Rate-equilibrium carbocations

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.

Figure 1.3. Rate-equilibrium correlation for hydration of carbocations triarylmethyl and 9-aryl-9-fluorenyl ( and , respectively, slope =—0.60) diarylmethyl (A, —0.54) aryltropylium (O, —0.68) 9-xanthylium and cyclic phenyldialkoxycarbocations ( and A, respectively, slope = —0.63).

A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (Sn2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate-equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. 

Although the value of the coefficient 1.16 in (20) does not have as direct a physical significance as the a-exponent in the extended Brpnsted equation (19) because the reaction, solvents and temperature are different, there is still a good linear rate-equilibrium relationship for benzhydryl carbocation formation the overall correlation embraces clearly concave partial correlations with varying slopes for the respective Y series. The whole pattern of substituent effects, pXr vs should be essentially identical (with only the ordinate scale being slightly different) to that of log (/ xy/Z hh) vs 2 a for the solvolyses shown in Fig. 8. 

The identity of r values for solvolysis reactivities and the gas-phase stabilities of the corresponding carbocations implies the generality of the extended Brpnsted relationship or Hammond-Leffler rate-equilibrium relationship for benzylic solvolyses, i.e. (37a,b),... 

The rate constants for the solvent-recombination process of the carbocations [3C (X,Y,Z)] were determined by the use of the azide clock method (Richard etal., 1984 Richard and Jencks, 1984a,b,c McClelland et al., 1991) and the rate constant of the forward reaction was derived using (38b) as /Ch = /CwXr+ (McClelland et al., 1989,1991). While ordinary Hammett-type relationships were found to be inapplicable to the substituent effects on solvent recombination, there is a rate-equilibrium correlation for all available data on triarylmethyl cations, shown as the linear log/c , vs. p/Cr<- plot, in Fig. 34 with a slope of 0.64. Such a relationship was earlier suggested by Arnett and Hofelich (1983) and Ritchie (1986). The correlation of ky, with the cr scale was... 

Ritchie, 1986 McClelland et al., 1989, 1991) for a wide set of triarylmethyl cations, and that there is a reasonably linear correlation encompassing the entire set of triarylmethyl carbocations over 16 p/Cr+ units with a small amount of scatter (Fig. 34). The implication of this behaviour is that despite a change in the cation stability, there is a little change in the apparent position of the transition state, at least as revealed in this rate-equilibrium relationship. 

Figure 5.4 An energy diagram for the first step in the reaction of ethylene with HBr. The energy difference between reactants and transition state, AG, defines the reaction rate. The energy difference between reactants and carbocation product, AG°, defines the position of the equilibrium.

Boruah, R. C. Skibo, E. B. Determination of the pKa values for the mitomycin C redox couple by tritration, pH rate profile, and Nemst-Clark fits. Studies of methanol elimination, carbocation formation, and the carbocation/quinone methide equilibrium. J. Org. Chem. 1995, 60, 2232-2243. 

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. 

The determinations of absolute rate constants with values up to ks = 1010 s-1 for the reaction of carbocations with water and other nucleophilic solvents using either the direct method of laser flash photolysis1 or the indirect azide ion clock method.8 These values of ks (s ) have been combined with rate constants for carbocation formation in the microscopic reverse direction to give values of KR (m) for the equilibrium addition of water to a wide range of benzylic carbocations.9 13... 

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... 

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)°... 

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)°... 

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. 

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