We numerically examine the mass transport into a fluid in the classical driven cavity problem and in the limit of large Peclet number, Pe. The species absorbed into the fluid is allowed to undergo a simple first-order chemical reaction. Two particular types of boundary conditions are imposed: a macroscopic gradient between the bottom and top surface and a zero-flux condition. We demonstrate that, in the absence of a chemical reaction and when a macroscopic gradient is present, mass transport into the liquid is enhanced due to a recirculation zone in the cavity which is connected to the top and bottom surfaces through two boundary layers. The corresponding enhancement is large and scales as Pe(1 2). In the presence of a chemical reaction with rate constant k, adsorption into the liquid is further enhanced with the flux at the top surface now scaling as k(1 2) for k much greater than Pe, However, for k = O(Pe), the chemical reaction removes the central spatially uniform concentration region from the cavity as well as the boundary laver at the bottom wall.