Ideal gases and partial volume

1. Apr 29, 2013

sgstudent

What does it mean by 21% oxygen and 79% nitrogen by volume?

Because won't the oxygen and nitrogen have the same volume which is the volume of the whole container?

nTRT/VT=nO2RT/VT+nN2RT/VT so why would we say oxygen is 21% by volume since the volume of the oxygen and nitrogen is the same which is the volume of the container?

I managed to find a link that kinda says that "by volume" represents the (w/v) ratio rather than the (v/v) ratio. Here it is at the bottom (http://forum.onlineconversion.com/showthread.php?t=11470). So if it was w/v the w would represent the weight of the gas in g while if the v represent the volume of the entire container?

But if the "by volume" is w/v how can I use that ratio to get my mole fraction? Because if I had 10000m3 at 1 atm and 298K with 21% oxygen and 79% nitrogen by volume (w/v), then the mass of oxygen is 2.1x109g and the mass of nitrogen would be 7.9x109g. So now if I used the formula mass/mr equals moles, I'd get a different total number if I used 10000000dm3/24dm3.

So I'm quite confused about what this "by volume" means and partial volume. Hope you guys can enlighten me here. Thanks :)

2. Apr 29, 2013

Staff: Mentor

It is confusing. In practice, the term volume fraction really means mole fraction, and the term volume percent really means mole percent. Why they use the term volume fraction has never made sense to me.

Chet

3. Apr 30, 2013

Andrew Mason

Just to add to what ChesterMiller has said, if you separated the O2 and N2 and put them into separate balloons at the same external pressure, the balloon with O2 would be 21/79 times the volume of the N2 balloon (ie. the volume of the balloon with the O2 would be 21% of the total volume of the two balloons). These volumes are in the same proportion as the numbers of O2 and N2 molecules.

AM

Last edited: Apr 30, 2013
4. Apr 30, 2013

sgstudent

Hi thanks for the great reply. However I thought that the by volume would mean w/v? Because in this case what would the v stand for?

Thanks again :)

5. Apr 30, 2013

Staff: Mentor

Thanks Andrew. I don't know if this clears it up for the OP, but it does for me (finally).

Chet

6. Apr 30, 2013

sgstudent

Hi Andrew :) actually I thought that the by volume meant either w/v or v/v. Is that not the case?

7. Apr 30, 2013

Andrew Mason

I am not sure what you mean by w/v or v/v.

The volume occupied by a gas depends on the number of molecules of the gas, as well as the external force/area (pressure) on the gas molecules and the average translational kinetic energy (temperature) of the gas molecules. It does not depend directly on the weight or mass of the molecules.

AM

8. Apr 30, 2013

sgstudent

Hi I was thinking that it was the v/v where the formula is volume of solute/volume of solution multiplied by 100%. But I guess it doesn't really apply here.

But actually I was reading the Amagat's Law for the additive volumes, I don't really understand how VT=V1+V2...+Vn. If I had a mixture of oxygen and nitrogen won't both Vo2 and Vn2 be the same since they are in the same container? So how can there be a partial volume here?

9. Apr 30, 2013

Andrew Mason

The concept of volume is clearer with a separation of the gases ie. the volume each would occupy on its own at the same T and P.

You can think of each gas a occupying only part of the volume - in proportion to n. You can determine this from the equation of state. For an ideal gas V = nRT/P so if n is the no. of moles of gas, 21% of which are oxygen and 79% of which are nitrogen, then Vox = .21nRT/P and Vnitr = .79nRT/P.

Or you can think of the different gases providing partial pressures which combine to the total pressure. The total pressure is determined by the force/area caused by the change in momentum per unit time of all the gas molecules due to collisions of gas molecules with the walls of the container. If 21% of the molecules are O2 and 79% are N2, then the partial pressures are in the same proportion.

AM

10. Apr 30, 2013

sgstudent

Hi I was thinking about this more deeply and when we used partial pressures the V of oxygen and of nitrogen are the same? So if I were to split them up won't the their volume change and hence their pressure individually? So in that scenario if I added up their separate individual pressures together I won't get the same answer again right?

11. May 1, 2013

Andrew Mason

Yes.
Yes.
You don't add the pressures together if they are separated. Pressure is the average time rate of change of momentum per unit area of the gas molecules in colliding with the container walls. That does not change by simply separating the types of molecules.

AM

12. May 1, 2013

sgstudent

Oh but then what does the 21% or 79% mean here? Does it mean if I separate them such that they have the same partial pressure respectively then their volumes would be 21% or the original container?

13. May 1, 2013

Staff: Mentor

Hi sgstudent,

You are obsessing and getting bogged down on this. Please don't do this to yourself. Your time is very valuable, and you need to move on to much more important learning. Andrew Mason did a wonderful job of trying to provide motivation for how the term volume fraction for gases came about, but in the great scheme of things, it is not important whether you are comfortable with every last detail of this. All you really need to remember is that those percentages by volume mean mole percentages. The terms volume mixing ratio and volume fraction are synonymous with mole fraction.

Chet

14. May 2, 2013

sgstudent

Ok then. I guess I should just follow the Px=Vx/VT.PT=nx/nT.PT?

15. May 2, 2013

Staff: Mentor

I don't understand your equations. Is it possible to write them in Latex, or else to use parenthesis?

16. May 2, 2013

sgstudent

17. May 2, 2013

Staff: Mentor

Yes, if you mean that the partial pressure of an ideal gaseous constituent is equal to the mole fraction of the constituent times the total pressure.