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### Topic: Gas Laws and volume  (Read 7360 times)

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##### Gas Laws and volume
« on: April 29, 2013, 04:22:53 AM »
When learning Dalton's Law, the requirements for it is that the temperature and volume of the container must remain constant. So if i was given a mixture of gases when using the formula PV=nRT, the T and V are constants.

In a question, I was given a mixture of gases that's 21% oxygen and 79% nitrogen by volume that has a total volume of 10000m3and I was asked to find the partial volume and partial pressure of the 2 gases.

But now I'm having problems understanding what they meant by 21% oxygen by volume. Won't the oxygen be in 10000m3? So I don't get how I can use 21/100 for the mole fraction.

Thanks for the help

#### Borek

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##### Re: Gas Laws and volume
« Reply #1 on: April 29, 2013, 05:04:06 AM »
Volumes of gases are additive (well, of ideal gases, but we pretend to deal with ideal gases for most of the time). So 10000 m3 is equivalent to mixing 21% of that volume of oxygen with 79% of that volume of nitrogen.

You are right that the gases both occupy whole 10000 m3, just with different partial pressures.
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##### Re: Gas Laws and volume
« Reply #2 on: April 29, 2013, 06:59:32 AM »
Volumes of gases are additive (well, of ideal gases, but we pretend to deal with ideal gases for most of the time). So 10000 m3 is equivalent to mixing 21% of that volume of oxygen with 79% of that volume of nitrogen.

You are right that the gases both occupy whole 10000 m3, just with different partial pressures.

What do you mean by additive? Because the only way I can imagine adding more oxygen into a fixed container is by adding more moles of oxygen rather than adding volume because isn't the V the volume of the container?

Like if I put 1 mole of oxygen and 1 mole of oxygen together I'll have 2 moles in total. But I can't say I put 10 dm3 and 10 dm3 to get 20 dm3 because the volume is dependent on the volume of the container?

#### Borek

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##### Re: Gas Laws and volume
« Reply #3 on: April 29, 2013, 07:43:51 AM »
Additive means final volume is a sum of volumes (assuming constant pressure). If you add 10 L of oxygen to the cylinder containing 10 L of nitrogen, and there is movable piston keeping a constant pressure inside, final volume will be exactly 20 L.

But if you mix 10 L of pure ethanol with 10 L of pure water, you end with a 19.3 L of mixture - (again, assuming constant pressure) - volumes of liquids are not additive.
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#### Corribus

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##### Re: Gas Laws and volume
« Reply #4 on: April 29, 2013, 09:23:37 AM »

Imagine you have 100 people in a room that is 100 ft by 100 ft square (or 10,000 ft2).  There are 40 women and 60 men.  If all these people are milling about, it would be accurate to say that the total area on average occupied by the women is 10,000 ft2, because they can be anywhere in the room at any moment.  However each person has their own little area element at any given time, and assuming that people are, on average, the same distance apart, at any given time the fraction of the total volume occupied by any given person is the total area available divided by the total number of people, or 100 ft2.  Now the total area of women (compared to that occupied by men) at this instant in time (or any instant in time) is the total available area multiplied by the fraction of people who are women - or 10,000 ft2 * 4/10, or 4,000 ft2.  The partial area of men would be then 6,000 ft2.  The partial volumes are additive because if you add up the area occupied by men plus the area occupied by women, at any instant in time, you get the total area available.

This is what is meant by partial volumes being additive, except with gas molecules you deal with volumes instead of areas.  Of course gasses don't always behave ideally.  In our analogy, if there are enough people in the room, maybe some of them know each other, and they stick together and have conversations.  Now we can't say that every person on average is the same distance apart.  Just so with real gasses.  They stick together when the concentration (pressure) gets high enough, and so partial pressures and volumes are no longer additive.  But we usually assume that gasses behave ideally . or that people are antisocial.

Make sense?
« Last Edit: April 29, 2013, 10:49:26 AM by Corribus »
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#### billnotgatez

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##### Re: Gas Laws and volume
« Reply #5 on: April 29, 2013, 09:46:20 AM »
@Corribus and @Borek

Strictly looking at the PV=nRT algebraically

If R is a constant with T and V held constant
Then
only P and n can be changed

I am still not sure the question is answered
But, I am probably being to dense here

Let us say we have 21 moles of Oxygen and 79 moles of Nitrogen in a 2240 liter container.
(assume 1 mole of ideal gas a STP is 22.4 L)
Can you give me some more insight

#### Corribus

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##### Re: Gas Laws and volume
« Reply #6 on: April 29, 2013, 10:28:52 AM »
The mixture is 21% oxygen and 79% nitrogen.  Then the partial volumes are 0.21*2240 L oxygen (595 L) and 0.79*2240 L nitrogen (1769.6 L).  Yes both gasses occupy the entire space when time-averaged, but two molecules can't occupy the same space at any instant.  Every molecule has its own volume element and the average volume element is just the total volume divided by the total number of molecules - assuming the gasses don't interact with each other.

I mean, look at it this way: in your container with certain volume you have 21% oxygen and 79% nitrogen.  We know these gasses are mixed, but supposing for a moment you had a magic wand that allowed you to put all the oxygen at the top of the container and all the nitrogen at the bottom of the container.  What would be the volume of the oxygen part and what would be the volume of the nitrogen part?

I think it's worth pointing out (as though it weren't already obvious) that the concept of partial volumes is mathematical in nature and doesn't have any real physical significance (because you can't separate gasses in such a way).  The principle has a name, which may help you find more about it on the web - Amagat's Law.

http://en.wikipedia.org/wiki/Amagat's_law

http://en.wikipedia.org/wiki/Partial_pressure
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#### billnotgatez

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##### Re: Gas Laws and volume
« Reply #7 on: April 29, 2013, 10:32:53 AM »
Now I am getting more clear headed

I hope I did not confuse Needaask

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##### Re: Gas Laws and volume
« Reply #8 on: April 29, 2013, 11:02:59 AM »

Imagine you have 100 people in a room that is 100 ft by 100 ft square (or 10,000 ft2).  There are 40 women and 60 men.  If all these people are milling about, it would be accurate to say that the total area on average occupied by the women is 10,000 ft2, because they can be anywhere in the room at any moment.  However each person has their own little area element at any given time, and assuming that people are, on average, the same distance apart, at any given time the fraction of the total volume occupied by any given person is the total area available divided by the total number of people, or 1000 ft2.  Now the total area of women (compared to that occupied by men) at this instant in time (or any instant in time) is the total available area multiplied by the fraction of people who are women - or 10,000 ft2 * 4/10, or 4,000 ft2.  The partial area of men would be then 6,000 ft2.  The partial volumes are additive because if you add up the area occupied by men plus the area occupied by women, at any instant in time, you get the total area available.

This is what is meant by partial volumes being additive, except with gas molecules you deal with volumes instead of areas.  Of course gasses don't always behave ideally.  In our analogy, if there are enough people in the room, maybe some of them know each other, and they stick together and have conversations.  Now we can't say that every person on average is the same distance apart.  Just so with real gasses.  They stick together when the concentration (pressure) gets high enough, and so partial pressures and volumes are no longer additive.  But we usually assume that gasses behave ideally . or that people are antisocial.

Make sense?

I think I'm starting to get it. But I'm still confused about why oxygen would take up 595L while nitrogen 1769.6L. How can we say that the oxygen would take up a specific amount (21%) when it will go on to fill up the entire volume of the container?

I think I get what you meant by the people analogy. But since the oxygen and nitrogen would space themselves out evenly, won't the partial volume still be the volume of the container?

Sorry for being slow here. Somehow there aren't a lot of information on partial volumes online. Thanks

#### Borek

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##### Re: Gas Laws and volume
« Reply #9 on: April 29, 2013, 11:19:57 AM »
Imagine adding a membrane that separates both gases. Each has the same pressure, each occupies its own volume.

Now you remove the membrane. The only thing that changes is that the gases mix, but neither the pressure nor the total volume changes. Partial volume of each gas is that it occupied before you removed the membrane.
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#### Corribus

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##### Re: Gas Laws and volume
« Reply #10 on: April 29, 2013, 11:29:15 AM »
Quote
I think I get what you meant by the people analogy. But since the oxygen and nitrogen would space themselves out evenly, won't the partial volume still be the volume of the container?
Yes, the true time averaged volume the body of gas occupies will be the entire volume of the container.  But suppose you flash freeze the entire container such that all molecular motion stopped, and you zoom in and look at all the molecules.  You're not going to find any oxygen and nitrogen occuping the exact same space.  Right?  You have two substances in the container.  So a portion of the total volume is going to be oxygen and a portion is going to be nitrogen. Whatever real space the nitrogen molecules occupy cannot be occupied by oxygen molecules, and viceversa.  So at the least you should be able to understand that the entire volume can't be taken up by nitrogen at any instant in time, because there is also oxygen in there!

Now, keep in mind that in reality a LOT of the volume won't have anything at all.  There will be a lot of empty space between molecules (vacuum).  This is the case even for a pure substance.  Suppose you have a container just of nitrogen.  We say the nitrogen occupies the entire container (and it does, in a time-averaged sense), but at any instance of time, how much volume does nitrogen actually occupy?  Well that'd be the volume of a single nitrogen atom (found by the radius of a nitrogen atom) multiplied by the number of nitrogen atoms.  I think you'd find the "real" volume of nitrogen to be much smaller than the total volume available in the container. (And even then, a lot of each atom is empty space, right?  Most of the mass is in the nucleus, which is only a tiny portion of the volume occupied by the comparatively light electrons.) Unless you're in a neutron star, there's gonna be a lot of empty space.

So what we do is award some of the empty space as "territory" for each molecule.  If you've got a container with V volume and N molecules, the total volume per molecule is just V/N.  That's just a mathematical construct of course, because it doesn't mean anything REAL.  The volume explored by all molecules is V, and V/N is the amount of space, on average, alotted to each molecule.

Adding another gas species to the mix doesn't change anything, because in an ideal gas every molecule of gas is basically assumed to be identical.  They don't interact at all - they're just ping-pong balls flying around the volume alotted to them.  Partial volumes then become just a bookkeeping tool at that point.  If we have two species, each one is going to occupy a fraction of the volume, and the fraction will be proportional to the fraction of each species in the container.  Assuming ideal behavior, of course.
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##### Re: Gas Laws and volume
« Reply #11 on: April 29, 2013, 07:26:28 PM »
I think I get it now. I agree that most of the space is empty and only a small volume is taken up compared to the total volume of the container and that the V/n is an average space taken per gas molecules.

So now when I use the gas laws, should my V be the total volume or the partial volume of the gas only?

Lastly, I was reading up on my A chem notes and I saw a "by volume" ratio which was the (v/v) ratio. This seems quite different from the V/n  ratio though.

Thanks so much for the help

#### Corribus

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##### Re: Gas Laws and volume
« Reply #12 on: April 29, 2013, 08:00:31 PM »
So now when I use the gas laws, should my V be the total volume or the partial volume of the gas only?
Depends on what is being asked, but in most problems only the total volume is needed.  Partial pressures are encountered far more frequently than partial volumes.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

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##### Re: Gas Laws and volume
« Reply #13 on: April 29, 2013, 08:39:34 PM »
So now when I use the gas laws, should my V be the total volume or the partial volume of the gas only?
Depends on what is being asked, but in most problems only the total volume is needed.  Partial pressures are encountered far more frequently than partial volumes.

Oh ok. Actually I was wondering if the "by volume" meant (w/v) because I read here http://forum.onlineconversion.com/showthread.php?t=11470 that that's the case.

However I'm unsure what the volume in the w/v represents. Cos I tried out in this question 10000m3 of 21% oxygen and 79% nitrogen by volume at 298K and 1 atm. So I divided 10000000dm3 by 24dm3 to get the total number of moles. Then I compared it with the w/v where v is the volume of container (1x109cm3) and got the mass of it. Then dividing them by their respective molar masses and adding them up didn't get me the same answer as when I use the volume conversion.

Thanks

#### Corribus

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##### Re: Gas Laws and volume
« Reply #14 on: April 29, 2013, 09:24:03 PM »
I'm not sure what your question is.  These are just different ways of measuring concentration.  (v/v, w/w etc.)
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