Question

Express the average kinetic energy per molecule of a monatomic gas

Answer 1

For a monatomic ideal gas (such as helium, neon, or argon), the only contribution to the energy comes from translational kinetic energy. The average translational kinetic energy of a single atom depends only on the gas temperature and is given by equation:

Kavg = 3/2 kT.

Answer 2

The average KE of a gas particle has 1/2kT per energy mode (k is Boltzmann’s constant, and T is its absolute temperature in Kelvin). So, for a monatomic particle, it has an av KE of 3/2kT, 1/2 kT for each translational mode, of which it has three, for the three independent directions in which it can travel. A diatomic gas, like oxygen, also has two rotational modes (rotation about the axis which connects the atoms is not included, since this mode stays in its ground state, up to very high temperatures). It also has a vibrational mode, which counts as two modes, because it has PE as well as KE. So, it has seven energy modes, and the average KE of a molecule is 7/2kT. At least, that is its theoretical value, and for oxygen it agrees quite well with the experimentally measured molar heat capacity at constant pressure. The theoretical value is within 1.7 % of its measured value, at 300K and 1 atm pressure.