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Chapter 9

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.

Step-by-Step

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.