Entropy drives the thorough mixing when two gases are combined.
Work Step by Step
When two gases mix, their potential energy stays the same, so it's not that that drives the mixing. But rather, it's because of entropy - the measure of randomness or disorder in a substance. Any gas has kinetic energy and when they're separated, the kinetic energy is stuck in that area. When the gases mix, the kinetic energy of each gas becomes spread out over a larger area/volume/space. The mixture of the two gases has greater entropy/energy dispersal than their separated components. The tendency for energy to spread out when they are not confined is the reason that the two gases mix thoroughly.