Ab initio free energy and rate calculations are performed to investigate two activated mobility processes observed, respectively, in neutron scattering and anelastic spectroscopy experiments on sodium alanates. The system is modeled as a Na(3)AlH(6) crystal hosting one hydrogen vacancy. We identify the process observed via neutron scattering with a positively charged hydrogen vacancy diffusing from the AlH to one of the AlH groups. As for the anelastic spectroscopy experiments, our calculations negate the current hypothesis on the process, i.e. local rearrangement of the H vacancy around the pentacoordinated Al group.