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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)?

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Probability distribution for kinetic energy far from the surface should be the same for all chemicals, as it is given by the Boltzmann distribution. Thus, it depends only on temperature, not on chemical nature of the molecules.

Near the liquid surface, however, molecules with kinetic energy that is sufficient for the molecule to escape the liquid phase into the gas phase will be escaping. If more molecules are escaping than coming in back from the gas phase (so liquid evaporates away) there should be less fast molecules in the thin liquid surface layer than the Boltzmann equilibrium value predicts.

1) no, except for above non-equilibrium near the surface layer and only for energies close to the escape energy from the surface layer, which depends on the chemical nature of the liquid. Or if temperature is very low, like for liquid helium, then Boltzmann's distribution is no longer adequate and probability of kinetic energy may depend on other characteristics than temperature and becomes more characteristic of the chemical.

2) I don't know.

3) Vapor pressure has nothing to do with the probability distribution of kinetic energy, except that it depends on temperature too. The equilibrium vapor pressure of liquid depends mainly on the forces between the molecules (which depend on their chemical nature and density and temperature), and on curvature of the liquid surface.

Regarding the last point, the smaller the liquid drop, the higher its vapor pressure just above the surface. Conversely, liquid surface with negative curvature (like water in glass capillary) has lower vapor pressure than completely flat water surface. This is why in time, smaller drops in mist of water droplets either evaporate away or become much larger.

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