The present work describes the mass transfer process between a moving fluid and a slightly soluble plane surface buried in a packed bed, in alignment with the direction of flow. The bed of inert particles is taken to have uniform voidage. The elliptic equation resulting from a differential mass balance was solved numerically over a wide range of the relevant parameters and the resulting values of Sherwood number are seemed to depend only of the Peclet number. Experiments measurements of mass transfer in water were performed on the dissolution of plane surfaces of 2-naphthol and benzoic acid at temperatures that differ significantly from ambient value. The soluble plane surfaces used in the experiments were made of either 2-naphthol or benzoic acid and the range of temperatures covered were 278 to 368 K, for the dissolution of 2-naphthol, and 278 to 338 K, for benzoic acid in water. The results illustrate a simple and accurate method for the measurement of the coefficient of molecular diffusion of slightly soluble solutes.