Hydrogenation of free-standing silicene, the two-dimensional allotrope of silicon, is investigated in detail using first-principles methods and compared with the adsorption of H atoms on graphene. Similarly to graphene, chemisorption of a single H atom on silicene induces the formation of a semilocalized state around the adatom, a sharp peak in the density of states at the Fermi level which acts as a strong resonant scatterer for charge carriers. This state hosts an unpaired electron, the itinerant electron of the resonating valence bond picture which primarily resides on the ``majority'' sublattice and biases the reactivity towards specific lattice positions. Contrary to graphene, sticking of hydrogen atoms is barrierless, on both the pristine and the hydrogenated surface. As a consequence, hydrogen adsorption on silicene is expected to proceed randomly under typical laboratory conditions, and preferential binding to form balanced dimers (or clusters) only occurs when thermodynamic equilibrium conditions prevail. The absence of clustering can be experimentally confirmed using scanning tunneling microscopy techniques since simulated imaging shows that the investigated structures provide distinguishable features that should allow their easy identification, if present on the surface. Overall, our findings can be rationalized by the fact that in silicene p bonds are weaker and the lattice is softer than in graphene and suggest that in silicene adatoms may severely limit carrier mobility.