Kresge equation

Equation (17.73) is the Kresge equation that describes the functional dependence of Ar on the isotopic composition, n, of the solvent (Kresge, 1964 Kresge et al, 1982). A conduct of a full proton inventory from the Kresge equation is never practical. However, if some simplifying assumptions are introduced into the Kresge equation, useful information may be obtained under special circumstances. For example, if we assume that is equal to unity, Eq. (17.73) reduces to a polynomial function of n ... 

Kresge et a/.498 have drawn attention to the fact that detritiation of [3H]-2,4,6-trihydroxy- and [3H]-2,4,6-trimethoxy-benzenes by concentrated aqueous perchloric acid gives correlations of log rate coefficient with — H0 with slopes of 0.80 and 1.14 respectively. Protonation to give the carbon conjugate acids is, however, governed by h0lA0 and h0l 9S, respectively, which suggests that the difference in kinetic acidity dependence is a property of the substrate and should not be interpreted as a major difference in mechanism. The kinetic difference can be eliminated by an appropriate comparison of kinetic and equilibrium acidity dependencies. In equation (230)... 

It has been proposed that the acid-catalyzed ketonization of simple enols is concerted that is, both of the processes shown in the equation take place simultaneously. This would mean that in these cases the forward reaction is also concerted. For evidence in favor of this proposal, see Capon, B. Siddhanta, A.K. Zucco, C. J. Org. Chem., 1985, 50, 3580. For evidence against it, see Chiang, Y Hojatti, M. Keeffe, J.R. Kresge, A.J. Schepp, N.P. Wirz, J. J. Amer. Chem. Soc., 1987, 109, 4000 and cited references. 

Kresge and Tobin80 investigated the /1-silicon effect on the hydrolysis of vinyl ethers (equation 29) and found a rate acceleration on the hydrolysis of 175 compared with 176, and hence a stabilizing effect of the /1-silyl group on the intermediate -ethoxy carbocation 177 compared with 178. The acceleration is small the rate factor (175) (176) of 129 is equivalent to a free energy of activation difference AAG of 2.9 kcalmol-1,... 

Similar arguments apply to the six a-carboxy-substituted ketones that have been studied by Kresge and coworkers (entries acetoacetate to oxocyclobutane-2-carboxylate in Table 1). Kresge already noted that the rate constants kucK observed for the uncatalyzed ketonization of some of these compounds would give unrealistically high calculated values for k e near or above 1011 m-1 s-1 using Equation (18). Indeed, these calculated values of k are about two orders of magnitude above those expected from the Marcus relation except that for 4,4,4-trifluoroacetate. The rate constants k c observed for the formation of these a-carboxy-substituted ketones are, however, close to those expected for the protonation of the neutral enols by water, k = kf. 

We note that for the case of keto/enol interconversion, it is simple, useful and remarkably accurate to equate the difference of Gibbs energies in aqueous media of the two tautomers and the difference of enthalpies of formation in the gas J. R. Keefe and A. J. Kresge, J. Phys. Org. Chem., 5, 575 (1992). We are pleased. 

Since we are dealing in all these equations with dimensionless ratios of mole fractions, we may replace mole fractions by molarities (designated by square brackets) or, indeed, any convenient molecular concentration units. The distribution of H and D among isotopically mixed species is then generally given by a Poisson distribution, i.e. we have for the fractional abundance F of a species XDJ)Hni i, (Cadogan et al., 1955 Kresge, 1964) ... 

Experimental evidence for equation (55) was first reported by Kresge (1964) for proton (deuteron) addition to 1,3,5-trimethoxybenzene in H20-D20 the rate constants are obtainable from an analysis of kinetic measurements of hydrogen isotope exchange reactions. 

Gold (1960) and Kresge (1964) have derived equation (18) for relating kx, the rate constant in a D20-H20 mixture containing X atom fraction... 

Evidence from NMR spectra (Kresge and Allred, 1963 Gold, 1963) supports the intuitively attractive idea that only the M30+ unit of M+, in an isotopically mixed solvent, has an isotopic composition significantly different from the water. The isotopic equilibrium constant, l (0-69, Section IIA4), then pertains to the distribution of isotopes between MsO+ and M20. It could be calculated if the frequency distributions (including librations and restricted translations) were known for liquid H20, D20, and H+ and D+ in those solvents. Since only uncertain approximations of typical frequencies are available, an unsophisticated estimate, made by means of equation (62) (Bunton and Shiner, 1961a)... 

Attempts were made to observe a curvature of the Bronsted plots for ketone ionisation. Cohen and Marcus (1968) and Bell (1973) (see also J. R. Jones, 1973 Kresge, 1975b) collected data for the reaction of carbonyl compounds (including ketones, esters and keto-esters) with bases and have observed a slight curvature. The data fit the Marcus equation with AG% = 10 kcal mol-1 and Wr = 4 kcal mol-1 (Hupe and Wu, 1977). 

Equation (29), derived in this form by Kresge (1964) and by Long s group (Salomaa et al., 1964a, b Schaleger et al., 1966) has not been widely applied since the direct measurement of in aqueous solution is not usually attempted. The use of an experimental value of < a fnr acetic acid together with precise measurements of in equation... 

This explanation is complementary with the fraction of a fraction explanation advanced by Kresge, which says that development of resonance stabilization will, at most, be proportional to the loss of Cl -Nl bond order. However, the rehybridization of Cl from tetrahedral to planar is not complete, resulting in only partial resonance stabilization due to poorer electronic overlap. Thus, resonance stabilization is only a fraction of the fraction of Cl -Nl bond breakage. These explanations are also consistent with the idea that TS imbalance is correlated with changes in atom hybridization, which is in turn consistent with the results of calculations on the dissociation of methyl nicotinamide (equation 7). The sum of total bond orders to Nl (X ni) was a linear function of the main process, i.e. loss of the Nl-Cl bond, as was the sum of Nl-C bond orders within the ring (data not shown). The essential difference between this and the oxocarbenium ion example is... 

The oxidation of benzaldehyde catalyzed by manganese(II) and (III) acetate, cobalt(II) naphthenate, and cerium(IV) naphthenate has been studied by Kresge [46] with acetic acid as the solvent at a temperature of 50°C and an oxygen pressure of about 1 atm. In the case of oxidation in the presence of manganese with an aldehyde concentration of less them 0.5 mole 1 1 and a manganese concentration of less than 10 5moler1, the kinetics of the initial oxidation follow the empirical equation... 

In a series of studies by Kresge and coworkers the chemistry of ynols was examined in aqueous solution " ". In this research phenylhydroxyacetylene (6) was generated as a transient intermediate by flash photolysis of phenylhydroxycyclopropenone (5) (equation 3) and its subsequent transformations were investigated kinetically . ... 

Equation (25) could serve to express an approximate correlation between isotope effects and reactivity. It was shown (Simonyi et al., 1967c) that the isotope effect increased with increasing rate of hydrogen atom transfer. Although several measured (Bell and Oooda 1966 Longridge and Long, 1967 Kresge et al., 1968 Hanna et al., 1969) and calculated (More O Ferrall and Kouba, 1967 and references therein) maxima have been presmited for the isotope-effect dependence on... 

The constants contain molecular parameters, and a more detailed description of the derivation of this equation is given in Ref. [6]. Surprisingly, pore sizes can be adjusted by applying mixtures of chemically similar but different-sized amphiphilic molecules, as shown in Fig. 2d. This is a key result, because it is now possible to obtain every pore size between two borders determined by the "parent templates." Nevertheless, it is worth mentioning alternative ways to influence and control pore size. It was already demonstrated that a possible way would be to select an amphiphilic molecule with a suitable molecular composition in order to obtain the desired pore size. However, it is practically impossible to get all of these amphiphiles, or at least it is tedious to synthesize them. The dependence of the pore size on the length of ammonia-based surfactants was demonstrated by the first works of Beck, Vartuli, Kresge, et... 

While the equations above suggest that Bronsted plots should be linear, curved plots can arise in some circumstances, as discussed by Kresge, A. J. Chem. Soc. Rev. 1973,2,475. Curved Bronsted plots may also result when a change in the rate-limiting step of a two-step mechanism accompanies the change in base or acid catalyst. For a discussion, see reference 199. 

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