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## Q. 9.2

Consider the gases HF and Ne, both at a (room) temperature of 300 K. Compare the average translational kinetic energy and total kinetic energy of the two types of molecules.

## Verified Solution

The HF and Ne molecules have about the same molecular mass, about 20 u, where recall 1 u = 1 atomic mass unit $=1.66054 \times 10^{-27}$ kg. According to the equipartition theorem, the molecules’ translational kinetic energies are the same, $\frac{3}{2} k T$ per molecule or $\frac{3}{2} R T$ per mole. However, the diatomic HF has two rotational degrees of freedom, so its total kinetic energy is predicted to be $\frac{3}{2} R T+R T=\frac{5}{2} R T$ per mole. The monatomic Ne gas has no rotational degrees of freedom, so its total kinetic energy is $\frac{3}{2} R T$ per mole.