We have studied the dynamics of energy-rich hydrogen molecules produced on a graphite surface through H(g) + H(ad)/C(gr) → $H_2$ + C(gr) at thermal conditions mimicking the interstellar medium using a classical trajectory procedure. The recombination reaction of gaseous H atom at 100 K and the adsorbed H atom on the interstellar graphite grains at 10 K efficiently takes place on a subpicosecond time scale with most of the reaction exothermicity depositing in the product vibration, which leads to a strong vibrational population inversion. The molecules produced in nearly end-on geometry where H(g) is positioned below H(ad) rotate clockwise and are more highly rotationally excited. but in low-lying vibrational levels. The rotational axis of most of the molecule rotating clockwise is tilted from the surface normal by more than 30°, the intensity peaking at 35°. The molecules produced when H(ad) is close to the surface rotate counter-clockwise and are weakly rotationally excited, but highly vibrationally excited. These molecules tend to align their rotational axes parallel to the surface. The number of molecules rotating clockwise is eight times larger than that rotating counter-clockwise.