[SleepyHead]

I am reading about the Kinetic-Molecular Theory and I am confused about why the average kinetic energies of the molecules in a sample of HCl at 298K is the same as the average kinetic energies of the molecules in a sample of H₂ at 298K.

My book says the average kinetic energy is calculated by this equation: KE = 1/2 m v^2,  so shouldn't HCl have a larger average kinetic energy than H₂?

However, I also know that the Kinetic-Molecular Theory states that "the average kinetic energy of a gas depends only on the absolute temperature, not on the identity of the gas". So why do they tell you that the average kinetic energy is calculated by the equation KE = 1/2 m^2 ? It makes no sense. Is the mass assumed to the best same for all gaseous species according to the Kinetic-Molecular Theory? What would the mass be?

Thanks!

[Corribus]

You are forgetting that there are two factors that make up kinetic energy: mass and velocity. So, if the atoms/molecules in an ideal gas have the same amount of kinetic energy per atom/molecule (1.5 k_BT on average), and the atoms/molecules in gas A are heavier than the atoms/molecules in gas B, what can you conclude?

Do note that real molecules are a bit more complicated, because they can store energy in their various vibrations and rotations. This becomes important when you want to start talking about specific heats and other properties that are impacted by the way in which energy gets distributed in each molecule in an ensemble. The simplification above only applies to translational kinetic energy.