Now here is a (potentially) unexpected fact - the average kinetic energy of the molecules of any gas at the same temperature are equal. Let us think about how that could be true and what it implies about gases. Under most circumstances the molecules in a gas do not interact with each other significantly, all they do is collide with one another, very much like billiard balls. Given that the temperature of a gas is directly related to the average kinetic energy of the gas, it must be that when two gases are at the same temperature, their molecules have the same average kinetic energy. However, the molecules that compose the gases will be different - more than likely, the mass of the molecules of one gas is different from the mass of the molecules of the other.

5.1 Systems
5.2 Temperature
5.3 Vibrations
5.4 Phase changes
5.5 Thermodynamics
5.6 Phases, again

Since the average kinetic energies are the same, but the molecular masses are different, the average velocity of the molecules in the two gases must be different.  For example: let us compare molecular hydrogen (H₂) gas (molecular weight = 2 g/mole) with molecular oxygen (O₂) gas (molecular weight 32 g/mole), at the same temperature. If the average kinetic energy of H₂ = average kinetic energy of O₂, then the H₂ molecules must be moving, on average, rather faster than the O₂ molecules.

So the average speed at which an atom or molecule moves depends on its mass. Heavier particles tend to move more slowly, on average - it makes perfect sense. Consider a plot of the behavior of the noble (monoatomic) gases, all at the same temperature. On average, helium atoms move much faster than xenon atoms, which are over 30 times heavier. As a side note - gas molecules tend to move very fast. At 0 °C the average H₂ molecule is moving at about 2000 m/s, that is more than a mile per second (and the average O₂ molecule is moving at approximately 500 m/s).

Question to answer:

• Why don’t all the gas particles move with the same speed at a given temperature?
• Where (and why) would krypton appear on the plot above?
• Consider air, a gas composed primarily of N₂, O₂, and CO₂. At a particular temperature, how will the average kinetic energies of these molecules compare to one another?
• What would a plot of kinetic energy vs probability look like for the same gas at different temperatures?
• What would a plot of kinetic energy (rather than speed) vs probability look like for different gases (e.g. the noble gases) at the same temperature?
  

Questions to ponder:

• If gas molecules are moving so fast, why do most smells travel at significantly less that a mile a second?
• Why does it not matter much if we use speed, velocity, or kinetic energy to present the distribution of motion of particles in a system?