1) Calculate the translational, rotational, vibrational (calculate excluding and including the zero point energy term), and electronic (calculate taking the zero of energy to be that of the ground state molecule and that of the separated atoms) contributions to the internal energy (U) for gaseous ammonia at 25 ºC and 1 bar (such that the volume is that appropriate for 1 mole of molecules). The mass is 17.024 amu. The rotational constants are 9.44, 9.44, and 6.2 cm^-1. The vibrational constants (and degeneracies) are 3336 (1), 932 (1), 3443 (2), and 1616 (2) cm^-1. The ground electronic state has a degeneracy of 1 (the state is ¹A₁) and the atomization energy is D₀ = 1158 kJ/mol.

2) Calculate the translational, rotational, vibrational (calculate excluding and including the zero point energy term), and electronic (calculate taking the zero of energy to be that of the ground state molecule and that of the separated atoms where D₀ = 1158 kJ/mol) contributions to the constant volume heat capacity (C_V) for gaseous ammonia at 25 ºC and 1 bar (such that the volume is that appropriate for 1 mole of molecules). Compare your answer with the experimental value of 26.75 J/K mol. 

3) For a system of independent, distinguishable particles that have only two quantum states with energies of 0 and eand degeneracies of g₀ and g₁, it can be shown that the molar heat capacity of such a system is given by

C_V/n = R g₁ (be)²exp(-be) / [1+exp(-be)]². 

Calculate this value for e = 404, 881, and 3685 cm^-1 (the excitation energies of the ²P_1/2 excited states of F, Cl, and Br, respectively) at T = 300 K. 

4) Evaluate q_Trans/N for one mole of

a) O₂(g) at its normal (1 atm) boiling point of 90.20 K. Use the ideal-gas equation of state to calculate the volume and m(O₂) = 32.0 amu.

b) He(g) at its normal boiling point of 4.22 K. Use the ideal-gas equation of state to calculate the volume and m(He) = 4.0 amu.

c) electrons in sodium metal at 298 K. Use a density r = m_NaN/V value of 0.97 g/mL where m_Na = 23.0 amu.