Final answer:
The molar enthalpies of vaporization increase from methane to propane due to the increasing strength of London dispersion forces as the molecular size and mass increase, requiring more energy to vaporize the larger molecules.
Step-by-step explanation:
The molar enthalpies of vaporization for methane (CH4), ethane (C2H6), and propane (C3H8) increase in the order CH4 < C2H6 < C3H8 because as the molecular mass and size of these hydrocarbons increase, the extent of London dispersion forces increases as well.
These forces are the result of temporary dipoles caused by the movement of electrons around large molecules. Consequently, the number of atoms and electrons in the molecules increase, leading to stronger intermolecular forces (IMFs) and requiring more energy to overcome these forces during vaporization.