The problem of quasi-steady state evaporation and condensation of aerosol droplets is re-examined to determine the effect of the molecular interaction model, on the predicted mass transfer rates in the Knudsen regime. A new expression for the mass flux is obtained that contains explicitly the dependence of the rate process on the accommodation coefficient and on the molecular weight ratio of the vapor and gas molecules. The analysis, based on the solution of the Boltzmann equation by the method of Grad for Maxwellian molecules, is shown to yield results in the near-continuum regime (Kn < 1) very close to a number of previous theoretical analyses based on hard sphere molecules and semi-theoretical correlations, including the Fuchs-Sutugin equation. These results indicate that the theoretical predictions are not sensitive to the molecular interaction model used, but depend strongly on the method of solution in the near-free-molecule regime where the method of Grad fails. As the continuum regime is approached, the solution becomes independent of the accommodation coefficient. Theoretical predictions agree with previously published evaporation data for isothermal evaporation of dibutyl phthalate (DBP) in air and dibutyl sebacate (DBS) in nitrogen using an accommodation coefficient of 1.0 for DBP and 0.9 for DBS.