# Ideal gas question

1. Mar 9, 2017

### zanyzoya

1. The problem statement, all variables and given/known data
X and Y are two gas bottles that are connected by a tube that has negligible volume compared with the volume of each bottle. There is a valve in the tube that is initially closed. X has a volume of 2V and contains hydrogen at a pressure of p, Y has a volume V and contains hydrogen at a pressure of 2p. X and Y are initially at the same temperature. The valve between the two bottles is now opened, Assuming that there is no change in temperature, what is the new gas pressure?

2. Relevant equations
pV=nRT

3. The attempt at a solution
rearranging R = pV/nT so
(PxVx)/(Tx nx) = (PyVy)/(Ty ny)
T's cancel so
(PxVx)/nx = (pY Vy)/ny
Vx = 2Vy and Px = 1/2 Py so...
1/2Py x 2Vy / nx = Py Vy / ny
PyVy/nx = PyVy/ny
hence nx = ny

therefore PxVx/Tx = PyVy/Ty
temperatures cancel so
PxVx = PyVy
Vx = 2Vy and Px = 1/2 Py so...
1/2 Pyx 2Vy = PyVy
PyVy = Py Vy ?!?!?!?

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2. Mar 9, 2017

### BvU

You want to use the gas law, apparently before and after opening. How does that show in your working ?

3. Mar 9, 2017

### Staff: Mentor

If T is the temperature, how many moles are present in each container to begin with (in terms of p, V, and T)?

4. Mar 9, 2017

### zanyzoya

2PV/RT moles in each container. Therefore a total number of 4PV/RT moles in the system.
Hence After opening
3P2= 4P
I.e. P2= 4/3 P
Am I right?

5. Mar 9, 2017

### Staff: Mentor

You know you are.

6. Mar 9, 2017

### zanyzoya

Thanks for the help