The sticking of hydrogen on $400\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ 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 $72\ifmmode\pm\else\textpm\fi{}15\phantom{\rule{0.3em}{0ex}}\mathrm{kJ}∕\mathrm{mole}$ ${\mathrm{H}}_{2}$, 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.