This paper reports on studies of the behaviour of a Brownian walker that diffuses in a bidimensional non-homogeneous medium constituted by immobile spherical adsorbing obstacles residing in a continuous solvent. Results show that the probability that the random walker is adsorbed, for a given adsorbing interaction potential between the walker and the surface, depends only on the full adsorbing surface S in the reaction medium, and does not show any appreciable dependence on the size of the adsorbing obstacles. Also, the diffusion coefficient of the random walker depends only on the value of S (for a given adsorbed interaction) if the adsorption energy is large enough. In contrast, when the adsorption energy between the walker and the surface of the adsorbing obstacles is zero, the diffusion coefficient decays exponentially with the volume fraction occupied for the obstacles. The efficiency of the walker to visit all obstacles in the simulation cell depends strongly on the concentration of obstacles and on the adsorbing interaction energy, decreasing quickly to zero with an increase in these parameters.