[needsHelp]

I have a homework problem that I'm having trouble with.  A box has a divider inside of it, on one side is a gas, with a pressure, and on the other side is another gas with a different pressure.  Then the divider is removed.  So, when the divider is removed, I know what the temp, and volume is. So, what I need is to find n, but first I need to figure out what the pressure is, to use the ideal gas equation.  Can I just add P1 and P2 to get Ptotal?  

[Donaldson Tan]

you cannot sum the pressures directly because pressure is not an extensive property.

Pressure arrises due to molecular bombardment on the walls of the container. If the volume of the container increases, then the frequency of bombardment decreases. This results in a drop in pressure.

Since we are dealing with perfect gas, then its behavior is governed by the perfect gas equation (PV = nRT)

the number of particles in the box is the sum of particles in each compartment. There is no chemical reaction when the divider is removed, so the total number of particles remain unchanged.

[Borek]

you cannot sum the pressures directly because pressure is not an extensive property.

Total pressure is a sum of partial pressures - so your statement is not 100% valid.

[Juan R.]

I have a homework problem that I'm having trouble with.  A box has a divider inside of it, on one side is a gas, with a pressure, and on the other side is another gas with a different pressure.  Then the divider is removed.  So, when the divider is removed, I know what the temp, and volume is. So, what I need is to find n, but first I need to figure out what the pressure is, to use the ideal gas equation.  Can I just add P1 and P2 to get Ptotal?  

More data? For example, how is "removed" the divider?

If it is "removed" to a new place in the box you need know "where".

If is removed from the box, then there is a problem of final equilibrium.

Are you sure that Temperature is not constant in the process?

[GCT]

I have a homework problem that I'm having trouble with.  A box has a divider inside of it, on one side is a gas, with a pressure, and on the other side is another gas with a different pressure.  Then the divider is removed.  So, when the divider is removed, I know what the temp, and volume is. So, what I need is to find n, but first I need to figure out what the pressure is, to use the ideal gas equation.  Can I just add P1 and P2 to get Ptotal?  

So the pressures are different initially, then the becomes equal at mechanical equilbrium right?  You're being very vague with the problem, post the ACTUAL problem.

[jdurg]

You can use the partial pressure of P1 + P2 = Ptot only if you calculate the pressure of the first gas in the new volume and the pressure of the second gas in the new volume.  You can't just add the pressure of each gas in their smaller volumes since as geodome mentioned earlier, the pressure changes when the volume does.  Here's an example.

Side 1 Pressure = 2 atm, volume is one Liter.
Side 2 Pressure = 4 atm, volume is one Liter.

If you just add those two, you get a a total pressure of 6 atmospheres, but that's the pressure in one Liter of space.  To get the proper pressure, you need to calculate the individual pressures.

P1 = 2 atm/2 Liters of space to give you an overall pressure of 1 atmosphere for P1.
P2 = 4 atm/2 Liters of space to give you an overall pressure of 2 atmosphere for P2.

The final total pressure would then be 3 atmospheres.

So in a sense, you can add the two pressures together, but you then have to divide by the total volume of the box to get the total overall pressure.

[needsHelp]

sorry, i tried to post the problem this morning but got an internal server error

so, what i know is the volume of the box, but not the volume of each compartment.  the temperature is constant throughout.  it says that the divider is removed, and the gases mix.  I am given the pressure of gas 1 when the divider is present, and the pressure of gas 2 when the divider is present.  i am also given the mole fraction of one, which i then found the other by subtracting from 1.  i need to find the volume of each original compartment.  so what I tried to do was find the pressure of the box without the divider, and then i tried to use the mole fractions to determine moles of each.  then i was going to go back and use pv=nrt for each compartment, once i knew the # of moles, and find the volume with that.  it didn't work, so i assumed it was because i couldn't just add the pressures together like that.  

[Juan R.]

You said

"Then the divider is removed.  So, when the divider is removed, I know what the temp, and volume is."

Now you say that temperature is constant. As said GCT you may first explain your problem correctly to others.



Ok, if i understand correctly now your problem then I have a solution. I use notation (') for the final state.

You have a process for an ideal gas. The equation of state is PV = nRT.

Composition and temperature are constant in the process (only vary both P and V). therefore

nRT = cte

This is valid for both gas 1 and 2. You can write

P₁V₁ = n₁RT

P₂V₂ = n₂RT

Divide equations for two gases

P₁V₁ / P₂V₂ = n₁RT / n₂RT

you can compute n₁ / n₂ from molar fractions (i asume that you can do this). You already know initial presures, then you can obtain

V₁ / V₂

You have two variables, thus you need other equation, this is V₁ + V₂ = V_box or (divide by V₂)

(V₁ / V₂) + 1 = V_box / V₂

[ppithermo]

I have examples problems of this sort in my ebook
Introductory Thermodynamics, an ideal complement to your course material.

You did not present the problem accurately.