An understanding of heat and mass transfer to and from aerosol particles is important for determining the cloud droplet size distribution used in cloud physics models. Uncertainty in our ability to quantify the rate of droplet growth by condensation is a significant contributor to the uncertainty in the magnitude of the aerosol indirect effect reported by the IPCC. In this work we present direct measurements of the molecular flux of water at the surface of single aqueous aerosol particles as a function of pressure, particle size and solute concentration. Using aerosol optical tweezers, sub nanometre changes in droplet radius arising from modulating the temperature of a trapped droplet with a secondary heating laser beam can be followed with sub second time resolution. By comparing experimentally measured rate constants with model predictions, this technique provides a novel means for determining the mass accommodation coefficient, a_m.