Kinetics of the reactions of halide anions with carbocations:: Quantitative energy profiles for SN1 reactions

Rate constants for the reactions of Laser flash photolytically generated benzhydrylium ions (diarylcarbenium ions) with halide ions have been determined in various solvents, including neat and aqueous acetonitrile as well as some alcohols. Substitution of the rate constants into the correlation equation log k = s(N+ E) yields the nucleophilicity parameters N for the halide ions in different solvents. Linear correlations with negative slopes are found between the nucleophilicity parameters N for Cl- and Br- in different solvents and the solvent ionizing powers Y of the corresponding solvents. Increasing halide solvation reduces the rates of carbocation/chloride combinations by approximately half as much as it increases the rates of ionizations of benzhydryl chlorides. Comparison of the solvent dependent nucleophilicity parameters N of halide anions and the nucleophilicity parameters N, for solvents yields a quantitative prediction of common ion rate depression, as demonstrated by the analysis of a variety of literature reported mass-law constants a. Combination of the rate constants for the reactions of benzhydrylium ions with halide ions (k(-1)) reported in this work with the ionization constants of benzhydryl halides (k(1)) and the recently reported rate constants for the reactions of benzhydrylium ions with solvents (k(2)) yields complete quantitative free energy profiles for solvolysis reactions. The applicability of Hammond's postulate for interpreting solvolysis reactions can thus be examined quantitatively.