Protoplanetary disks are the target of many chemical studies (both observational and theoretical) as they contain the building material for planets. Their large vertical and radial gradients in density and temperature make them challenging objects for chemical models. In the outer part of these disks, the large densities and low temperatures provide a particular environment where the binding of species onto the dust grains can be very efficient and can affect the gas-phase chemical composition. We attempt to quantify to what extent the vertical abundance profiles and the integrated column densities of molecules predicted by a detailed gas-grain code are affected by the treatment of the molecular hydrogen physisorption at the surface of the grains. We performed three different models using the Nautilus gas-grain code. One model uses a H2 binding energy on the surface of water (440 K) and produces strong sticking of H2. Another model uses a small binding energy of 23 K (as if there were already a monolayer of H2), and the sticking of H$_2$ is almost negligible. Finally, the remaining model is an intermediate solution known as the encounter desorption mechanism. We show that the efficiency of molecular hydrogen binding (and thus its abundance at the surface of the grains) can have a quantitative effect on the predicted column densities in the gas phase of major species such as CO, CS, CN, and HCN.Read less <