The adsorption probabilities of methane and propane on Pt(111), and propane on Pt(110)-(1X2) have been successfully predicted for a wide range of incident energies and angles with classical stochastic trajectory simulations, using a pairwise additive Morse methyl-platinum potential previously developed from the measured trapping probabilities of ethane on Pt(111). These predictions, along with those for ethane adsorption on Pt(110)-(1x2), comprise a unified model for the molecular adsorption of alkanes on platinum surfaces. The simulations show the initial trapping probabilities of methane and propane on Pt(111) are determined to within approximately 10% by the fate of the first bounce. They also indicate that at normal incidence on Pt(111) energy conversions from perpendicular translational motion to both cartwheeling rotation and lattice phonons play increasingly important roles in increasing the trapping probability as the alkane increases in size and molecular weight. For methane itself excitation of parallel translational momentum after the first bounce serves as the most effective energy storage mechanism which facilitates trapping, whereas for propane cartwheel rotational motion plays the dominant role. Excessive excitation of these modes of motion, however, can cause scattering on subsequent bounces by reconversion of the energy into perpendicular translational energy. Collisions of methane with the hollow and bridge sites on the Pt(111) surface appear less effective in trapping than do atop sites. The simulations also suggest excitation of the C-C-C bending mode of propane has little effect on the trapping of propane on platinum surfaces for beam energies below 55 kJ/mol.