Loyola College M.Sc. Chemistry Nov 2003 Thermodynamics & Statistical Mechanics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

M.Sc., DEGREE EXAMINATION – CHEMISTRY

CH-2800/815  – THERMODYNAMICS & STATISTICAL MECHANICS

28-10-2003                                                                                                     Max:100 marks

1.00 – 4.00

PART – A                                           (10×2=20 marks)

1. If V = for 1mole of an ideal gas show that dV is a complete differential.
2. Kp for the reaction at 500oC is 3.99×10-3 atm-1 Calculate DGo for the reaction.
3. Show that .
4. What is chemical potential? Is it extensive or intensive?
5. How many components are present in a system in which NH4Cl (s) undergoes thermal decomposition?
6. Calculate the number of ways of distributing 20 identical objects with the arrangement 1, 0, 3, 5, 10, 1.’
7. What is the significance of partition function?
8. What is the residual molar entropy of CO at T = O?
9. Identify the systems for which it is essential to include a factor of on going from molar partition function to molecular partition function a) a sample of CO2 (g) b) water vapour.
10. Calculate the ratio of the translation partition functions of D2 and H2 at the same temperature and pressure.

PART – B                                           (8×5=40 marks)

1. Derive expressions for isothermal reversible expansion of 1 mol of Vander Waal’s gas for a) W b) D
2. DS of a solid in cal/k/mole is given by the equation Cp = 6.2 + 1.3 x 10-3T in the temperature range 27oC to 600o Calculate DS when 1 mole of this metal is heated from 300 k to 600 k.
3. Derive any two Maxwell equations.
4. The volume of an aqueous soltuon of NaCl at 25oC was measured in series of molalities (m) and it was found that the volume fitted the expression

V (CC) = 1003 + 16.62m + 1.77 m3/2 + 0.km2 where V is the volume of a solution of molality 1.  Calculate the partial molar volume of a the components in a solution of molality 0.1.

1. 325 g of N2O4 when heated was found to occupy a volume of 500 ml at 45oC and at 800 mm Hg pressure Calculate i) Kp ii) pressure at which the degree of dissociation is 50%.
2. Explain how partition functions can be separated.
3. Calculate the standard molar entropy of Xenon gas at 100 K.
4. Calculate the electronic partition function of a Tellurium atom at 500 K using the following data.

Term                Degeneracy                 Wave number (cm-1)

Ground                 5                                     0

1                      1                                   4707

2                      3                                   4751

3                      5                                 10559

1. Explain how the absolute entropy of a gas at 25oC can be determined using third law of thermodynamics.
2. Compare Maxwell – Bolltzmann, Fermi – Dirac and Bose – Einstein statistical distributions.
3. Calculate the molecular rotational partition function for N2 (g) at 27o

(I = 13.9 x 10-47 kgm-2).

1. Derive an expression for transnational partition function.

PART – C                                           (4×10=40 marks)

1. a) Derive Gibbs – Duhem equation.
2. b) Show that for 1 mole of a van der waal’s gas.
3. a) Explain how activity coefficient of an electrolyte be determined using EMF data.
4. b) Derive thermodynamically phase rule equation.
5. a) The virial equation of state for N2(g) at OoC is

PV = RT – 1.051 x10-2 P + 8.63 x 10-5 P2 + ….

Where P is in atm; V is in litres.  Find the fugacity of N2 at OoC and 100 atm.

pressure.

1. b) Deduce the expression for the variation of chemical potential with i) temperature ii)

pressure.

1. State the postulates of Maxwell – Boltzmann statistics and hence derive an expression for the most probable distribution.
2. Compare Einstein’s theory of heat capacity of solids with Debye’s theory.
3. a) Explain how equilibrium constant of a reaction be obtained using statistical mechanics.
4. b) Explain transition state theory using statistical concepts.
5. a) Derive the relation

E = .

1. b) Calculate the vibrational contribution to the entropy of Cl2 at 500K if the wave

number of the vibration is 560 cm-1.

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