LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
M.Sc., DEGREE EXAMINATION – CHEMISTRY
SECOND SEMESTER – NOVEMBER 2003
CH-2800/815 – THERMODYNAMICS & STATISTICAL MECHANICS
28-10-2003 Max:100 marks
1.00 – 4.00
PART – A (10×2=20 marks)
Answer ALL questions.
- If V = for 1mole of an ideal gas show that dV is a complete differential.
- Kp for the reaction at 500oC is 3.99×10-3 atm-1 Calculate DGo for the reaction.
- Show that .
- What is chemical potential? Is it extensive or intensive?
- How many components are present in a system in which NH4Cl (s) undergoes thermal decomposition?
- Calculate the number of ways of distributing 20 identical objects with the arrangement 1, 0, 3, 5, 10, 1.’
- What is the significance of partition function?
- What is the residual molar entropy of CO at T = O?
- 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.
- Calculate the ratio of the translation partition functions of D2 and H2 at the same temperature and pressure.
PART – B (8×5=40 marks)
Answer any EIGHT questions.
- Derive expressions for isothermal reversible expansion of 1 mol of Vander Waal’s gas for a) W b) D
- 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.
- Derive any two Maxwell equations.
- 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.
- 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%.
- Explain how partition functions can be separated.
- Calculate the standard molar entropy of Xenon gas at 100 K.
- 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
- Explain how the absolute entropy of a gas at 25oC can be determined using third law of thermodynamics.
- Compare Maxwell – Bolltzmann, Fermi – Dirac and Bose – Einstein statistical distributions.
- Calculate the molecular rotational partition function for N2 (g) at 27o
(I = 13.9 x 10-47 kgm-2).
- Derive an expression for transnational partition function.
PART – C (4×10=40 marks)
Answer any FOUR questions.
- a) Derive Gibbs – Duhem equation.
- b) Show that for 1 mole of a van der waal’s gas.
- a) Explain how activity coefficient of an electrolyte be determined using EMF data.
- b) Derive thermodynamically phase rule equation.
- 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.
- b) Deduce the expression for the variation of chemical potential with i) temperature ii)
- State the postulates of Maxwell – Boltzmann statistics and hence derive an expression for the most probable distribution.
- Compare Einstein’s theory of heat capacity of solids with Debye’s theory.
- a) Explain how equilibrium constant of a reaction be obtained using statistical mechanics.
- b) Explain transition state theory using statistical concepts.
- a) Derive the relation
E = .
- 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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