Kinetic theory of condensation on soluble nuclei has been developed using fundamental thermodynamic characteristics of heterogeneous nucleation. Kinetic equation describing process of the fluctuation overcoming of the activation barrier by drops nucleating in supersaturated vapor on soluble condensation nuclei has been derived. It has been shown that activation energy for heterogeneous condensation is height drop between potential hill and potential well of the drop formation work instead of the height of potential hill as for the case of homogeneous nucleation. Specific parameters of condensation process on soluble nuclei have been evaluated for the case when condensation nucleus is surface - inactive substance.