A new stochastic model is introduced to emulate intramolecular vibrational relaxation in molecules undergoing isomerization. In this model the Hamiltonian flow is punctuated at random times by an exchange of vibrational kinetic energies. When applied to the study of the rate of barrier crossing, this model reproduces many of the salient features of rate processes in real molecules. For example when the mean time tau between kinetic energy exchange events is short compared to the crossing time of a well the model gives the Rice-Ramsperger-Kassel-Marcus (RRKM) rate constant. When tau is longer than the crossing time the rate constant is smaller than the RRKM value. In this paper the stochastic kinetic energy exchange model (SKEEM) combined with the Bhatnagar-Gross-Krook model for impulsive collisions with a bath is used to explore the dependence of the rate constant on collision rate. This model clarifies why at low collision rates the rate constant for barrier crossing reflects the full dimensionality of the molecule, whereas;at higher collision rates the rate constant seems to reflect a lower dimensionality.