Equilibrium constants carbocations

As thermodynamic stability indexes for the hydrocarbon ions, pA R+ and pA a values [(4) and (5)] have been widely applied for the carbocation and carbanion, respectively, in solution. Here K + stands for the equilibrium constant for the reaction (6) of a carbocation and a water molecule stands for the equilibrium constant for the reaction (7) of a hydrocarbon with a water molecule to give the conjugate carbanion. The equilibrium constants are given by (8) and (9) for dilute aqueous solutions. Obviously, the reference system for the pKn+ scale is the corresponding alcohol, and... 

Alcohols are heterolysed into carbocations and water in the presence of the hydronium ion (6). From the equilibrium constant the free energy of heterolytic dissociation of the carbon-oxygen a bond, AGSe,(ROH + H30+), can be calculated. The AG°het(ROH + H3O+) value is related to the pi R+ of the carbocation by (26). 

Richard, J. P. Amyes, T. L. Bei, L. Stubblefield, V. The effect of beta-fluorine substituents on the rate and equilibrium-constants for the reactions of alpha-substituted 4-methoxybenzyl carbocations and on the reactivity of a simple quinone methide. J. Am. Chem. Soc. 1990, 112, 9513-9519. 

Table 1 Rate and equilibrium constants for partitioning of substituted a-methyl carbocations R (R2)CCH3+ between nucleophilic addition of solvent (ks) and deprotonation (kp) (Scheme 7)°... 

Table 1 summarizes experimentally determined values of the following rate and equilibrium constants for the reactions of aliphatic and benzylic a-methyl carbocations (Scheme 7). 

Values of pA"R for the addition of water to carbocations to give the corresponding alcohols. The equilibrium constants KR (m) were determined as the ratio Hoh/ h> where fcHOH (s 1) is the first-order rate constant for reaction of the carbocation with water and H (m 1 s ) is the second-order rate constant for specific acid-catalyzed cleavage of the alcohol to give the carbocation.9,12 13... 

Values of Kadd for the addition of water (hydration) of alkenes to give the corresponding alcohols. These equilibrium constants were obtained directly by determining the relative concentrations of the alcohol and alkene at chemical equilibrium. The acidity constants pATaik for deprotonation of the carbocations by solvent are not reported in Table 1. However, these may be calculated from data in Table 1 using the relationship pA ik = pATR + logA dd (Scheme 7). 

The rate and equilibrium constants for the reactions of ring-substituted 1-phenylethyl carbocations (X-[6+]) in 50/50 (v/v) trifluoroethanol/water (Table 2 and Scheme 8),13 14 17 43, and for interconversion of ring-substituted 1-phenyl-... 

Table 2 Rate constants, equilibrium constants, and estimated Marcus intrinsic barriers for the formation and reaction of ring-substituted l-phenylethyl carbocations X-[6+] (Scheme 8)°... 

Fig. 5 Logarithmic plots of rate-equilibrium data for the formation and reaction of ring-substituted 1-phenylethyl carbocations X-[6+] in 50/50 (v/v) trifluoroethanol/water at 25°C (data from Table 2). Correlation of first-order rate constants hoh for the addition of water to X-[6+] (Y) and second-order rate constants ( h)so1v for the microscopic reverse specific-acid-catalyzed cleavage of X-[6]-OH to form X-[6+] ( ) with the equilibrium constants KR for nucleophilic addition of water to X-[6+]. Correlation of first-order rate constants kp for deprotonation of X-[6+] ( ) and second-order rate constants ( hW for the microscopic reverse protonation of X-[7] by hydronium ion ( ) with the equilibrium constants Xaik for deprotonation of X-[6+]. The points at which equal rate constants are observed for reaction in the forward and reverse directions (log ATeq = 0) are indicated by arrows.

Table 3 The effects of a-carbonyl and a-thiocarbonyl substituents on the rate and equilibrium constants for the formation and reaction of a-methyl 4-methoxybenzyl carbocations R-[14+] (Scheme 1 l)a... 

A comparison of rate and equilibrium constants for partitioning of the cyclic carbocation [18+] with those for the l-(4-methylphenyl)ethyl carbocation Me-[6+] (Table 5) shows that placement of the cationic benzylic carbon in a five-membered ring results in the following complex changes in the reactivity of the carbocation towards deprotonation and nucleophilic addition of solvent (Scheme 15). 

Table 5. Rate and equilibrium constants for the formation and reaction of cyclic benzylic carbocations [18 + ] and [20+ ] and analogous ring-substituted 1-phenylethyl carbocations (Scheme 15)°... 

As a measure of their thermodynamic stability, the pAfR+ values for the carbocation salts were determined spectrophotometrically in a buffer solution prepared in aqueous solution of acetonitrile. The KR+ scale is defined by the equilibrium constant for the reaction of a carbocation with water molecule (/CR+ = [R0H][H30+]/[R+]). Therefore, the larger p/CR+ index indicates higher stability for the carbocation. However, the neutralization of these cations was not completely reversible. This is attributable to instability of the neutralized products. The instability of the neutralized products should arise from production of unstable polyolefinic substructure by attack of the base at the aromatic core. 

Carbon atoms in organic molecules are most often neutral. Positively charged carbocations have attracted the interest of synthetic organic chemists, because of their use as intermediates in reactions leading to formation of carbon-carbon bonds. Our work on carbocations has focused on defining the stability of these species as intermediates of solvolysis reactions, through the determination of rate and equilibrium constants for these stepwise reactions (Scheme 1). This has led to the development of experimental methods to characterize these parameters for carbocations that are sufficiently stable to form in aqueous solution. 

In retrospect, it should have been clear to me - as I am sure it was to Bill Jencks -that the rate and equilibrium constants for addition of solvent to 1-phenylethyl carbocation intermediates of solvolysis of 1-phenylethyl derivatives would serve as the first step in the characterization of the dynamics of the reactions of their ion pair intermediates. Therefore, this earlier work has served as a point of departure for our experiments to determine relative and absolute barriers to the reactions of ion pair intermediates of solvolysis. 

The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the stoichiometric generation of cations by flash photolysis or radiolysis under conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18 20 The second was the identification of nucleophiles reacting with carbocations under diffusion control, which could be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for reactions of carbocations determined by these methods with rate constants for their formation in the reverse solvolytic (or other) reactions furnished the desired equilibrium constants. 

Important contributors to these developments were McClelland and Richard, who have published reviews of their own and related studies.3 8 The present chapter will focus on recent work therefore and present earlier results mainly for comparison with new measurements. It will consider two further methods for deriving equilibrium constants (a) from kinetic measurements where the reverse reaction of the carbocation is controlled by diffusion or relaxation of solvent molecules23 25 and (b) from a correlation of solution measurements with the more extensive measurements of stabilities of carbocations in the gas phase.26 It will also show that stabilities of highly reactive carbocations can be determined from measurements of protonation and hydration of carbon-carbon double bonds. 

The choice of equilibrium constant for measuring the stability of a carbocation depends partly on experimental accessibility and partly on the choice of solvent. A desire to relate measurements to the majority of existing equilibrium constants implies the use of water as solvent. Water has the advantage and disadvantage that it reacts with carbocations. It follows that the most widely used equilibrium constant is that for the hydration reaction shown in Equation (1), which is denoted KR (or pAR). A simple interpretation of AR is that it measures the ratio of concentrations of unionized alcohol to carbocation in an (ideal) solution of aqueous acid of concentration 1 M. 

As pointed out by Mayr,28 Ritchie,15 and Hine33,34 KR also measures the relative affinities of R+ and H30+ for the hydroxide ion. It can be regarded as providing a general affinity scale applicable to electrophiles other than carbocations.33,35 It can also be factored into independent affinities of R+ and H30+ as shown in Equations (2) and (3). Such equilibrium constants have been denoted If by Hine.33 AR corresponds to the ratio of constants for reactions (2) and (3) and, in so far as Kc for H30+ is the inverse of Kw the autoprotolysis constant for water, KR = KCKW... 

For carbocations, an electrophilicity (Lewis acidity) scale can be based on ions other than the hydroxide ion as is shown in general for X- in Equation (6), for which the equilibrium constant can be denoted A1R. Scales based on chloride ion, for example, have been used in the gas phase2,17,36 and are also appropriate for nonaqueous solvents. 

The problem arises, which equilibrium constant offers the most effective measure of carbocation stability A good discussion of this question has been provided by Mayr and Ofial,29 who point out that a rigorous comparison of stabilities is possible only for isomeric cations. Comparisons between nonisomeric cations depend on the equilibrium chosen for the measurements. They argue that the appropriate choice depends on the context and imply that it is not possible to identify a best measure of carbocation stability. While this is certainly true it is worthwhile pursuing further the likelihood that some equilibria provide better measures of stability than others, and to assess their effectiveness and limitations. 

Turning to experimental measurements, the majority of equilibrium constants measured for carbocation formation refer to ionization of alcohols or alkenes in acidic aqueous solution, and correspond to pAR or pAa. Considering the instability of most carbocations it is hardly surprising that only unusually stable ions such as the tropylium ion l49 or derivatives of the flavylium ion 250,51 are susceptible to pA measurements in the pH range. 

In addition to carbocations, extensive measurements of pK s of oxygen and nitrogen protonated bases have been undertaken, including pK s of proto-nated ketones.65,74 As described below, these lead indirectly to p fR values for a-hydroxycarbocations if the equilibrium constants for hydration of the ketones are known. 

Surprisingly, the kinetic measurements now available for the nucleophilic trapping of carbocations with water are not always matched by measurements of rate constants for formation of the carbocation from the corresponding alcohol required to evaluate the equilibrium constant AR. Although carbocations are reactive intermediates in the acid-catalyzed dehydration of alcohols to form alkenes,85,86 the equilibrium in this reaction usually favors the alcohol and the carbocation forming step is not rate-determining. Rate constants may... 

For such unstable carbocations, an alternative approach to pAR can be developed, by recognizing the relationship that exists between pATR and pAa implied in Equation (15) (p. 30). For carbocations with [3-hydrogen atoms, loss of a proton normally yields an alkene. Then, as discussed by Richard, pATR and pAa form two arms of a thermodynamic cycle, of which the third is the equilibrium constant for hydration of the alkene, pAH2o, as already indicated in Scheme 1. The relationship between these equilibrium constants is shown for the t-butyl cation in Scheme 4. In the scheme the equilibria are... 

We will return to a comparison of values of these equilibrium constants for different carbocations, but first pursue pKA and p fR for the benzenonium ion. In azide buffers this cation reveals no trapping by azide ion. This poses the problems, how do we (a) find a value of kp to combine with kA to obtain pKA and (b) determine p h2o to derive p fR We consider first p h2o and then kp. 

This concludes the discussion of the stabilities of carbocations with hydrocarbon-based structures and also of different methods for deriving equilibrium constants to express these stabilities. The remainder of the chapter will be concerned mainly with measurements of stabilities for oxygen-substituted and metal ion-coordinated carbocations. Consideration of carbocations as conjugate acids of carbenes and derivations of stabilities based on equilibria for the ionization of alkyl halides and azides will conclude the major part of the chapter and introduce a discussion of recent studies of reactivities. 

By contrast, measurement of pATR = 4.7 for the Fe(CO)3-cooordinated cyclo-hexadienyl cation 44 (Scheme 26) indicates a 107-fold more favorable equilibrium constant for carbocation formation than for the uncoordinated cation.197 However, a more dramatic effect of coordination is to render nucleophilic reaction with water more favorable than loss of a proton. A pXa = 9 can be estimated by computing the energy differences between coordinated and uncoordinated benzene and coordinated cyclohexadiene. This compares with the value of —24.5 for the uncoordinated cyclohexadienyl cation. The large difference must reflect the unfavorable effect of Fe(CO)3 coordination on benzene, an effect analogous to that found by Mayr for Fe (CO)3 coordination on the tropylium ion.196 As expected, both the coordinated cyclohexadienyl and tropylium ions are highly stereoselective toward exo attack by water. 

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