Mass transfer around a slightly soluble cylinder, aligned with the direction of liquid flow in a packed bed of sand particles, is analysed for transport by advection and molecular diffusion. The theoretical analysis applies to cylinders that are large in comparison with the inert particles, so that the bed may be treated as a continuum. Experimental measurements of mass transfer in water were carried out at temperatures that differ significantly from ambient value. The soluble cylinders used in the experiments were made of either salicylic acid or cinnamic acid and the range of temperatures covered were 278 to 343 K, for the dissolution of salicylic acid, and 278 to 328 K, for cinnamic acid in water. Using the mass transfer theory presented in this work the molecular diffusion coefficient of the two solutes was determined, and good agreement with literature values was found.