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.
- K
_{p}for the reaction at 500^{o}C is 3.99×10^{-3}atm^{-1}Calculate DG^{o}for the reaction. - Show that .
- What is chemical potential? Is it extensive or intensive?
- How many components are present in a system in which NH
_{4}Cl (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 CO
_{2}(g) b) water vapour. - Calculate the ratio of the translation partition functions of D
_{2}and H_{2}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 C
_{p}= 6.2 + 1.3 x 10^{-3}T in the temperature range 27^{o}C to 600^{o}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 25
^{o}C was measured in series of molalities (m) and it was found that the volume fitted the expression

V (CC) = 1003 + 16.62m + 1.77 m^{3/2} + 0.km^{2} 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 N
_{2}O_{4}when heated was found to occupy a volume of 500 ml at 45^{o}C 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 25
^{o}C 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 N
_{2}(g) at 27^{o}

(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 N
_{2}(g) at O^{o}C is

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

Where P is in atm; V is in litres. Find the fugacity of N_{2} at O^{o}C and 100 atm.

pressure.

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

pressure.

- 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 Cl
_{2}at 500K if the wave

number of the vibration is 560 cm^{-1}.

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