.157 The intrinsic rate constants for proton transfer were relatively high for all four carbon acids and showed little solvent dependence. This is in contrast with nitroalkanes, which have much lower intrinsic rate constants and show a strong solvent dependence.158... 

The vapor pressure ratio measures the intrinsic tendency of component 1 to enter the vapor phase relative to component 2. Likewise, ri measures the tendency of Mi to add to Mi - relative to M2 adding to Mi-. In this sense there is a certain parallel, but it is based on Mi - as a reference radical and hence appears to be less general than the vapor pressure ratio. Note, however, that ri = l/r2 means kn/ki2 = k2i/k22- In this case the ratio of rate constants for monomer 1 relative to monomer 2 is the same regardless of the reference radical examined. This shows the parallelism to be exact. 

The extent to which the effect of changing substituents on the values of ks and kp is the result of a change in the thermodynamic driving force for the reaction (AG°), a change in the relative intrinsic activation barriers A for ks and kp, or whether changes in both of these quantities contribute to the overall substituent effect. This requires at least a crude Marcus analysis of the substituent effect on the rate and equilibrium constants for the nucleophile addition and proton transfer reactions (equation 2).71-72... 

The product ratio a /b (statistically corrected for the number of competing H migrants), gives the relative migration rate of Ha vs. Hb, or k /kub- The rate constant for the migration of Ha corresponds to the intrinsic migratory aptitude of Ha (M[H]) multiplied by the bystander assistance factor for Y, B[Y], The carbon atom that bears Hb has no bystander substituent, so that km, is simply A/[H], We thus obtain Eq. 24. 

The consequence of Equation (3) is that the relaxation process is related to the sum of the rate constant for the pseudo-first-order association process and the rate constant for the dissociation process. The association process can be influenced by changes in the concentration of H, but the value of k is intrinsic to the system and cannot be manipulated by external parameters, such as concentrations of reactants. The relaxation process can be dominated by the association or dissociation process depending on the relative value of k+[H] compared to k. The lifetime for the relaxation process is the inverse of the observed rate constant (r0bs — l/kefe). 

The relative order of the catalytic activities of the crown ethers ([20] + [21]) > [9] > [ 11 ] > [ 13] > [8]) is the same as the relative order of their capacities to bind K+ (Table 4). However, the intrinsic reactivities of the ion pairs were also dependent on crown-ether structure, as was shown by experiments in which the alkylation rates were determined at various crown/phenoxide molar ratios. The curve obtained (Fig. 2) is similar to the curves found in titration experiments (Live and Chan, 1976 De Jong et al., 1976b), and shows that the rate constant reaches a maximum (called plateau kinetics in the literature) when all of the salt is complexed. 

---