In this work we explore the micro-ring resonator platform to study the diffusion-driven mass transport of small molecules within microfluidic channels. The micro-ring resonators are integrated on a silicon-on-insulator photonic chip and combined with microfluidics in poly(dimethylsiloxane) (PDMS). We apply a strong initial gradient in the solute concentration and use the micro-ring resonators to observe how this concentration evolves over time and space. This can be achieved by tracking the optical resonances of multiple micro-rings as they shift with changing solute concentration. Experiments are performed for both glucose and NaCl and at different temperatures. The measured concentration profiles are used to calculate the diffusion coefficient of both glucose and NaCl in water. The good agreement between measurement and theoretical prediction demonstrates the relevance of this method.