Ideal Gases equilibrium question

[Sky.Anthony]

Homework Statement

Containers A and B in the figure hold the same gas. The volume of B is four times the volume of A. The two containers are connected by a thin tube (negligible volume) and a valve that is closed. The gas in A is at 300 K and pressure of 1.0*10⁵Pa. The gas in B is at 400 K and pressure of 5.0*10⁵Pa. Heaters will maintain the temperatures of A and B even after the valve is opened.

After the valve is opened, gas will flow one way or the other until A and B have equal pressure. What is this final pressure?

Homework Equations

PV=nRT or PV=Nk_BT
P₁V₁/T₁ = P₂V₂/T₂

The Attempt at a Solution

I've been messing around with this question for awhile and I'm getting nowhere. My initial thought was to use P₁V₁/T₁ = P₂V₂/T₂ but then I realized that all of the variables are given. Since the volume and temperature of each container is fixed, in order for pressure to change, there must be a change in number of gas molecules in each container... but this is where I'm stuck. I'm not sure how to integrate and establish an equation with number of particles per container where P_A=P_B while taking into account their fixed volumes and temperatures.

 

[ehild]

Opening the valve, gas will flow from B to A till the pressure is the same in both containers. Meanwhile the temperature of both containers is kept at the same level.

You have to collect the initial and final data for both containers and apply the the ideal gas law: PV=nRT, to get the initial and final number of moles (n) in both containers.


Container A:

initial state

Vi(A):V
Ti(A)=300 K
Pi(A)=1*10^5 Pa

ni(A)=1*10^5*V/(R*300)

final state
Vf(A)=V
Tf(A)=300 K
Pf (A)=P
nf(A)=PV/(R*300)

Do the same for the other container: express ni(B) and nf(B). The gas can not escape so ni(A)+ni(B)=nf(A)+nf(B). Use this equation to get the final pressure.

ehild

 

[Eastonc2]

Sorry to drag up an old thread, but I have the same basic problem with different data. is there anyone who can show me a step by step work through of this problem? the previous reply just isn't helping. It's an online assignment and I have already used up all my submissions, and just want to know how to do this problem.

Edit:

I've Determined the moles of gas in each container prior to the valve opening, but that's as far as I can get. Determining the moles of gas in each container after opening the valve is completely eluding me. The change in pressure and temperature from container A to B is really throwing me for a loop.

The work I've attempted is setting [P(a)V(a)/n(a)]+[P(b)V(b)/n(b)]=P(f)V(f)/n(f)
This never really looked right, but it was the closes I ever got to the right answer. I know the temperature difference must have something to do with it, but I am unsure of how to account for that.