Phase changes cause confusion. For a pure substance, a phase change (melting, boiling, etc.) takes place at a constant temperature. The average kinetic energy in each phase is the same. In spite of what students seem to think, there is no increase in average kinetic energy when a liquid boils, for example. There usually is a difference in mean free path, however. Mean free path indicates how far atomic and molecular particles move before experiencing collisions. The mean free paths are larger (longer) in the less dense phase. While this does not matter much in condensed phases where molecules are shoulder to shoulder, it does matter when condensed phases become gases.
The energy added to accomplish a phase change does not lead to increased kinetic energy. Instead, it leads to intermolecular bonding changes. The added energy reduces the amount of intermolecular bonding.