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Calculate the number of moles in a real gas

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data
    I would like to know how to calculate how much moles of gas I have in the following in a cylinder with a certain volume and pressure.

    The gas in the cylinder is a mixture of air, with added oxygen and helium, the mixture is 18% Oxygen, 36,6% Nitrogen, 45% Helium and 0,4% Argon. The cylinder is 24 liters big, the pressure in the cylinder is 200bar.
    I can calculate the a and b values for the gas mixture.

    P = 200 bar
    V = 24 L
    T = 293,15 K
    R = 0,083145 L bar K-1 mol -1
    a = 0,8746 L2bar mol-2
    b = 0,0388 L mol-1

    2. Relevant equations
    PV = nRT ( ideal gas law)

    P = nRT (V-nb)-1 - n2a V-2

    3. The attempt at a solution
    According to the ideal gas law this should be 196,93 moles, but that is not right, since if I use the Vanderwaals equation I end up at a pressure of 234,6 bar to accomodate 196,93 moles of this gasmixture.

    Using the Vanderwaals equation I can't calculate the exact number of moles, this is where is end up:
    200 = 24,37n (24 - 0,0388n)-1 - 0,00152n2

    So please enlighten me, how can I proceed to calculate the value for n?
     
  2. jcsd
  3. Jan 19, 2010 #2

    Char. Limit

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    First, remember that the Van Der Waals pressure doesn't have to match the ideal pressure: in fact, it won't, unless a is 0. With an a as large as yours, the pressure can actually have quite a bit of variation between ideal and Van Der Waals.

    For that last equation, have you considered quadratics?
     
  4. Jan 20, 2010 #3

    ehild

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    Gold Member

    You can apply some iteration procedure. Rewrite the Van der Waals equation in the form

    [tex]n=\frac{PV}{RT}(1+\frac{n^2a}{PV^2})(1-\frac{nb}{V}) [/tex]

    Plug in the data, start with n you got for the ideal gas, substitute for n at the right side, and you get a new n. Continue the procedure with the new n... You get a value near 174 mol, if I am not mistaken.

    ehild
     
  5. Jan 20, 2010 #4
    Thanks, I know that it doesn't match the actual pressure and the ideal pressure do not have to match...
    I know for sure that the pressure in the cylinder is 200 bar, or actually 201 bar, because I am reading the pressure from a gauge.

    What do you mean by "considering quadratics"?
     
  6. Jan 20, 2010 #5
    Ok, that indeed helps me a lot! I do not have to be completely spot on, however the closer the better.
     
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