A dynamically biased (d-) precursor mediated microcanonical trapping (PMMT) model of the ac- tivated dissociative chemisorption of methane on Pt(111) is applied to a wide range of dissociative sticking experiments, and, by detailed balance, to the methane product state distributions from the thermal associative desorption of adsorbed hydrogen with coadsorbed methyl radicals. Tunneling pathways were incorporated into the d-PMMT model to better replicate the translational energy dis- tribution of the desorbing methane product from the laser induced thermal reaction of coadsorbed hydrogen and methyl radicals occurring near Ts = 395 K. Although tunneling is predicted to be in- consequential to the thermal dissociative chemisorption of CH4 on Pt(111) at the high temperatures of catalytic interest, once the temperature drops to 395 K the tunneling fraction of the reactive thermal flux reaches 15%, and as temperatures drop below 275 K the tunneling fraction exceeds 50%. The d- PMMT model parameters of {E0 = 58.9 kJ/mol, s = 2, ηv = 0.40} describe the apparent threshold energy for CH4/Pt(111) dissociative chemisorption, the number of surface oscillators involved in the precursor complex, and the efficacy of molecular vibrational energy to promote reaction, relative to translational energy directed along the surface normal. Molecular translations parallel to the surface and rotations are treated as spectator degrees of freedom. Transition state vibrational frequencies are derived from generalized gradient approximation-density functional theory electronic structure cal- culations. The d-PMMT model replicates the diverse range of experimental data available with good fidelity, including some new effusive molecular beam and ambient gas dissociative sticking mea- surements. Nevertheless, there are some indications that closer agreement between theory and exper- iments could be achieved if a surface efficacy less than one was introduced into the modeling as an additional dynamical constraint.