Reactivities of triarylmethyl and diarylmethyl cations with azide ion investigated by laser flash photolysis. Diffusion-controlled reactions

Article abstract of DOI:10.1021/ja00003a040

By use of the technique of laser flash photolysis, rate constants k_Az and k_s have been directly measured for the reactions at 20 °C in acetonitrile-water (AN-W) solutions of varying composition of 18 triarylmethyl and 10 diarylmethyl cations with azide and solvent. The cations have k_s that depend on substituent and vary from ～10¹ to ～10⁷ s^-1. For the more stable ions k_Az also varies, increasing with decreased electron donation and also increasing by as much as 10³ with increasing acetonitrile content. For less stable cations, however, the rate constant becomes independent of substituent. The break occurs when k_s has reached ～10⁵ s^-1. The limiting rate constants have magnitudes in the vicinity of 10¹⁰ M^-1 s^-1; these do depend on solvent and type of cation, with diarylmethyl cations reacting at the limit 1.6 ± 0.2 times faster than triarylmethyl. The data can be fit by a model where there is diffusional encounter of the cation and azide to form an ion pair, with the combination within the ion pair rate-limiting for the more stable cations and the diffusion step rate-limiting for the less stable ones. The limiting rate constants represent the latter, diffusional encounter of the cation and azide. The Debye-Smoluchowski equation for diffusion-controlled reactions predicts rate constants that are larger than observed by factors of 2-2.5 for diarylmethyl and 4 for triarylmethyl. Deviations can be attributed to nonproductive encounters where the anion has approached the cation in the plane of one of the rings and thus cannot form a proper reacting configuration. The difference between the two types of cations is explained by the greater difficulty of achieving this configuration with the more sterically congested triarylmethyl cation. Ratios k_Az/k_s obtained from product analysis (competition kinetics) have previously been found to show adherence to the reactivity-selectivity principle. This has been interpreted (Rappoport, Jencks) in terms of the reaction with azide having reached the diffusion limit. The directly measured k_Az establish that this is indeed the case. This study also validates the use of azide as a "clock" (Jencks, Richard) for converting such ratios to absolute rate constants through use of a value of 5 × 10⁹ M^-1 s^-1 for k_Az. The directly measured diffusion-limited k_Az are somewhat larger than this, but the differences are small, at most a factor of 4.