2010-09-12 10:20:53How is ppmv measured?
PatriciaW
Patricia Warwick
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I just read an article which states that: The concentration of CO2 in our atmosphere is measured in “parts per million”, which simply means a ratio of CO2 molecules per million molecules in our atmosphere.

I feel this is inaccurate. It is my understanding that 350ppmv means 350 parts in a million parts by volume e.g. 350 liters in a million liters.

However, a molecule of CO2 does not occupy the same volume as a molecule of nitrogen (or any other gas.) So is the above definition correct or not? I've googled and not found a clear definition yet.

2010-09-12 17:37:41It's laboratory chemistry, not nanotechnology
nealjking

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The volume under consideration is the volume of the gas(es), not the sum of the volumes of the constituent molecules. It is derived from the perfect gas law, which is very well obeyed for a large range of temperatures and pressures, regardless of the size of the molecules.

Suppose you have N1 molecules of Gas1 and N2 molecules of Gas2, in separate containers:

Because of the perfect gas law, each gas satisfies:

Pressure * Volume = N * kB * Temperature

where Pressure = pressure in the container, Volume = volume of the container, kB is Boltmann's constant

So:

P1 * V1 = N1 * kB * T

So if both containers are arranged so that the pressure is the same, and equals the local atmospheric pressure (in the lab), then:

P1 = P2 = PLAB

Each can easily be set to have the same temperature:

T1 = T2 = TLAB

Therefore:

V1 = N1 * kB * T1/P1 =  N1 * kB * TLAB/PLAB = N1 * (kB*TLAB/PLAB)

and likewise 

V2 =  N2 * (kB*TLAB/PLAB)

So the point is that, when you have separated the constituent gases into separate containers, and arranged the containers to have the same pressure and temperature,  their separate volumes are each proportional to the different numbers of molecules.

The terminology "ppmv" is used to indicate that the measurement is done on a "per volume" basis. "ppmw" indicates measurement of quantities of the substances on a "per unit weight" basis.

(The above explanation should be right in principle, but I might have the lab arrangement wrong; I actually flunked chemistry. But hey!, the perfect gas law is part of physics, anyway!)

2010-09-13 12:36:51Is the argument about numbers of molecules wrong?
PatriciaW
Patricia Warwick
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64.231.154.249

An interesting and detailed explanation (and although I studied physics in University I don't remember the perfect gas law.) So in summary you are saying that the numbers of molecules are all that matter. Thus 350 molecules of CO2 in 1,000,000 molecules of atmosphere are 350ppmv.

Thanks

2010-09-13 18:10:45
nealjking

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91.33.124.246

PatriciaW,

With regard to the meaning of 350 ppmv:

- Yes, 350 molecules of CO2 out of 1 Million molecules of gas (total) is 350 ppmv.

- Also: For the purposes of chemistry and laboratory measurements, 1 molecule of N2, 1 molecule of CO2, and 1 molecule of H all "take up" the same amount of volume even though the actual dimensions of the molecules are different, because they "occupy" space in the laboratory container by bouncing around and "keeping other molecules out of their territory". Think of a roomful of 4th-grade kids: The number of kids you can fit into the room is not determined as much by the body size of the kids as it is by the fact that they're running around bumping into each other. Too many kids, they'll be packed in too close and be having fights, etc.