1. Answer ALL parts.

(a)    What is the practical relevance of the Liouville theorem?

[5%]

(b)    Calculate the coordination number, up to r = 6 Å, for a model liquid of number density 0.01

Å-3 which g(r) can be written as:

g(r) = ✓ ◆ +1

[20%]

(c)    The vibrational temperature of the K2 and O2 molecules is 133 K and 2256 K, respectively. Sketch on the same plot the qualitative trend of the population of the vibrational levels of  both K2 and O2 at 300 K.

[20%]

(d)    Consider the following ionization reaction:

K ! K+ + e −

i.     Calculate the translation partition function of reactants and products at temperature T = 2000 K. Consider a volume V = 1 m3 . The mass of K and e- is 6.49•10-26  Kg and 9.1•10-31  Kg.

[25%] ii.     Calculate the electronic partition function of reactants and products, assuming they

are all in their ground state. Note that K has the following electronic configuration: [Ar]4s1 , which is characterised by a degeneracy of 2. The electron is also             characterised by a degeneracy of 2.

[20%] iii.     Write down the equilibrium constant for this reaction in terms of partition functions.

[10%]