Jets are a common way to transfer mass among fluids, or from a fluid to a surface. At moderate Reynolds numbers and low turbulent intensities the jet exhibits a Near Field Region (NFR) several diameters long. The paper presents numerical results and a theoretical model for the passive scalar diffusion of a submerged free jet in the NFR. Large Eddy Simulations (LES), in the Reynolds number range of 5000-40,000 and the Schmidt number range 1-100, are performed obtaining the passive scalar fields. Three mathematical models for the passive scalar diffusion are presented; the first one is valid in the NFR, specifically in the Undisturbed Region of Flow (URF), and the other two, obtained under the hypotheses of Tollmien and Gortler momentum spreading, are valid in the Potential Core Region (PCR). The last two models employ a turbulent Schmidt number inversely proportional to the mean velocity gradient, conclusion obtained from the LES numerical results. The self-similar solutions of the passive scalar show good agreement with the LES results. The wide range of Reynolds and Schmidt numbers investigated gives generality to the results. (C) 2017 Elsevier Ltd. All rights reserved.