A hydrogen atom can either physisorb or chemisorb onto a graphene surface. To describe the interaction of H with graphene, we trained the C-C, H-H, and C-H interactions of the ReaxFF CHO bond order potential to reproduce Density Functional Theory (DFT) generated values of graphene cohesive energy and lattice constant, H2 dissociation energy, H on graphene adsorption potentials, and H2 formation on graphene using the Eley-Rideal (ER) and Langmuir-Hinshelwood (LH) processes. The results, generated from the trained H-graphene potentials, are in close agreement with the corresponding results from DFT. The advantage of using optimized CH potentials is, for example, the inclusion of physisorption interactions and quantum mechanical features of chemical bonding in the functional forms of the potentials. The trained CH potentials are utilized to study the energetics of formation of an H2 molecule on graphene using the Eley-Rideal and Langmuir-Hinshelwood processes. Potential energy surfaces for the formation of H2 through ER are generated for the collinear and oblique approach of the second hydrogen atom. Energetics of the formation of H2 through LH is studied for a variety of cases such as when hydrogen atoms are chemisorbed or physisorbed and when hydrogen occupies ortho, meta, or para chemisorption sites. The likelihood of H2 formation through LH for various configurations is discussed. Furthermore, the tunneling probability of an atom through a continuous symmetric/asymmetric barrier is calculated and applied to an adsorbed hydrogen atom on graphene.