[yingyang]

I am very confused on understanding about percent by volume of gas. I encountered with one problem, and it said "O2 is about 20 percent by volume of air in the container". The reason I am confused is that I always think that gases in the same container have the exact same volume. I am going to use variable "V" denoting the volume of container. According to the problem, if the volume of O2 really equals to 20 percent by volume of air in the container; thus, I am going to have Vo2 = (20/100)*V = V/5. But O2 is in the container with the volume of V. Isn't that strange to have volume of O2 equals to V/5 but not the volume of container. Can someone explain this to me? If I did something wrong, feel free to tell me.

[Hunter2]

But O2 is in the container with the volume of V.

No thats wrong.

It saying if you  have 1 l of air then this air contains 20% means 0,2 l oxygen. The rest is 0,78 l nitrogen and 0,02 l other Gases, like CO2, noble Gases, etc.

[yingyang]

So, O2 that is in the container doesn't have to have the exact same volume to its container, am I right?

[Hunter2]

Air is a mixture of oxygen, nitrogen, carbondioxide, etc.
So it cannot have the same volume as the Containers volume.
This is only true if you fill 100% oxygen in, like in bottles for welding.

[yingyang]

Ohh. So I have always misunderstood that the volume of all gases has to be equal to theirs container. Ok But now I have little doubt. If I say that O2 is 20 percent by volume of air in the container, can I always say that percent by mole of O2 to the air in the container also equals to 20 percent by mole too.

[Hunter2]

If p, and T are constant yes.

pV = nRT

V ~ n

[yingyang]

I am not sure that the pressure will be constant. Because from Dalton's partial pressure, I know that P total = Po2+Px+Py+... . And in the problem it said the pressure of air in the container equals to 1 atm. If the pressure is not constant, do you have any idea on how to find mol and pressure of O2. (T is constant by the way)

[Hunter2]

Again with pV = nRT

Partial pressure is equal percentage. 1 atm means 0,2 atm O2.

P = 0,2 atm, V of the container is constant and T is also constant. So you can calculate the mole.

https://en.m.wikipedia.org/wiki/Partial_pressure

[yingyang]

Thank you for clarifying things. I really appreciate your help.

[Hunter2]

You wellcome

[Borek]

Air is a mixture of oxygen, nitrogen, carbondioxide, etc.
So it cannot have the same volume as the Containers volume.

Sure it can, sure it does - by definition gas occupies all available volume, OP is perfectly right.

However, it doesn't mean all gases in the mixture have the same partial pressure. So, each gas occupies full volume of the container, but has a different partial pressure.

When we say "20% by volume" we mean "as if the gas was kept at the same pressure as other mixture components".

So, 20% by volume of oxygen in the air means if you have 1L of the air at 1atm you can think about it as if it was a mixture prepared by using 0.2L of oxygen at 1atm with (approximately) 0.8L of nitrogen at 1atm. The real 1L of air contains 1L of oxygen at the partial pressure of 0.2atm and 1L of nitrogen at the partial pressure 0.8atm.

And yes, if you take PV=nRT you will find the PV part is the same no matter whether you take 0.2L of oxygen at 1atm or 1L of oxygen at 0.2atm. That's why expressing composition as volume percentages works.

[yingyang]

Air is a mixture of oxygen, nitrogen, carbondioxide, etc.
So it cannot have the same volume as the Containers volume.

Sure it can, sure it does - by definition gas occupies all available volume, OP is perfectly right.

However, it doesn't mean all gases in the mixture have the same partial pressure. So, each gas occupies full volume of the container, but has a different partial pressure.

When we say "20% by volume" we mean "as if the gas was kept at the same pressure as other mixture components".

So, 20% by volume of oxygen in the air means if you have 1L of the air at 1atm you can think about it as if it was a mixture prepared by using 0.2L of oxygen at 1atm with (approximately) 0.8L of nitrogen at 1atm. The real 1L of air contains 1L of oxygen at the partial pressure of 0.2atm and 1L of nitrogen at the partial pressure 0.8atm.

And yes, if you take PV=nRT you will find the PV part is the same no matter whether you take 0.2L of oxygen at 1atm or 1L of oxygen at 0.2atm. That's why expressing composition as volume percentages works.

Wow, this is very easy to understand. If I say, I have 5 dm^3 of air in the container with the pressure of 3 atm. Let's say oxygen is 20 percent by volume in the air. First, I have to have (20/100)*5 = 1 dm^3 of oxygen gas with the pressure of 3 atm, and the others of 4 dm^3 with the pressure of 3 atm. From, P1V1/n1T1 = P2V2/n2T2, let's consider O2
P1V1 = P2V2
3(1) = Po2 * (5)
Po2 = 0.6 atm. (So 3-0.6 = 2.4 is the sum of all partial pressure of the other gases)

Is it correct to think in this way?

[Borek]

Yes, looks OK.

[yingyang]

Thank you so much for your help.