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Stabilities and partitioning of arenonium ions in aqueous media

The phenathrenonium ion is formed as a reactive intermediate in the solvolysis of 9-dichloro-acetoxy-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 × 10 10 and kH2O ) 1.5 × 108 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 pKR ) -11.6. For a series of arenonium and benzylic cations, correlation of log kp with pK a, taking account of the limit to kp set by the relaxation of water (1011 s-1), leads to extrapolation of k p ) 9.0 × 1010 s-1 and pKa ) -24.5 for the benzenonium ion and kp ) 6.5 × 1010 s-1 and pKa ) -22.5 for the 1-naphthalenonium ion. Combining these pKa's with estimates of equilibrium constants pK H2O 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) ) 0.46pK H2O - 3.7. It implies that kp exceeds kH2O only when KH2O > 108. 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.