A large subset of primary marine aerosols can be initially (immediately upon formation) treated using an "inverted micelle" model. We study the thermodynamics of heterogeneous water condensation on such a marine aerosol. Its hydrophobic organic coating can be processed by chemical reactions with atmospheric species; this enables the marine aerosol to serve as a nucleating center for water condensation. The most probable pathway of such "aging" involves atmospheric hydroxyl radicals that abstract hydrogen atoms from organic molecules coating the aerosol (first step), the resulting radicals being quickly oxidized by ubiquitous atmospheric oxygen molecules to produce surface-bound peroxyl radicals (second step). Taking these two reactions into account, we derive an expression for the free energy of formation of an aqueous droplet on a marine aerosol. The model is illustrated by numerical calculations. The results suggest that the formation of aqueous droplets on marine aerosols is most likely to occur via Köhler activation rather than via nucleation. The model allows one to determine the threshold parameters necessary for the Köhler activation of such aerosols. Numerical results also corroborate previous suggestions that one can omit some chemical species of aerosols (and other details of their chemical composition) in investigating aerosol effects on climate.