Chemistry Paper 1 PDF 2007 (PG/I/CHEM/I/07)

Total Pages--9. PG/I/CHEM/I/07 2007 CHENIISTRY PAPER-I Full Marks :7 5 Time : 3 hours The Figures. in the right hand margin indicate marks Candidate...

Total Pages--9. PG/I/CHEM/I/07 2007 CHENIISTRY PAPER-I Full Marks :7 5 Time : 3 hours The Figures. in the right hand margin indicate marks Candidates are required to give their answers in their own- words as far as practicable Illustrate the answers wherever necessary GROUP-A Answer any one question (a) Define precise values and expectation values in quantum mechanics. ( b). State and prove `Turn Over ' rule. (c) Find the  ( 2 ) Or (a) Find the commutator (1) [Lz L] (ii) [L L"J Z, where L. and L are raising and lowering operators respectively. ( b) What is tunneling? Explain this with the help of uncertainty principle. A A (c) Prove that if A and B are Hermitian operators then [ A, B ] is anti-Hermitian. ( d) If AV= a, , what is the value of 'b ' in the eigen-equation eA.V bye (3 + 3) + 3 + 4 + 2 2. (a) Show that A. A (LL , z) =2A(9L, -Lyz) ( b) What is meant by phase velocity and group velocity ? How can it be shown that the energy of subatomic material particles is transported by wave packet? 5+(4+6) PG/I/CHEM/I/07 ( Continued )  3 GROUP - B Answer any two questions (a) Obtain the expression for the thermodynamic probability of the distribution of n. particles in i-different energy states , the i state being g. -fold degenerate and hence obtain the Boltzmann distribution formula in term of the energy multiplier 0 and the molecular partition function. (b) Using Boltzmann distribution formula calculate the ratio of population of particles in two nondegenerate levels with energies.10 and 20 K cal/mole at 27° C. 11+4 4. (a) Find out the expression for molecular partition function due to rotational motion and hence show that the molar rotational. energy is RT. (b) What is fugacity co-efficient ? What is its utility ? ( c) Define a grand-canonical ensemble. PG/I/CHEM/I/07 ( Turn Over)  4 ) ( d) 2 gm-moles of water initially at 27°C are converted to a final state of vapour at 227°C at 1 atmospheric pressure. Given that heat capacity of water and water vapour are 1 cal/gm and 0.40 cal/gm respectively , latent heat of vaporisation of water is 540 cal/gm, compute the total change in entropy. (Assume ideal behaviour of vapour ). (5+2)+(1+ 1)+3+3 5. (a) Considering the following consecutive reaction, kI k2 A -, B -b obtain expressions for the maximum concentration of B and also for the time when concentration of B will be maximum. ( b) What is flow method ? What are its limitations? (c) Relaxation time for the fast reaction kI A r=' B is 10µs. and equilibrium constant is k_I 1.0x 10-3. Calculate kl andk _r. 7+4+4 6. (a) How does the electron transfer reactions by inner sphere mechanism occur ? Show with a suitable example. Illustrate with an example. PG/I/CHEM/I/07 ( Continued)  5 ( b) Write down the salient. features of transition state theory. (c) The protein catalase catalyzes the reaction 2H202 ( aq) -'2H20 (1)+02(g) andhasaMichaelisconstant km =25 x 10-3mo1 dm-3 and :a turnover number of 4.0 x 107S-1. Calculate the initial rate of this reaction if the total enzyme concentration is 0-0 16 x 10-6 mot dm-3 and the initial substrate concentration is 4-32x 10 - 6 mol dm" 3. Calculate vm,,, for this enzyme. Catalase has a single active site. 6+4+5 GROUP -C Answer any two questions 7. (a) Solve linearised Poisson -Boltzmann equation for dilute ionic solution (given below) and find its approximate solution ( +) _ z e2 f l r2 dr i (r) r2. dr KB T j (symbols have their usual meaning). PG/I/CFIEM/I/07 ( Turn Over)  ( 6 ( b) Define Debye-Huckel reciprocal. length (rnH) and show that 500 DEO KB T 1/2 rnH - 2 NAeI (symbols have their usual meaning). (c) Calculate Debye-Huckel reciprocal length of ionic atmosphere for 5 x 10 - 3 (N) K2S04 solution in a solvent of dielectric constant 60 at 27°C. 5+5+5 8. (a) Writedown the Butler-Volmer equation for one- step single electron transfer electrodic reaction and explain the terms involved. Show that V)) near equilibrium it reduces to Ohm's law for interfaces and (ii) far away from equilibrium it becomes an exponential Tafel's law. ( b) Describe the basic principle for determination of dissociation constant of a week electrolyte precisely by a conductometric method. (c) Describe the basic principle of cyclic voltametry briefly. 8+4+3 PG/I/CHEM/I/07 ( Continued )  (a) Writedown the selection rule and hence deduce the expression of frequency for the P and R branch of line in vibration-rotation combined spectrum. (b) Partial infra-red spectral data of 12C 160 molecule under high resolution are as follows : Line w, cm- Line w, cm- P, 2139.43 RI 2147 08 P2 2135.55 R2 2150.86 P3 2131.63 R3 2154.59 P4 2127.68 R4 2158.31 Calculate the bond length of 12C 160. (c) Energy expression of a diatomic molecule exhibiting Morse potential is given by, E= (v+21 by - hvxe (+!) 2 For what value of vibrational quantum number, the molecule will dissociate. Deduce an expression for the dissociation energy of the molecule. (1+2+2)+5+(3+2) PG/I/CIEM/I/07 May} Over)  ( 8) 10. (a) What is Raman Scattering? How does classical. mechanics account for the existance of Rayleigh as well as Raman fines ( b) What do you mean by London dispersion energy? F2 and Cl2 are gases at room temperature, Br2 is liquid ' and 12 is solid. Explain. (c) Explain, why only molecules having permanent dipole moment are rotationally active. 1Z+J)+(S+Z)±3 a) Define rotational constant of a molecule. The rotational constant for H35 Cl is observed to be 10.5909 cm''. What - is the value of the rotational constant for 2 D 3501 (b) On what. factors does the intensity of a spectral line depend ? Show that the intensity of a spectral line in the rotation spectra will be maximum when ( Continued)  ( 9 ) (c) Show that in the spectrum of a non-rigid rotator, the separation between successive lines decreases steadily with increasing ! value. 5+5+5 PG/I/CIIEM/I/07 MV-150