QUESTION 4 [TOTAL MARKS: 25] Molecular hydrogen is initially at atmospheric pressure (105 Pa = 1 atm) and room temperature T= 300 K corresponding to an initial number density n of H2 molecules. Q 4(a) [15 Marks) The gas is heated under thermodynamic equilibrium conditions. Ideal gas behaviour is assumed throughout. As the temperature increases, the H, molecules dissociate into atomic hydrogen H species following the reaction H22H. At the final temperature T >> 300 K, the number densities of the molecular and atomic species are n₁, and nн, respectively, and their values given by the Law of (n) 3.554x10" U mass action according to which nH₂ dis -exp = f(T), where T2 kBT Udis = 4.476 eV is the dissociation energy of the H2 molecule in its ground electronic state 'Σ. The function f(T) is known and plotted below on a log scale in the 4750 K <T<6000 K temperature range. (x = T in the equation displayed on the graph). 4-1026 3-1026 2-1026 4.476x11500 y3.554x10 X m 1 8-1025 7-1025 6-1025 5-1025 41025 3:1025 2-1025 25 8-1024 4750 5000 7-1024 5250 5500 5750 6 Temperature (K) 6000 6250 5-1024 PS302 Statistical Physics Semester 1 Examinations 2019/2020 Page 5 of 8 The degree of dissociation α of the gas is defined as the fraction of the number of original molecules that have dissociated into atoms, i.e. α=- n-nh. n (i) Estimate the temperature at which a fraction a = 0.6 of the initial molecules has dissociated. [10 Marks] (ii) What is the dissociation fraction of the gas at T = 8000 K? [5 Marks] Hint: 1 eV = 1.6x10-19 J = 11,500 K