CH 2810 – THERMODYNAMICS AND STATISTICAL MECHANICS

Date : 24/04/2008 Dept. No. Max. : 100 Marks

Time : 1:00 – 4:00

PART A

Answer ALL the questions. (10 x 2 = 20 Marks)

Show that m_i (Chemical potential) = (dE/dn_i)_S,V,nj
Give the cause and the manifestation of Peltier effect.
The mean ionic activity coefficient g_±for Al₂(SO₄)₃ in 0.1 m solution at 25⁰C is 0.13. Find m_± and a_±
For the reaction, CuSO₄.3H₂O(s) ⇌ CuSO₄.2H₂O(s) + H₂O(g). The equilibrium pressure is 7.37 ´ 10^-3 atm at 25° Calculate DG⁰ for the reaction at 25°C.
Write down the Onsager relationship between the forces and the flux, when three fluxes (J_1,J₂ and J₃) and the conjugate forces (X₁, X₂ and X₃) are coupled.
Calculate the ratio of number of ways of distributing particles at 25⁰C if the energy levels are separated by 10 kJ /mol
Evaluate ln N!, when N = 10 using Stirling’s formula and calculate the % error introduced by this formula.
At what temperature Q_vib = 10 for N₂? (= 2355 cm^-1)
Calculate C_V of PH₃ (g) using equipartition principle.(R=8.314 J K^-1 mol^-1)
What is meant by residual entropy?

PART – B

Answer ANY EIGHT questions (8 x 5 = 40 Marks)

Explain the use of Ellingham Diagram with reference to the extraction of metals.
Calculate the fugacity of H₂ at 100 atm and 298 K if the fugacity at 25 atm and 298 K is 25.4 atm. The van der Waals constants are a=0.245 l² atm mol^-2 and b = 2.67 x 10^-2 l mol^-1.
Partial molar volume of methanol in a methanol-water solution in which the mole fraction of methanol is 0.39, is 39.2 cm³ mol^-1. If the density of the solution is 0.91 g cm^-3, calculate the partial molar volume of water in the solution
With the help of a phase diagram, explain fractional distillation of a non-ideal solution consisting of a minimum boiling point mixture of water and ethyl acetate.
How are mass and energy conserved in irreversible thermodynamics?
Explain the entropy production when heat is flowing into a system.
Explain how partition functions can be separated.
Calculate the translational entropy of HCl(g) at 298 K and at 1 atm pressure.
Derive the general relation connecting Helmholtz free energy ‘A’ and molecular partition function (Q)
One vibrational mode in CO₂ molecule has a frequency 672 cm^-1 and it is doubly degenerate. Calculate Q_vib for this mode at 298 K.
Derive an expression for rotational partition function for a diatomic molecule.
Compare the three statistical distributions.

Answer ANY FOUR questions (4 x 10 = 40 Marks)

23 a) How will you apply the Nernst distribution law for the determination of the activity of a solute? (5)

b) Consider a hypothetical solute A and when n₂ moles of A is dissolved in 1000 g of water, the DH can be expessed as, DH = 20.5 m₂ + 8.4 m₂². Calculate L₂ and L₁ for 1 molal solution.
a) One mole of each of N₂ and H₂ are allowed to react in a closed container at 10 atm pressure and 725 K. The formation of NH₃is given by the equation, ½ N₂(g)+3/2 H₂(g) ⇌ NH₃(g). The reaction is allowed to attain equilibrium. On analysis, 0.033 moles of NH₃ was found to be formed at equilibrium. Calculate the value of Kp at 725 K.
b) Draw and explain the phase diagram of a three component system involving two solids (B and C) and water (A) in which only pure components crystallize from aqueous solutions.
a) State the postulates of irreversible thermodynamics. (3)
b) How will you verify Onsager’s reciprocal relationship experimentally using Elecrokinetic effects?
Explain the postulates of Maxwell-Boltzmann distribution and hence derive an expression for most probable distribution.
Explain the postulates of Einstein’s theory of heat capacity of solids. Compare it with Debye’s theory.
Give an account of any two of the following a) Application of Bose-Einstein statistics b) Equipartition principle
c) Significance of partition function d) Expression for vibrational entropy