The kinetic energy distribution of trapped ions in an ion cyclotron resonance spectrometer (ICR) under a periodically phase-reversed rf potential is determined. At the operating pressures typical for the ICR (10(-7)-10(-5) Torr), the ions eventually achieve a kinetic energy distribution that varies across short time intervals (0.1 ms) but is constant on the time scale of bimolecular collisions. This provides the opportunity to study quantitatively the translational energy dependence of bimolecular reactions and sequential collisional activation processes. The kinetic energy distribution, although not Maxwell-Boltzmann, is readily calculable. Results obtained for the kinetic energy dependence of the reaction of Cl- + CH3Br are qualitatively and quantitatively consistent with reported nonstatistical behavior in that system. Experimental considerations are discussed.