We study via first principles molecular dynamics the dependence of the Free Energy barrier for the room temperature hydrogenation of the ultra small carbon nanotubes (4, 0) and (5, 0) on the lattice parameter along the tube axis. We find that upon stretching the tube (4, 0) the energy barrier for the incorporation of hydrogen provided by approaching H-2 molecules, undergoing dissociation, can be as low as similar to 0.5 eV per atom. For the bigger tube considered here, the (5, 0), the dependence of the barrier on the lattice parameter is less pronounced due to a higher stability of the tube. (C) 2010 Elsevier B. V. All rights reserved.