For a monoatomic ideal gas, the average kinetic energy per molecule is determined by the equipartition theorem. This theorem states that the energy is equally distributed among all the available degrees of freedom.

A monoatomic gas has three translational degrees of freedom, corresponding to motion in the x, y, and z directions. Each degree of freedom contributes an average energy of $\frac{1}{2} k_BT$, where $k_B$ is the Boltzmann constant and $T$ is the absolute temperature.

So for a monoatomic gas with three translational degrees of freedom, the average energy per molecule is: $$\frac{3}{2} k_BT.$$