This is not a case for the virial theorem.
The virial theorem
John Baez discusses the virial theorem on a page on his website, the virial theorem made easy
In general the force between particle A and particle B tends to be in proportion to some power n of the distance between A and B.
In the case of celestial mechanics n is -2, the inverse square law of gravitational attraction.
John Baez shows how the inverse square law of gravity gives rise to a particular conversion rate of kinetic energy and potential energy in the course of eccentric orbital motion.
That conversion rate generalizes from the case of two celestial bodies case to entire galaxies.
(Historically: the virial theorem was first stated in the context of statistical mechanics, but the validity of the conversion rate is independent of the number of particles involved.)
John Baez then generalizes to arbitrary power of n, with an expression for how the conversion rate comes out for each value of n. (Again independent of the number of particles involved.)
Other than that:
In the case of very low density gas the probability of a collision is low. I assume that for a given average velocity of the gas molecules the duration of a collisional interaction is a given. I would expect: the larger the density the larger the amount of collisions per unit of time, which would have the molecules spending a larger proportion of the time engaged in collisional interaction.
So if you would want to model how much proportion of time (on average) the internal energy is in the form of some potential energy, then you would need take the amount of collisional interactions per unit of time into account. So I expect it won't be a fixed ratio; I expect the density of the gas to be a factor.