A size-resolved droplet physico chemical model linked to a Lagrangian parcel framework was developed and used to study the heterogeneous sulphate production process in marine stratiform clouds. This model study provides a rigorous approach to cloud chemistry processing by treating the effects of non ideal chemistry on both aqueous phase equilibration and droplet growth using the Pitzer method to overcome many of the shortcomings of alternative thermodynamic methods. In addition, the current study uses a multi modal representation of sea-salt aerosol, rather than the single mode used in most previous work. The results of the model simulations showed a distribution of sulphate production across the aerosol size range that was non linear and that a significant fraction ((Minus tilde sign)75-90%) of the sulphate was produced in droplets formed on sea-salt aerosol particles. The number of sea-salt particles affected both the total amount of sulphate produced and the fraction produced on cloud droplets formed around non-sea-salt sulphate aerosol. Dissolved ozone and hydrogen peroxide were both important as oxidant species, although the ozone-driven oxidation pathway was dominant in droplets formed on sea-salt aerosol particles. The rate of sulphate production was found to be a non linear function of the gaseous sulphur dioxide concentration at cloud base and only very weakly dependent on sulphate nuclei concentration. A comparison of sulphate production in cloud and below cloud indicates that sulphate production in sea-salt nuclei is not limited by the carbonate buffer and that in-cloud production can exceed, many times, that of cloud-free production due to the "virtual" buffering capacity of the cloud. The use of non ideal solution effects appear important, particularly for clean-to-moderately polluted SO2 concentrations (< 500 parts per trillion) and when sea-salt nuclei are present, resulting in at least 40% lower sulphate production when compared to ideal solution simulations.