Gauhati University B.Sc. 3rd Year Chemistry-Major Questions on the Topics of Statistical Thermodynamics & Data Analysis (2001-05)

Year 2005 New: Q4(a). Derive the Sackur-Tetrode equation (about molar translational entropy) OR Find an expression for equilibrium constant of ideal gas reactions in terms of partition functions of reactant and product molecules. (6 marks) Q.4.(c) Prove that the vibrational partition function is q_vib = exp (–hn/(2kT)) [1– exp(–hn/(kT))]^–1 for each degree of freedom. OR What'll be the vibrational p.f. of a diatomic gas at 298.15 K if n = 2.676 x 10¹³ s^–1 (4 marks) Q.4.(e) Calculate the ratio of number of particles in two energy states having two degeneracy but energy difference of 17 kJ mol^–1 at 1000 K. (2 marks)

Q.6.(a) How many types of errors are there? Discuss. (5 marks). Q.6(b). When the method of least squares is used? What is average standard deviation? (3 marks).

Year 2005 Old: Q14(a). Discuss the physical interpretation of partition function. (? marks). Q14(b). Derive an expression for the rotational partition function. (? marks). Q14(c). Calculate the translational partition function for benzene in a volume of 100 cm³ at 127 ⁰C (? marks).

Year 2004 New: Q5(a). Calculate the population ratio of two energy levels with energy difference of 17 kJ mol^–1 at 727 ⁰C, the multiplicity of higher level being 3 and lower level being 2. (2 marks) Q.5.(b). Calculate the translational partition function for benzene in a volume of 100 cm³ at 27 ⁰C (3 marks). Q.5.(c) Prove that q_rot = 8p²IkT / (sh²) where the terms have usual meanings). (5 marks). Q.5.(d) What is characteristic rotational temperature? (2 marks) Q.6(a). Two students were given a sample of commercial zinc containing (49.06±0.02) % of zinc for analysis. Observation for the first student is 49.01, 49.21 and 49.08% while for the second student it is 49.40, 49.44 and 49.42%. Find the relative mean error and relative mean deviation for both. Who is more accurate and who is more precise? (5 marks) Q.6(b). Illustrate with examples what is meant by coefficient of variation? (3 marks)

Year 2004 Old: Q.14.(a) Find an expression for the most probable distribution of N particles among the various energy levels according to Bose-Einstein Statistics. OR Derive an expression for the translational partition function of a particle of mass W moving in a three-dimensional box of sides x, y, z assuming that potential energy is zero within the box. (? marks). Q.14.(b) Use Boltzmann distribution law and the related partition functions to calculate the internal energy of a system. Q.14.(c) Use concepts of partition functions to calculate the equilibrium constant of the reaction

aA + bB = cC + dD (? marks). Q.14.(d) State Debye theory of heat capacities. What do you mean by characteristic Debye temperature of vibration? (? marks).

Year 2003 New: Q.5.(a) Find an expression for molecular partition function for translational motion in three dimensions (6 marks). Q.5.(b) Deduce the relationship S = k lnW (4 marks). Q.5.(c) Show that for a mono-atomic gas u = 1.5 N_A k T (2 marks) Q.6.(a) Write briefly about the various types of errors in measurement. What do you understand by uncertainty in the measurement of physical quantities. Explain. (4 marks). Q.6.(b) The percentage of constituent A in the compound AB were found to be 48.32, 48.36, 48.23, 48.11 and 48.38 percent. Calculate the mean deviation and the relative mean deviation. (2 marks). Q.6.(c) Define accuracy and precision. (2 marks)

Year 2003 Old: Q.14.(a) Relate thermodynamic internal energy to partition function (? marks). Q.14.(b). Calculate the translational partition function for hydrogen atoms at 3000 K confined to move in a box of volume 2.5 x 10⁵ cm³. What is the physical interpretation of the partition function? (? marks). Q.14.(c) State and explain the Einstein theory of heat capacities of solids (? marks).

Year 2002 New: Q.1.(c) Find the expression for rotational partition function of an ideal diatomic gas. Calculate the value of characteristic rotational temperature of H₂ (g), given that moment of inertia of H₂(g) = 4.6 x 10^–48 kg m² (3+2 marks). Q.10.(a) Derive the Sackur-Tetrode equation for molar translational entropy (5 marks). Q.10.(b) Obtain an expression for the equilibrium constant of a chemical reaction in terms of partition functions. (5 marks). Q.11.(a) Interpret physically the significance of the Boltzmann distribution law (3 marks).

Year 2001 New: Q.10.(a) Deduce the relationship S = k lnW (4 marks). Q.10.(b) What is the physical significance of molecular partition function? Show that for a mono-atomic gas u = 1.5 N_A k T (1+2 marks). Q.10.(c) The vibrational frequency of a diatomic molecule is 1600 cm^–1. Find its vibrational partition function at 1000 K. (3 marks). Q.11.(a) Derive an expression for translational molecular partition function for an ideal gas. (4 marks). Q.11.(b) Calculate the translational partition function of a D₂ molecule inside a 100 cm³ box at 300 K. (2 marks). Q.11.(c) Find an expression for the heat capacity of Einstein crystal. What is the limiting value of heat capacity of a crystal at T à a? (3+1 marks).