Calculating Molar Gibbs Function

[LeePhilip01]

Homework Statement

For this question I'm to calculate the molar Gibbs function, G-G₀, at 2000K for BSi given that the bond distance is 1.905[itex]A^{\circ}[/itex], [itex]ω^{~}[/itex] = 772cm^-1, the ground electronic state has a degeneracy of 4, and the lowest energy excited electronic state, 8000cm^-1 above the ground state, also has a degeneracy of 4.

Homework Equations

Gibbs Function G = H-TS ... (1)

where H is enthalpy, T is temperature and S is entropy.


G-G₀ = -kT ln(Z) + nRT ... (2)

The Attempt at a Solution

So since it's molar I'm assuming there's going to be a volume term somewhere (in calculating partition function) and V=0.02446m³.

Do I need to work out all the individual contributions to the partition function, Z, then just simply plug them into (2) ?

 

[BigJDubs]

$G-G0 = -kT ln(Z) + nRT$ Where,$Z= Z_eZ_vZ_rZ_n$ $Z_e = 4$ (degeneracy of ground state) $Z_v = \frac{V}{h^3}$ (I think...) $Z_r = \frac{1}{2\pi mkT}$ (?) $Z_n = \frac{1}{2\pi hc}\int_{0}^{\infty}\frac{\omega^2}{e^{\frac{\omega}{kT}}-1}d\omega$ and then plugging into (2) I get $G-G0 = -kT ln\big(\frac{V}{h^3}\frac{1}{2\pi mkT}\frac{1}{2\pi hc}\int_{0}^{\infty}\frac{\omega^2}{e^{\frac{\omega}{kT}}-1}d\omega\big)+ nRT$