Calculate the translational partition function of a nitrogen, N₂, molecule in a sample of 0.010 mol of gas held in a vessel at a pressure of 1.00 bar and a temperature of 298 K.

Calculate the rotational partition function for a hydrogen chloride, ¹H³⁵Cl, molecule at 298 K.  The bond length of hydrogen chloride is 127 pm.

Calculate the vibrational partition function for the sodium dimer, Na₂, molecule at 298 K. The harmonic vibrational wavenumber is 159 cm^–1. 

The vibrational modes of a boron trifluoride molecule, ¹⁰BF₃, are listed below.  Calculate the vibrational partition function at 1000 K.

The ground configuration of the titanium oxide, TiO, radical gives rise to a ³P term, which comprises ³P₂, ³P₁ and ³P₀ levels.  The ²P₂ level lies lowest in energy and has a degeneracy of 5, the ²P₁ level lies the equivalent of 67 cm^–1 higher in energy and has a degeneracy of 3 and the ²P₀ level lies 141 cm^–1 higher in energy than the lowest level and has a degeneracy of 1.  Assuming that all other levels lie too high in energy to be significantly populated, calculate the electronic partition function at 298 K.

Predict a value for the standard constant volume heat capacity, C_Vʅ, of a closed-shell heteronuclear diatomic molecule at high temperature.

Residual entropy arises because of the different configurations that may exist even at 0 K. The entropy of the B³⁵Cl₂³⁷Cl isotopomer of boron trichloride is non zero even at 0 K because the molecules may be orientated within the crystal in different ways. Use the Boltzmann formula to calculate the residual molar entropy of a sample of B³⁵Cl₂³⁷Cl at 0 K.

Calculate the contribution that rotational motion makes to the molar entropy of bromine, Br₂, gas at a temperature of 298 K.  The rotational constant of Br₂ is 0.0808 cm^–1.

Calculate the standard molar Gibbs energy of sodium vapour, Na, at a temperature of 298 K, relative to that at 0 K. 

Hydrogen, H₂, may exist in two forms: in ortho-hydrogen, o-H₂, the nuclear spins are parallel, whilst in para-hydrogen, p-H₂, the spins are antiparallel.  Ortho-hydrogen is threefold degenerate, so that the nuclear partition function q^S(o-H₂) = 3, whilst para-hydrogen is singly degenerate and has a nuclear partition function q^S(p-H₂) = 1.  Only rotational levels with odd values of J are permitted for ortho-hydrogen, whilst only even values of J are permitted for para-hydrogen. 

The two forms of hydrogen coexist in equilibrium in the presence of a catalyst such as charcoal.  Calculate, by direct summation, the equilibrium constant for the conversion of ortho-hydrogen to para-hydrogen at a temperature of 200 K.  The rotational constant of hydrogen is 60.80 cm^–1.