REACTIVITIES OF TRIARYLMETHYL AND DIARYLMETHYL CATIONS WITH AZIDE ION INVESTIGATED BY LASER FLASH-PHOTOLYSIS - DIFFUSION-CONTROLLED REACTIONS

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-degrees-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 approximately 10(1) to approximately 10(7) s-1. For the more stable ions k(Az) also varies, increasing with decreased electron donation and also increasing by as much as 10(3) with increasing acetonitrile content. For less stable cations, however, the rate constant becomes independent of substituent. The break occurs when k(S) has reached approximately 10(5) s-1. The limiting rate constants have magnitudes in the vicinity of 10(10) 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 x 10(9) 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.