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Partition Theory of Nitrigen to determine ther quantities (eg U, H, F)

  1. Mar 16, 2009 #1

    TFM

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    1. The problem statement, all variables and given/known data

    For a mole of nitrogen (N2) gas at room temperature and atmospheric pressure, compute the following: U, H, F, G, S and μ. The internal partition function is purely rotational, and the rotational constant ε for N2 is 0.00025 eV. The electronic ground state is not degenerate.

    2. Relevant equations

    [tex] Z_{total} = \frac{1}{N!}_1^N [/tex]

    [tex] Z_1 = Z_{int} = \sum{exp(-E_{int}(s)/k_BT)} [/tex]

    [tex] U = -\frac{\partial}{\partial \beta} ln z [/tex]

    3. The attempt at a solution

    Okay, I am having a slight problem calculating the Z value. I have used:


    [tex] Z_1 = Z_{int} = \sum{exp(-E_{int}(s)/k_BT)} [/tex]

    and inserted 300 K, E = 0.00025 eV abd the Boltzmann Constant (in eV) into this, and have got 9.67 *10^{-3}

    I now want to use:

    [tex] Z_{total} = \frac{1}{N!}_1^N [/tex]

    but N is the number of particles, which is 1 Mole x Avagadros Number. This leaves with a large number which I have to find the factorial of, but it is too large for Excel. Have I gone wrong somewhere?

    TFM
     
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