Proton transfer reactions rate constant

The rates of proton transfer reactions cover a wide spectrum, from exasperatingly slow to diffusion controlled. Any theory which can rationalize this range has obvious merit. Such a rationalization is in fact accomplished, to a large degree, by Br nsted and Pedersen s (1923) relationship between rate (kinetic acidity) and p/sTa (thermodynamic acidity). The relationship, known as the Br0nsted equation, has the form (8) where B is the catalytic rate constant. The... 

In terms of equation (21) it is possible to give an explanation of the large substituent effect. When protonation of the intermediate is fast compared to decomposition, equation (22) reduces to the usual expression for h/ e- Since the substituent effect for k jk is expected to be small, the observed substituent effect is contained mainly in a/ 4, the rate ratio for C—0 bond breaking and 0—H bond making. Both 3 and 4 should increase with electron donor substituents and 3 would be expected to increase more because the 3 reaction is one bond closer to the substituent than the 4 reaction. Hence the ratio 3/ 4 will increase with electron donation. Maximal and minimal values of kgjk were calculated using various assumptions, as shown in Table 3. From these it can be concluded that the rate constant for proton transfer, step 4, is comparable in magnitude to the rate constant for the breakdown of the tetrahedral intermediate, step 3. Since the rates of proton transfer reactions are... 

The rates of proton transfer reaction in solutions and proteins are determined by the corresponding rate constants (e.g. Ref [3]). 

This chapter will be concerned mainly with the relation between the equilibrium constants of acid-base reactions and their forward and reverse rates. Relations between equilibrium constants and structure have already been considered in Chapter 6, so that the present discussion also implies relations between rates and structure. Moreover, there are many cases in which rates are easier to measure (though more difficult to interpret) than equilibria and can be compared directly with structures. We shall first consider the general basis and experimental evidence for this type of relation, followed by its molecular interpretation, with special reference to exceptional cases. We have seen in the two preceding chapters that the rates of proton-transfer reactions can be measured either directly, or indirectly through the study of acid-base catalysis, and in the following discussion information from both sources will be used indifferently. 

Table 4-1. Rate Constants for Proton Transfer Reactions in Water ...

A large red shift observed in polar solvents was indicative of the intramolecular charge transfer character of the triplet state. The change of dipole moment accompanying the transition Tj - Tn, as well as rate constants for electron and proton transfer reactions involving the T state of a-nitronaphthalene, were determined. The lower reactivity in polar solvents was attributed to a reduced n-n and increased charge transfer character of the triplet state... 

At this point several assumptions must be made. The first requires the absence of isotope effects on the rate of Reaction O—i.e., the rate constants of Reactions O, U + V, and W are identical this is termed k, and the plausibility of the assumption is indicated by the absence of isotope effects on the rate constant of Reaction I. The second assumption requires that in proton transfer reactions like Reaction O, a deuteron... 

Using either of the above approaches we have measured the thermal rate constants for some 40 hydrogen atom and proton transfer reactions. The results are tabulated in Table II where the thermal rate constants are compared with the rate constants obtained at 10.5 volt cm.-1 (3.7 e.v. exit energy) either by the usual method of pressure variation or for concurrent reactions by the ratio-plot technique outlined in previous publications (14, 17, 36). The ion source temperature during these measurements was about 310°K. Table II also includes the thermal rate constants measured by others (12, 13, 33, 39) using similar pulsing techniques. 

The occurrence of proton transfer reactions between Z)3+ ions and CHa, C2H, and NDZ, between methanium ions and NH, C2HG, CzD , and partially deuterated methanes, and between ammonium ions and ND has been demonstrated in irradiated mixtures of D2 and various reactants near 1 atm. pressure. The methanium ion-methane sequence proceeds without thermal activation between —78° and 25°C. The rate constants for the methanium ion-methane and ammonium ion-ammonia proton transfer reactions are 3.3 X 10 11 cc./molecule-sec. and 1.8 X 70 10 cc./molecule-sec., respectively, assuming equal neutralization rate constants for methanium and ammonium ions (7.6 X 10 4 cc./molecule-sec.). The methanium ion-methane and ammonium ion-ammonia sequences exhibit chain character. Ethanium ions do not undergo proton transfer with ethane. Propanium ions appear to dissociate even at total pressures near 1 atm. 

As an example, consider an early calculation of isotope effects on enzyme kinetics by Hwang and Warshel [31]. This study examines isotope effects on the catalytic reaction of carbonic anhydrase. The expected rate-limiting step is a proton transfer reaction from a zinc-bound water molecule to a neighboring water. The TST expression for the rate constant k is... 

The absolute values of the individual rate constants ks and kp for the nucleophile addition and proton transfer reactions. 

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... 

To what extent are the variations in the rate constant ratio /cs//cpobserved for changing structure of aliphatic and benzylic carbocations the result of changes in the Marcus intrinsic barriers Ap and As for the deprotonation and solvent addition reactions It is not generally known whether there are significant differences in the intrinsic barriers for the nucleophile addition and proton transfer reactions of carbocations. 

ApA < 1. In Fig. 2 the region of curvature is much broader and extends beyond — 4 < ApA < + 4. One explanation for the poor agreement between the predictions in Fig. 3 and the behaviour observed for ionisation of acetic acid is that in the region around ApA = 0, the proton-transfer step in mechanism (8) is kinetically significant. In order to test this hypothesis and attempt to fit (9) and (10) to experimental data, it is necessary to assume values for the rate coefficients for the formation and breakdown of the hydrogen-bonded complexes in mechanism (8) and to propose a suitable relationship between the rate coefficients of the proton-transfer step and the equilibrium constant for the reaction. There are various ways in which the latter can be achieved. Experimental data for proton-transfer reactions are usually fitted quite well by the Bronsted relation (17). In (17), GB is a... 

Since the rate for the tunneling of a proton is strongly dependent on barrier width, it is necessary that the molecular systems to be studied constrain the distance of proton transfer. Also, since the various theoretical models make predictions as to how the rate of proton transfer should vary with a change in free energy for reaction as well as how the rate constant should vary with solvent, it is desirable to study molecular systems where both the driving force for the reaction and the solvent can be varied widely. 

The overall rate constant for proton transfer will reflect the distribution of the reacting species of the distance R between species. As R decreases, the potential energy barrier in the proton-transfer coordinate decreases leading to an increase in the rate of reaction but at a cost of increasing the energy of the reactant and product states at short distances. The DKL model thus defines the rate of proton transfer as [10]... 

Another situation in which an already well-studied proton transfer reaction serves as a probe of a physical phenomenon has been suggested by Knight, Goodall and Greenhow (43, 44). They ionized water with single photons of Nd glass laser infrared radiation and measured an ion recombination rate constant for the reaction... 

The effect of ring substituents on the rate constants, deuterium kinetic isotope effects and Arrhenius parameters for ene-additions of acetone to 1,1-diphenylsilane have been explained in terms of a mechanism involving fast, reversible formation of a zwitterionic silene-ketone complex, followed by a rate-limiting proton transfer between the a-carbonyl and silenic carbon. A study of the thermal and Lewis acid-catalysed intramolecular ene reactions of allenylsilanes with a variety of... 

The usual method for establishing partially rate-limiting proton transfer, determination of the rate constants in D2O, would give ambiguous results (Bruice and Piszkiewicz, 1967). However, intramolecular general acid catalysis [equation (48)] is the preferred mechanism in view of the intermolecular buffer acid catalysis observed with the unsubstituted compounds. General acid catalysis [75] should therefore be favoured in the intramolecular reaction. 

Class (3) reactions include proton-transfer reactions of solvent holes in cyclohexane and methylcyclohexane [71,74,75]. The corresponding rate constants are 10-30% of the fastest class (1) reactions. Class (4) reactions include proton-transfer reactions in trans-decalin and cis-trans decalin mixtures [77]. Proton transfer from the decalin hole to aliphatic alcohol results in the formation of a C-centered decalyl radical. The proton affinity of this radical is comparable to that of a single alcohol molecule. However, it is less than the proton affinity of an alcohol dimer. Consequently, a complex of the radical cation and alcohol monomer is relatively stable toward proton transfer when such a complex encounters a second alcohol molecule, the radical cation rapidly deprotonates. Metastable complexes with natural lifetimes between 24 nsec (2-propanol) and 90 nsec (tert-butanol) were observed in liquid cis- and tra 5-decalins at 25°C [77]. The rate of the complexation is one-half of that for class (1) reactions the overall decay rate is limited by slow proton transfer in the 1 1 complex. The rate constant of unimolecular decay is (5-10) x 10 sec for primary alcohols, bimolecular decay via proton transfer to the alcohol dimer prevails. Only for secondary and ternary alcohols is the equilibrium reached sufficiently slowly that it can be observed at 25 °C on a time scale of > 10 nsec. There is a striking similarity between the formation of alcohol complexes with the solvent holes (in decalins) and solvent anions (in sc CO2). 

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