Use kinetic theory of gases

For any ideal gas molecule, the average translational kinetic energy at temperature $T$ is $\overline{K} = \frac{3}{2}kT,$ where $k$ is Boltzmann's constant.

What depends only on temperature?

From the formula above, $\overline{K}$ depends only on $T$, not on the nature of the gas.

So, for molecules of all gases at the same temperature, the quantity that remains the same is the average kinetic energy.

Check other options

• B: mass — Different gases have different molecular masses, so this is not same.
• C: momentum — Momentum depends on mass and speed, so it is not same for all gases.
• D: speed — From $v_{\text{rms}} = \sqrt{\frac{3kT}{m}},$ speed depends on molecular mass $m$, so different gases have different speeds at the same temperature.

Conclusion

The correct option is: $\boxed{\text{A: kinetic energy}}$