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### Topic: Average number of air molecules per cubic centimeter question  (Read 15402 times)

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#### eddzzz

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##### Average number of air molecules per cubic centimeter question
« on: October 23, 2011, 12:24:05 PM »
Hey guys. Hope you can help me out on this one. so heres the question:

At an altitude of 50km the average atmospheric temperature is 0^oC. What is the average number of air molecules per cubic centimeter at this altitude.

This is how fare I have got:

M = 28.97 g mol^-1
g = 9.81 ms^-2
R = 8.314 J K^-1 mol^-1
Ph = pressure at any given height
P0 = pressure at sea level

Ph = P0e^-Mgh/RT

p @ 50km = 75.944Pa

75.944 x 1 x 10^-2
Ph =  -------------------
8.314 x 273

=  3.346 x 10^-4

Is this correct? Thanks a lot.

Ed

#### Alberto_Kravina

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##### Re: Average number of air molecules per cubic centimeter question
« Reply #1 on: October 23, 2011, 01:21:44 PM »

75.944 x 1 x 10^-2
Ph =  -------------------
8.314 x 273

Beware: one cubic centimetre is not 10^-2 cubic metres. And, if we talk about molecules, you have to use Boltzmann constant instead of R

so

N / V = p(h) / ( k * T )

Use the correct units and volume and you'll have your result

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#### eddzzz

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##### Re: Average number of air molecules per cubic centimeter question
« Reply #2 on: October 23, 2011, 01:49:55 PM »
Ok. Thanks. So 1 cubic centimetre = 1 x 10^-6 cubic meters

so Ph = 75.444 * 50,000 * 1 * 10^-6
-----------------------------
(1.38 * 10^-23 * 273)

= 1.001 * 10^21 moles per cubic centimeter. Is this correct?

#### Borek

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##### Re: Average number of air molecules per cubic centimeter question
« Reply #3 on: October 23, 2011, 05:44:34 PM »
1.001 * 10^21 moles per cubic centimeter. Is this correct?

No, it can't be correct. At STP one mole has a volume of 22.4 L, 1021 moles in 1 cm3 would be way denser than neutron stars.

No Idea why Alberto called for Boltzmann constant. I think you were on the right track.
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#### eddzzz

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##### Re: Average number of air molecules per cubic centimeter question
« Reply #4 on: October 23, 2011, 07:38:24 PM »
I was thinking that myself. Nowhere I look does it mention the Boltzman constant?? So the answer I receive when I use R is * 10^-3. Can someone please confirm this. Thanks

#### Alberto_Kravina

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##### Re: Average number of air molecules per cubic centimeter question
« Reply #5 on: October 24, 2011, 10:49:36 AM »
No Idea why Alberto called for Boltzmann constant. I think you were on the right track.
I missed being corrected by you the last 4 years

p*V = n * R * T (n = number of moles)

p*V= N * k * T (N=number of molecules)

Since the initial question is to get the number of molecules if you use the second equation you dont have to divide the final result with Avogadros number.
The very first equation you posted is correct, you`ll get the number of moles if you put in the right conversion factor for the conversion of volume, but then do not forget to divide by avogadros number to get how many molecules there are+

Sorry if I caused any confusion, both paths lead to exactly the same result, though

#### eddzzz

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##### Re: Average number of air molecules per cubic centimeter question
« Reply #6 on: October 25, 2011, 05:52:28 PM »
Ok so:

Ph = P0e^-Mgh/RT

p @ 50km = 75.944Pa

75.944 x 1 x 10^-6
Ph =  -------------------
8.314 x 273

=  3.346 * 10^-8. And then I need to divide this by 6.022 * 10^23

=  5.556 * 10^-32. Is this correct?