The sticking of hydrogen on 400 A thick magnesium films, grown under ultrahigh vacuum conditions, have been measured under conditions relevant for hydrogen storage, i.e., elevated temperatures and pressures. A model which describes the hydrogenation and desorption kinetics of the pure magnesium films at H/Mg ratios less than 2% is developed. The activation barrier for hydrogen dissociation is 72 +/- 15 kJ/mole H-2, and a stagnant hydrogen uptake is observed. For platinum-catalyzed films, the barrier is significantly reduced, and there is no stagnation in the uptake rate.