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Ideal Gases equilibrium question

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations

    PV=nRT or PV=NkBT
    P1V1/T1 = P2V2/T2

    3. 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 PA=PB while taking into account their fixed volumes and temperatures.
     
  2. jcsd
  3. Feb 9, 2010 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    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
     
  4. Sep 5, 2011 #3
    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.
     
    Last edited: Sep 5, 2011
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