The 7th energy level is the maximum population.
Fraction of molecules in
each rotational level at 300 K
The 13th energy level is the maximum population.
Array below is for 3:
Fraction of molecules in
each rotational level at 1000K
At 10,000 K about 14.6% of the vibrations are in the second state. Thus we can say that the energy difference between the ground state and the first excited state is a large amount.
The electronic partition function is equal to 1 because the first level is equal to the degeneracy (here g = 1). The other levels do not play a role because the energy gaps between the levels are so large that the probability of filling them is extremely low.
7.
CO2 has four vibrational modes. The third and fourth mode listed above are degenerate (bending modes).
These are the vibrational temperatures for the modes of vibration of water at 15 C.
8. The rotational heat capacity depends on the symmetry of the molecule. CO2 is linear and has only two rotational degrees of freedom. Since it is linear, it has there is only one Thetar value (the two moments of inertia are equal) and σ =2. The qr for CO2 is
H2O is a nonlinar polyatomic and is an asymmetric top. This means water has three different moments of inertia and three different Thetar values. Now qr is
9. CO2 is a linear molecule so it has 2 rotational degrees of freedom. This leave 3n-5 for vibrational degrees of freedom. For CO2 (three atoms), there are 3*3-5 = 4 vibrational modes. For H2O, a nonlinear molecule, there are 3 rotational degrees of freedom. This leaves 3n-6 for vibrational degrees of freedom. Water also has three atoms so there are 3*3-6 = 3 vibrational modes for water.
11. The statistical mechanical calculations are very accurate. For water, the difference between the calculation (25.169 J/mol*K) from the experimental (25.28 J/mol*K) is 0.44%. For CO2, the difference between the calucation and experimental (28.279 and 28.09 J/mol*K respectively) is 0.67%.