Stabilities and partitioning of arenonium ions in aqueous media

The phenathrenonium ion is formed as a reactive intermediate in the solvolysis of 9-dichloroacetoxy-9,10-dihydrophenanthrene in aqueous acetonitrile and undergoes competing reactions with water acting as a base and nucleophile. Measurements of product ratios in the presence of azide ion as a trap and 'clock' yield rate constants kp = 3.7 x 10(10) and kH2O = 1.5 x 10(8) s(-1), respectively. Combining these with rate constants for the reverse reactions (protonation of phenanthrene and acid-catalyzed aromatization of its water adduct) gives equilibrium constants pKa = -20.9 and pK(R) = -11.6. For a series of arenonium and benzylic cations, correlation of log kp with pKa, taking account of the limit to kp set by the relaxation of water (10(11) s(-1)), leads to extrapolation of kp = 9.0 x 10(10) s(-1) and pKa = -24.5 for the benzenonium ion and kp = 6.5 x 10(10) s(-1) and pKa = -22.5 for the 1-naphthalenonium ion. Combining these pKa's with estimates of equilibrium constants pKH2O for the hydration of benzene and naphthalene, and the relationship pKR = pKa + pKH2O based on Hess's law, gives pKR = -2.3 and -8.0 respectively, and highlights the inherent stability of the benzenonium ion. A correlation exists between the partitioning ratio, kp/kH2O, for carbocations reacting in water and KH2O the equilibrium constant between the respective reaction products, i.e., log(kp/kH2O) = 0.46pKH2O - 3.7. It implies that kp exceeds kH2O only when KH2O > 10(8). This is consistent with the proton transfer (a) possessing a lower intrinsic reactivity than reaction of the carbocation with water as a nucleophile and (b) being rate-determining in the hydration of alkenes (and dehydration of alcohols) except when the double bond of the alkene is unusually stabilized, as in the case of aromatic molecules.