What Is the Final Pressure in Both Containers After Equalization?

[vortex193]

Homework Statement

Container A holds an ideal gas at a pressure of 5x10^5 Pa and a temperature of 300 K. It is connected by a thin tube (and closed valve) to container B, with four times the volume of A. Container B holds the same ideal gas at a pressure of 10^5 Pa and a temperature of 400 K. The valve is opened to allow the pressures to equalize. What is the pressure in the two containers? Note: The temperatures in the containers do not go to an equilibrium and both temperatures stay at their original temperatures.

Homework Equations

PV = nRT (R = 8.31 J/mol*K)

The Attempt at a Solution

 

[Delphi51]

I hesitated to post because I'm not familiar with this problem.
You might try using your PV = nRT formula. The pressures will equalize so you'll have
P1 = P2
where each P = nRT/V.
You know the R,T and V for each. How will n1 and n2 be related?

 

[vortex193]

No relation was given for n1 and n2.

 

[Delphi51]

Is n the number of moles or molecules? If so, then you know n1 + n2 equals the n1 + n2 from the original configuration, which you can figure out and get an actual number for.

 

[vortex193]

n = number of moles. So the final pressure would equal.

P = (n1 +n2)RT/V

but what would T and V be? remember that both containers begin and end with the same temperature.

 

[Delphi51]

I think you misunderstood me. I said
P1 = P2
n1*R*T1/V1 = n2*R*T2/V2 and n1+n2 = n (known number).
You know R,T1,V1,T2,V2 so your have unknowns n1 and n2 and two equations relating them. Thus you can find n1 and n2. Then you can go back and use P = n1*R*T1/V1 to find P.

 

[vortex193]

Actually V1 and V2 is not given. You only know that V2 is 4 times V1.

 

[Delphi51]

That will work - put in "v1" and "4V1" and cancel the V1's.

 

[vortex193]

I don't understand how you can find n1 and n2 if you do not have n.

 

[Delphi51]

n=PV/(RT) for the original container A + PV/(RT) for the original container B
Oh, yes you'll have V1's in there - but surely they cancel out when you put the n1 and n2 into n1*R*T1/V1 = n2*R*T2/V2

 

[vortex193]

Wow. This question really does not make sense to me. I don't even know how to isolate for either n1 or n2.

 

[Delphi51]

n=PV/(RT) for the original container A + PV/(RT)
=5*V/(R*300) + 1*4V/(R*400)
= .0267*V/R

n = n1 + n2 so n2 = .0267*V/R - n1
sub into n1*R*T1/V1 = n2*R*T2/V2 to get
n1*R*300/V = (.0267*V/R - n1)*R*400/(4V)
Take all the n1 terms to the left:
n1*R*300/V + n1*R*400/(4V) = .0267*V/R*R*400/(4V)
n1*300 + n1*400/(4) = .0267*V/R*400/(4) divide by R, mult by V
n1*(300 + 100) = 2.67*V/R
n1 = .006675*V/R

P1 = n1*R*T1/V1
= .006675*V/R*R*300/V
= 2
I put the pressure in units of 100 000 Pa so this is really 200 000 Pa.

 

[vortex193]

Wow. Thank you. I really appreciate it. Where is the thanks button on this forum so I can thank you? I'm in Grade 12 and I am sure this is not a high school level question. Thank you once again.