Same temperature, but different volume?

[dawn_pingpong]

Hi, I went for a test today, and one of the problem was as follows:(can't remember the exact wording though)

There is a sealed jar that is an insulator. It is divided in the middle with a piston that does not allow the 2 gases to mix, and is also a conductor. The piston has no mass and can move freely. The top of the jar contains 1.5mol of hydrogen gas, while the bottom contains 1 mol of oxygen gas.

It is known that at 320K 1ATM, The volume occupied by the hydrogen gas is 4 times the volume occupied by oxygen. At what temperature will the hydrogen gas occupy 3 times the volume of oxygen?

What I don't understand is how hydrogen can occupy so much more space compared to oxygen? Don't gases of the same mol occupy the same amount? Eg, 1mol of gas at rtp is 24 dm3, then 1mol at stp is 22.4dm3, so the H2 will occupy 1.5 times that of oxygen?

I'm thing along the lines of PV=nRT, which don't really make sense to me. Or is it some other stuff, like graham's law or something?

Any help will be greatly appreciated!

 

[kushan]

The rule follows in STP ( standard temp and pressure ) , in the jar STP type environment doesn't exist .Thats why the occupy different volumes .

 

[dawn_pingpong]

ok, in that sense, how to approach the problem then?

 

[kushan]

I guess use law of partial pressures .

 

[dawn_pingpong]

I thought the law of partial pressure is only usable for a mixture of gas, not in this instance, where the 2 gases are separate?

 

[voko]

The problem makes sense if the piston is not a conductor, but an insulator, and the temperature of hydrogen changes, but that of oxygen is constant. Then, indeed, it can be seen from the ideal gas law that the volume ratio will depend on the temperature of hydrogen.

If, however, you insist that the piston is a conductor, than both gases will have the same temperature and the same pressure, in which case the ratio of the volumes will be fixed.

 

[dawn_pingpong]

The problem makes sense if the piston is not a conductor, but an insulator, and the temperature of hydrogen changes, but that of oxygen is constant. Then, indeed, it can be seen from the ideal gas law that the volume ratio will depend on the temperature of hydrogen.

If, however, you insist that the piston is a conductor, than both gases will have the same temperature and the same pressure, in which case the ratio of the volumes will be fixed.

Yes, the piston is a conductor, so the temperature of both gases rises at the same time. I think it has something to do with the volume of the container being constant, while the temperature increases, leading to uneven pressure increase between the 2 gases?

 

[kushan]

Whats the problem?
The temperature will be at equilibrium at both the partitions .
It could be higher or lower than before.
What we want to focus her is that which one of the gases increase or decrease pressure more than the other .

 

[voko]

The piston moving freely means that the pressure is equal in both compartments. With temperature also equal, we get the ratio of volumes the same regardless of the temperature.

 

[ehild]

The two kind of gases are separated, it is not a mixture.
The piston moves freely, so the pressure is equal on both sides in equilibrium. The piston conducts heat, so the temperature is the same at both sides.
The gases can not penetrate through the piston. So for the two chambers, pV₁=n₁RT, pV₂=n₂RT, so the ratio V₁/V₂=n₁/n₂. It does not change, as Voko pointed out.
I think the OP did not remember the problem text correctly.

ehild

 

[kushan]

My bad

 

[dawn_pingpong]

Okay, thanks! I looked at the question and thought that it was weird too. The question should be correct I guess, cos I read it at least 5 times or so. Will just see how it goes then:/

 

[dawn_pingpong]

Sorry, just asked my friend, and she said that. The piston is massive. So it is pressing down on the oxygen gas. Sorry.

 

[ehild]

So the pressures are not equal, the pressure of oxygen (P_O) and the pressure of hydrogen (P_H) are related according to P_O=P_H+K, K is the constant pressure exerted by the massive piston.

One more question: The 1 atm pressure is given for which gas? As the cylinder is sealed, the external (atmospheric) pressure does not count.

ehild

 

[dawn_pingpong]

I think it is implied by the question that the orginal pressure of both segments (ie whole system) are 1 atm, though i might be wrong.

 

[ehild]

I think it is implied by the question that the orginal pressure of both segments (ie whole system) are 1 atm, though i might be wrong.

If the pressure and temperature are the same for both gases the volume ratio has to be equal to the ratio of the moles. Maybe, the pressure in the upper compartment was 1 atm before it was sealed.

ehild