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

1. Mar 16, 2009

### TFM

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

$$Z_{total} = \frac{1}{N!}_1^N$$

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

$$U = -\frac{\partial}{\partial \beta} ln z$$

3. The attempt at a solution

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

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

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:

$$Z_{total} = \frac{1}{N!}_1^N$$

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