When humans return to the surface of the Moon, there could be many circumstances under which gas is released out, from the pressurized components. Some of the cases are as follows:
Gas released from the life support system of the Exploration Extravehicular Mobility Unit (xEMU)
Accidental depressurization, etc.
What will happen to gas released from the Moon's surface?
Some of the possibilities I could think are as follows:
The constituent particles of the gas released will attain a stable orbit around the Moon (@Ags1's comment suggests even lighter molecules can stay in Moon's vicinity. Earlier, I thought lighter molecules would have greater RMS than Moon's Escape Velocity and would escape into somewhere(I don't know) and heavier molecules stay in the moon in sub-orbital trajectory. It would be great if you could clarify this point further.)
It may contribute to the gradual buildup of Moon's atmosphere, though very slowly. (After reading the answers linked below (hat-tip to @Uwe's comment), I realised that even though atmosphere buildup happens, there are lot other factors which can nullify this effect. For example, high energetic particles from the sun can peel of the atmosphere to a great extent.)
The gas escaped travels towards Earth and combines with its atmosphere.[*]
It gets accumulated in Earth-Moon Lagrange Points.[*]
It gets lost into deep space.[*]
[*]:The answers to the questions linked below do not explain this point clearly.
It would be great if you could explain which of the above possibilities (or something I forgot to mention) happens and the reason for it.
Even though this seems "meaningless" for some, I feel that there must be an answer for What will happen to the gas released from the Moon's Surface? Where will it eventually go? Is it not possible to estimate their behaviour based on our understanding of science?
Related questions with helpful answers, referenced above: