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Finding z @ STP

  1. Sep 20, 2007 #1
    1. The problem statement, all variables and given/known data
    Beginning Calculations in Physical Chemistry
    Barry R. Johnson & Stephen K. Scott

    Calculate the average number of collisions per second between [tex]N_{2}[/tex] and [tex]O_{2}[/tex] molecules in air @ 298K and @ a pressure of 1 X [tex]10^5[/tex] in a room of volume V = 100[tex]m^3[/tex]. (Assume air has the composition 0.8[tex]N_{2}[/tex] & 0.2[tex]O_{2}[/tex])

    2. Relevant equations

    I follow the solution in the text, however, do you need the given volume to calculate z?
    Can't it be calculated from z = [tex]\sigma[/tex] [tex]\overline{c}_{rel}[/tex] [tex]\eta[/tex] using p/kT?

    3. The attempt at a solution
    Last edited: Sep 20, 2007
  2. jcsd
  3. Sep 21, 2007 #2


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    Staff: Mentor

    To get the collision density, n (collsions/ cm3-s), i.e. collisions per unit volume per second, one does not need the volume.

    To get the total number of collisions/sec, N, in the room as called for in the problem, one needs N = nV, where V is the total volume.
  4. Sep 21, 2007 #3
    zzzzzz @ STP

    Alrightee then. When I calculate z, I get an answer on the order of magnitude of [tex]10^9[/tex], and the book/authors get something on the order of [tex]10^38[/tex]. What is the descrepancy here?
    Last edited: Sep 21, 2007
  5. Sep 21, 2007 #4


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    Staff: Mentor

  6. Sep 22, 2007 #5
    ...will the real z @STP please stand up

    z= [tex]\sigma_{{N_2}{O_2}}[/tex] [tex]\overline{c}_{rel}[/tex] [tex]\eta[/tex]

    I can't figure out how to make the above read sigma c rel eta. I keep getting the error above even though the syntax is the same as below

    and [tex]\sigma_{{N_2}{O_2}}[/tex] = 0.415[tex]nm^2[/tex]

    [tex]\mu_{{N_2}{O_2}}[/tex] = 14.93gs/mol

    gives [tex]\overline{c}_{rel}[/tex] = 650m/s

    [tex]\eta_{{N_2}{O_2}}[/tex] = N/V =n[tex]N_a[/tex]/V = n[tex]N_a[/tex]p/nRT

    and after canceling out Avogadro's number gives
    [tex]\eta_{{N_2}{O_2}}[/tex] = p/kT

    So z = (0.415 x [tex]10^{-18}[/tex])(650)(2.43 x [tex]10^{25}[/tex])
    z= 6.55 x [tex]10^9[/tex] sec-1

    The authors get z = 2.55 x [tex]10^{36}[/tex] sec-1

    They calculate [tex]Z__{{N_2}{O_2}}[/tex] = [tex]\sigma_{{N_2}{O_2}}[/tex] [tex]\overline{c}_{rel}[/tex] [tex]N_a{^2}[/tex] [[tex]N_2[/tex]][[tex]O_2[/tex]] = 2.55 x [tex]10^{34}[/tex] sec-1 m-3
    and multiply this value by the volume 100[tex]m^3[/tex] to get 2.55 x [tex]10^{36}[/tex] sec-1.

    So where is my error?
    Last edited: Sep 22, 2007
  7. Sep 24, 2007 #6
    z @ STP

    I still can't figure out why there is such a large difference in the book's calculated value for z and my value. They do emphasize "total" collisions but this is because it is a mixture of gases.
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