This is a bit of a cross-over between a physics and a chemistry question.
When we say a liquid has temperature $T$ we make a statement about the mean kinetic energy of a particle in that liquid. That doesn't mean that every particle has the same kinetic energy however - the kinetic energy of any particle forms a probability distribution with mean $T$. This explains why water will evaporate when left alone at room temperature without ever getting close to its boiling point.
I'm interested in that probability distribution for different liquids. For simplicity let's assume pure liquids (e.g. pure water or pure helium).
Do different liquids have (significantly) different probability distributions of the kinetic energy of their particles?
If yes, have we mapped out some of these probability distributions and/or have theories as to why they differ? Do they differ just in a simple parameter or have interestingly different shapes?
To what extent is the vapor pressure of a liquid determined by the shape of the probability distribution of kinetic energy of its particles as opposed to other effects (van der Waals force, dipole moments, etc)?