Chemistry Paper I

(a) One real gas equation is van der Waals equation (P + n²a/V²)(V − nb) = nRT Which parameter in the above equation reflects the intermolecular force of attraction and which one reflects the intermolecular force of repulsion? Give their units in SI system. (5 marks) (b) The surface tension of liquid A is greater than that of liquid B. Which liquid will show larger (i) vapour pressure, (ii) cohesive force, (iii) boiling point, (iv) capillary action and (v) wetting property? Explain. (5 marks) (c) Two blocks of a metal having same mass have same heat capacity 15 J K⁻¹ (presumed independent of T), but are at different temperatures 300 K and 400 K, respectively. Calculate the final temperature and entropy change, if the blocks are in thermal contact and reach equilibrium. (Assume two blocks together constitute the isolated system) (5 marks) (d) At 300 K temperature and 1 atm pressure, dinitrogen tetraoxide is 20 percent dissociated into nitrogen dioxide. Calculate the equilibrium constant (K_P) and standard free energy change for the reaction at this temperature : N₂O₄(g) ⇌ 2NO₂(g) (5 marks) (e) NH₄Cl(s) decomposes when heated. (i) How many components and phases are present when the salt is heated in a closed container? (ii) Now, suppose additional NH₃ is also present in the container. How many components and phases will be present? (5 marks) (f) One silver rod is immersed in a silver nitrate solution of the concentration C₁(AgNO₃) = 5×10⁻⁴ kmol m⁻³ and a second silver rod in the concentration C₂(AgNO₃) = 1×10⁻² kmol m⁻³. The electrolyte solutions are connected by salt bridge. Calculate the difference ΔE of the redox potential for the electrochemical cell at 25 °C (under equilibrium conditions). (5 marks) (g) Why is it necessary to measure the cell potential using potentiometer under zero-current conditions? (5 marks) (h) Everyday experience demonstrates that food will spoil outside in a hot summer day much faster than it would be in a refrigerator. Estimate the activation energy of these decomposition processes by assuming that food will spoil about 40 times faster at a temperature of 30 °C than at a temperature of 8 °C. (5 marks) (i) A flower is red in colour in daylight. What will be its colour in green light at night? Justify your answer. (5 marks) (j) Spontaneous adsorption of gas on solid surface favours low temperature. Explain, why. (5 marks)

(a) The Maxwell distribution of molecular speed of a gaseous system is dN_c = 4πN (M/2πRT)^(3/2) c² e^(−Mc²/2RT) dc (Symbols have their usual meanings) Plot (1/N × dN_c/dc) against c— (i) at two different temperatures T₁ and T₂; T₂ > T₁; (ii) at two molar masses M₁ and M₂; M₂ > M₁. Justify your plots. (15 marks) (b) (i) Two immiscible liquids A and B have surface tension values γ_A and γ_B, respectively. When both the liquids are taken in a container, then what would be the interfacial tension between the two liquid phases? (Given : γ_A > γ_B) (5 marks) (ii) Calculate the pressure differential across the surface of ethanol spherical droplet of radius 220 nm at 20 °C. The surface tension of ethanol at that temperature is 22·39 mN m⁻¹. (10 marks) (c) (i) At 25 °C, the latent heat of sublimation per mole of iodine is 62·3 kJ mol⁻¹ and the standard enthalpy of formation of HI(g) is 24·7 kJ mol⁻¹. Calculate the enthalpy change which occurs when HI(g) is formed from the gaseous elements at 225 °C. The mean molar heat capacities over the temperature range 25 °C to 225 °C are : H₂(g); C_p,m = 29·08 J K⁻¹ mol⁻¹ I₂(g); C_p,m = 33·56 J K⁻¹ mol⁻¹ HI(g); C_p,m = 29·87 J K⁻¹ mol⁻¹ (10 marks) (ii) Calculate ΔG° at 400 K temperature for the following reaction : ½ N₂(g) + 3/2 H₂(g) → NH₃(g) Assume that ΔS° is independent of temperature. (Given : ΔG°₂₉₈ K = −16·496 kJ mol⁻¹ S°_NH₃ = 192·45 J K⁻¹ mol⁻¹ S°_N₂ = 191·61 J K⁻¹ mol⁻¹ S°_H₂ = 130·68 J K⁻¹ mol⁻¹) (10 marks)

(a) (i) Derive the expressions of chemical potential of a component in a mixture system in terms of extensive thermodynamic properties U, H, A and G. (10 marks) (ii) Cadmium (m. pt.=321 °C) and bismuth (m. pt.=271 °C) do not form solid solutions or compounds with one another. Their eutectic point lies at 61 weight percent of bismuth and 146 °C. Sketch their phase diagram and label each region to show what phases are present. Explain the cooling curves of this eutectic mixture. (10 marks) (iii) How does acetone-dry ice freezing mixture work? (5 marks) (b) In a homogeneous electric field E = 5 V cm⁻¹, the speed υ of Zn²⁺ ions in aqueous solution at 25 °C is 2·74×10⁻⁵ m s⁻¹. (i) Estimate the radius r of the hydrated Zn²⁺ ion. The coefficient of viscosity η of water at the given temperature is 0·890 mPa s. (ii) Calculate the diffusion coefficient D of the ion. (10 marks) (c) (i) Calculate the energy of 800 nm electromagnetic radiation per einstein in SI system. (5 marks) (ii) The photodecomposition of HI(g) takes place following three elementary steps : HI(g) + hν → H(g) + I(g) H(g) + HI(g) —k₂→ H₂ (g) + I(g) I(g) + I(g) —k₃→ I₂ (g) Find the expression of −d[HI(g)]/dt, quantum yield (φ) and kinetic order of the reaction. (10 marks)

(a) Draw and discuss the polarographic wave obtained in the case of a dropping mercury electrode in polarography. (10 marks) (b) (i) The equilibrium A ⇌ B + C at 25 °C is subjected to a sudden temperature increase that slightly increases the concentrations of B and C. The measured relaxation time is 3·0 μs. The equilibrium constant for the system is 2·0×10⁻¹⁶ mol dm⁻³ at 25 °C, and the equilibrium concentrations of B and C at 25 °C are both 2·0×10⁻⁴ mol dm⁻³. Calculate the rate constants involved in the system. (15 marks) (ii) A substance B converts simultaneously to the products D and D′ by two parallel elementary reactions D ←k₁— B —k₂→ D′. The initial concentration of B is C_B,0 = 0·5 kmol m⁻³. After 40 minutes, the concentration of B has decreased to 0·05 kmol m⁻³; in the same time, the product D′ with a concentration C_D′ = 0·1 kmol m⁻³ is formed. Calculate the rate coefficients k₁ and k₂. (10 marks) (c) The kinetic order of the solid-surface catalyzed gas-phase decomposition reaction varies with the pressure of the gaseous reactant. Explain with plausible mechanism. (15 marks)

(a) What is the de Broglie wavelength for a baseball (140 g) moving at 40 m s⁻¹? Comment on your finding. (5 marks) (b) Distinguish between cis- and trans-dichloroethylene by using dipole moments. (5 marks) (c) Provide the resonance structures with formal charges for the nitrate ion. (5 marks) (d) What is the shortest distance between two successive 111 planes of simple cubic lattice of edge length 200 pm? Explain. (5 marks) (e) What is ferredoxin? How is it classified? (5 marks) (f) What is chelate effect? How is it affected by the ring size? (5 marks) (g) Why is ferrocene termed as a sandwich compound? Explain its structure. (5 marks) (h) What is ionization isomerism? Mention the type of isomerism in the given pairs of complexes : (i) [Cr(H₂O)₆Cl₃] and [CrCl(H₂O)₅]Cl₂·H₂O (ii) [Co(NH₃)₅SO₄]NO₃ and [Co(NH₃)₅NO₃]SO₄ (iii) [Pt(NH₃)₄][PtCl₆] and [Pt(NH₃)₄Cl₂][PtCl₄] (5 marks) (i) What is inorganic benzene? Explain it with structure. (5 marks) (j) What is actinide contraction? Explain. (5 marks)

(a) (i) Predict the Lewis structures and geometry of the following as per VSEPR theory : (1) SO₂, (2) I₃⁻, (3) SF₄, (4) BrF₅, (5) XeF₄ (10 marks) (ii) Draw the molecular orbital diagram for F₂ molecule, and mention its bond order and magnetic behaviour. (10 marks) (b) (i) Why is the electronic spectrum of [Co(H₂O)₆]²⁺ pale pink, whereas the spectrum of [CoCl₄]²⁻ is deep blue? Explain. (10 marks) (ii) What is EAN rule? Calculate the EAN value of the following : (1) [Cr(CO)₆] (2) [Fe(CN)₆]⁴⁻ (3) [Co(NH₃)₆]³⁺ (4) [Ni(NH₃)₆]²⁺ (10 marks) (c) Describe the bond order and quadruple bonding in [Re₂Cl₈]²⁻ ion. (10 marks)

(a) (i) Show that ψ(x) = e^(αx) is an eigenfunction for the operator  = dⁿ/dxⁿ. What is the eigenvalue? (5 marks) (ii) The time-independent Schrödinger equation for a free particle (of mass m) in a box of length L (inside the box potential energy is zero, but outside the box is infinity) is d²ψ/dx² + 2mE/ħ² ψ(x) = 0; 0 ≤ x ≤ L. The solution of the above equation is ψₙ(x) = √(2/L) sin(nπx/L); where n = 1, 2, 3, ... . Why is n = 0 not allowed? Explain. (5 marks) (b) (i) Find the minimum uncertainty in momentum and speed if we wish to locate an electron within an atom so that Δx ≈ 50 pm, using Δp_x × Δx ≥ h. Comment on your two findings. (10 marks) (ii) What are the n, l and m_l values of 2p_z orbital? Explain. (5 marks) (c) (i) Out of three lattice structures SC, BCC and FCC, which one is most economically packed and which one least? Give your answer, calculating packing fraction of each lattice structure. (20 marks) (ii) For Bragg X-ray diffraction studies of crystalline solid, what is the Bragg condition for constructive interference? Explain. (5 marks)

(a) Differentiate between T and R conformation of hemoglobin. (10 marks) (b) (i) Describe the structure and bonding in diborane. (10 marks) (ii) How are silicates classified? Predict the names and structures of the following silicates : (1) SiO₄⁴⁻ ion, (2) Si₂O₇⁶⁻ ion, (3) Si₃O₉⁶⁻ ion (10 marks) (c) (i) Why do Eu³⁺ and Sm³⁺ not follow the trend of magnetic moment of lanthanides at 300 K? Explain. (5 marks) (ii) Why do the metallic radii decrease from La to Lu except at Eu and Yb? (5 marks) (iii) How are lanthanides separated by a complex formation method? Give description. (5 marks) (iv) Why do Ce³⁺ and Yb³⁺ not absorb in the visible region, but show sharp absorption in the ultraviolet region? (5 marks)