In a previous paper [McMurry and Friedlander, Atmos. Environ. 13, 1635 (1979)] a dimensionless theory for predicting rates of new particle formation in chemically reacting systems was described. In the present study mathematical approximations that were made in the previous work were eliminated and time-dependent solutions to dimensionless aerosol population balance equations were obtained numerically. It is shown that steady-state size distributions of sub-0.01 μm particles are typically established 10 to 300 min after the start of gas-to-particle conversion. These times depend on the rate of aerosol formation, the amount of preexisting aerosol and particle size; time scales for 1 nm particles are about an order of magnitude shorter than those for 10 nm particles. The theory shows that steady-state sub-0.01 μm size distributions increase sharply with decreasing particle size. While reliable measurements of aerosols in this size range cannot yet be made on a routine basis, such measurements are essential for testing this and other theories of aerosol formation by gas-phase chemical reactions.