We study some thermodynamic aspects of the activation of aqueous organic aerosols into cloud droplets considering the aerosols to consist of liquid solution of water and hydrophilic and hydrophobic organic compounds, taking into account the presence of reactive species in the air. The hydrophobic (surfactant) organic molecules on the surface of such an aerosol can be processed by chemical reactions with some atmospheric species; this affects the hygroscopicity of the aerosol and hence its ability to become a cloud droplet either via nucleation or via Köhler activation. The most probable pathway of such processing involves atmospheric hydroxyl radicals that abstract hydrogen atoms from hydrophobic organic molecules located on the aerosol surface (first step), the resulting radicals being quickly oxidized by ubiquitous atmospheric oxygen molecules to produce surface-bound peroxyl radicals (second step). These two reactions play a crucial role in the enhancement of the Köhler activation of the aerosol and its evolution into a cloud droplet. Taking them and a third reaction (next in the multistep chain of relevant heterogeneous reactions) into account, one can derive an explicit expression for the free energy of formation of a four-component aqueous droplet on a ternary aqueous organic aerosol as a function of four independent variables of state of a droplet. The results of numerical calculations suggest that the formation of cloud droplets on such (aqueous hydrophilic/hydrophobic organic) aerosols is most likely to occur as a Köhler activation-like process rather than via nucleation. The model allows one to determine the threshold parameters of the system necessary for the Köhler activation of such aerosols, which are predicted to be very sensitive to the equilibrium constant of the chain of three heterogeneous reactions involved in the chemical aging of aerosols.