1. Derive the partition functions of translational energy, vibrational energy, rotation energy and electronic energy.

2. Define and explain the 3^rd law of thermodynamics in the aspect of statistical thermodynamics.

3. The isotopic composition of chlorine is 75.4 atom% ³⁵Cl and 24.6 atom% ³⁷Cl. Suppose that in the limit of 0 K, crystals of Cl₂ contain a random mixture of isotopic species. Calculate the ΔS of mixing per mole of Cl₂. If Cl₂ were completely dissociated into atoms, what would be the ΔS of mixing?