# How to determine an unknown gas in a tube with a massless piston at equilibrium conditions?

There is a massless piston that can move freely in a horizontal tube that is closed at both ends. To the left, there is a sample of helium gas at $300~\mathrm{K}$ and $4~\mathrm{atm}$. To the right, there is a sample of an unknown gas $\ce{X}$ at $500~\mathrm{K}$ and $2~\mathrm{atm}$. At equilibrium, the piston is located at 1/9 the length of the entire piston from the right side. The molecules of $\ce{X}$ are homonuclear. What is most likely the identity of $\ce{X}$?

(From Chemistry Olympiad)

I'm confused by the equilibrium part. I tried $PV = n\mathcal{R}T$ to find the ratio of moles. But without molar mass, how do you solve for it? How would you solve it?

• To start, I would have to assume that the piston started in the middle; unless you left that out. Then I would determine the ratio of the number of moles for each gas. Then use the molar mass of helium to find the other gas. – LDC3 Nov 14 '14 at 3:45
• @LDC3 The question doesn't state whether the piston starts in the middle. Thus, we cant assume that. – John Kim Nov 14 '14 at 3:50
• Well, then I think there are too many unknowns to be able to identify X. – LDC3 Nov 14 '14 at 4:16
• Could you cite the source for the question, that might clarify some things. – Martin - マーチン Nov 14 '14 at 5:53