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Homework Help: Unspecified gas, preasure known, looking for number density.

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Integrated circuits are manufactured in vacuum chambers in which the air pressure is 7.00×10^(−11) mm of Hg. What are (a) the number density and (b) the mean free path of a molecule? Assume T = 21.0 C.

    I've double checked, this is all the information available. Quoted verbatim.

    2. Relevant equations

    101,300 Pa = 760 mm of HG. I was able to figure the pressure in Pa. Pa = 9.33 x 10^(-9).

    I've seen various equations involving pressure and N (number density), but they all involve volume and other variables. p = (1/3)(N/V)(m)(v)^2 where v is the RMS velocity. I don't know the m value for "air", etc. I know N will be the number of molecules per cube meter.

    3. The attempt at a solution

    I figured the pressure in Pa, but I don't know which formula to use when they all seem to have several unknowns. Am I missing something, or is the question not specific enough?

    Thanks.
     
  2. jcsd
  3. Apr 27, 2010 #2
    Ok. I see that pV = NkT. Where k is Boltzzmans (sp?) constant. T is temperature. Etc.

    I suppose I just assume that V is a cubic meter, since the units of number density are molecules per cubic meter?
     
  4. Apr 28, 2010 #3

    ehild

    User Avatar
    Homework Helper

    Yes, you are on the right track. k is the Boltzmann constant, and you need the number of molecules in one cubic meter.

    ehild
     
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