For a gas at a particular temperature on an average, the quantity which remains same for all molecules is

The kinetic theory describes gas molecules in continuous random motion with frequent collisions, causing velocity and momentum to vary constantly among molecules.

Angular momentum also differs across molecules due to varying rotational motions and positions relative to axes.

The average translational kinetic energy per molecule, given by $KE_{\text{avg}} = \frac{3}{2}kT$, remains constant for all molecules at a fixed temperature. Although instantaneous kinetic energies vary, this ensemble average is uniform across the gas.

The correct choice is $\boxed{C}$.