Download 4 Advanced Physical Chemistry – Exercizes 4.1 Calculate the

4 Advanced Physical Chemistry – Exercizes
4.1
Calculate the thermal de Broglie wavelengths of the following objects:
a) a “thermal” neutron at 300 K
b) a hydrogen molecule at 12 K
c) a hydrogen molecule at 300 K
d) a carbon dioxide molecule bei 300 K
e) a proton a 108 K
Compare the thermal with the“normal” de Broglie wavelength: What is assumed for the average speed of the molecules?
4.2
The hydrogen molecule has a moment of inertia of 4.603 × 10−48 kg m2 . Compute
a) the reduced mass and the bond length,
b) the energies of the first three rotation levels (assuming that the molecule can be regarded
as a rigid rotator),
c) the energy differences, the wavenumbers and the wavelengths for the transitions between
the rotational levels with the quantum numbers 0 and 1, 1 and 2 as well as 2 and 3,
d) the population ratios (relative to level 0) of level 1–3 at 70 K! Which consequences follow
for the Raman spectrum?
4.3
How many energy levels contribute more than 0.1% to the vibrational partition function
of iodine at 298.15 K and at 373.15 K (ν̃0 = 214.6 cm−1 )?
4.4
The energy difference between ground state and first excited state of a molecule amounts
to 10 kJ/mol.
a) Assume that the molecule has only these two states, and compute the partition function,
the internal energy , and the Helmholtz energy at 25 ◦ C, 35 ◦ C, and 45 ◦ C.
b) Calculate the same properties for a molecule that has an infinite number of equidistant
states (all 10 kJ/mol apart).