Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

CH273 – Statistical Mechanics

Revision Lecture – Mock Exam

(a) Explain why and how the thermal De Broglie wavelength is relevant in the context of choosing which statistics (Boltzmann, Fermi-Dirac or Bose-Einstein) to apply to the treatment of a system of indistinguishable particles within the canonical ensemble. [10%]

(b) The vibrational temperatures of HCl and HBr are 4227 K and 3787 K, respectively. Which of these two diatomic species is characterised by a higher value of its vibrational partition function? Why? [30%]

(c) Consider the following gas phase reaction, taking place in the stratosphere at the temperature T = 230 K:

SO + O2 → SO2 + O

(i) Write down the expression of the equilibrium constant Kc(T) in terms of molecular partition functions. [10%]

(ii) Calculate the rotational contribution to Kc(T) using the Euler-Maclaurin summation formula. The rotational temperatures of SO, O2 and SO2 are 3.24 K, 2.07 K and 6.84 K, respectively. Treat SO2 as a linear molecule. [25%]

(iii) Calculate Kc(T), knowing that the translational and vibrational contributions at the temperature of interest are equal to 0.83 and 12.75, respectively. Note as well that the dissociation energies D0 for SO, O2 and SO2 are 178 kcal/mol, 118 kcal/mol and 298 kcal/mol, respectively. Assume that in computing the vibrational contributions the zero of energy has been chosen to correspond to the vibrational ground state. [25%]