The theoretical model presented in this work allows quantitative prediction of the rate of Brownian coagulation of pollutant particles on a condensing aerosol droplet. The coupling of the processes of condensation and Brownian coagulation is established through the hydrodynamic-diffusiophoretic force acting upon the Brownian particles in the vicinity of the droplet. The new analytical approach is based on the Grad's moment method of solution to the Fokker Planck equation. The aerosol system is assumed to be isothermal and close to the thermodynamic equilibrium (i.e., the condensation and coagulation fluxes are small). The numerical predictions of the diffusiophoretic enhancement of Brownian coagulation rates are provided for NaCl-water droplets capturing small (primary) soot particles. The results of calculations show substantial enhancement (10 to 200 times) of the capture of soot particles by the condensing marine droplets for typical conditions that occur on the north-eastern coast of the U.S.A.