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Homework Help: Ideal Gas- molecules applying pressure

  1. Nov 6, 2008 #1
    1. The problem statement, all variables and given/known data
    In a period of 1 s, 5 x 10^23 nitrogen molecules strike a wall with an area of 8 cm^2. Assume the molecules move with a speed of 300 m/s and strike the wall head-on in elastic collisions. What is the pressure exerted on the wall? (The mass of one N2 molecule is 4.68 x 10^-26 kg.)

    2. Relevant equations
    P = 2/3(N/V)(1/2mo(v^2)avg = F/A = [mo/d(N)(v^2)]/A

    3. The attempt at a solution
    I found the moles of N2 (I think this is how you do it, I was never strong in chemistry and haven't taken it in two years...)
    n = N/Na = 5 x 10^23/6.022x10^23 = 0.83 moles
    I believe n = N/V as well, so...
    P = 2/3(n)(1/2mo(v^2)avg
    I'm thinking I need to find the average speed... since I have vx, I can do the force one

    F = (4.68 x 10^-26)/d(5 x 10^23)(300^2)
    So I need to find 'd'...

    I'm stuck, I'm not sure whether to try and find 'd' (length of the wall the molecules are hitting), or try and find v.avg (I'm thinking I'd somehow do that with the time interval and the vx value, but I'm not sure how...)

    Thanks in advance.
  2. jcsd
  3. Nov 6, 2008 #2

    D H

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    You are off on a chemistry tangent; this is not a chemistry problem. You are given the average speed of the molecules hitting the wall, the number of elastic collisions with the wall during some time period, and the area of the wall. You aren't using this information!

    Hint: Try looking at it from a perspective of momentum rather than energy.
  4. Nov 6, 2008 #3

    (F)deltaT = deltap = movx
    F(1) = (4.68 x 10^-26 x 5 x 10^23)(300 m/s)
    F = 7.02 N

    P = F/A
    P = 7.02/0.08 m^2
    = 87.75 Pa??

    Is this right?? I feel like I'm on a better track now, thanks so much!! I'm just afraid that the Force is not correct, my final answer seems shady...
  5. Nov 6, 2008 #4

    D H

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    Two things are wrong:
    (1) Your force calculation assumes perfectly inelastic collisions. The collisions are elastic.
    (2) 8 cm2 is not 0.08 m2.
  6. Nov 12, 2008 #5
    instead, my force equation should be:
    F(deltat) = -2mvx?
    Which makes my answer -14.04, except I read in the textbook that the velocity component of an elastic collision is reversed because the mass of the wall is so much greater than the mass of the molecule. I don't quite understand the theory behind that?, but it makes my force positive and my final answer 17550 Pa
    Thank you for all of your help!!
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