Chemistry

UPSC Chemistry 2023

All 16 questions from the 2023 Civil Services Mains Chemistry paper across 2 papers — 800 marks in total. Each question comes with a detailed evaluation rubric, directive word analysis, and model answer points.

16Questions
800Total marks
2Papers
2023Exam year

Paper I

8 questions · 400 marks
Q1
50M Compulsory solve Quantum chemistry, thermodynamics, electrochemistry, surface chemistry

(a) (i) Find the wavelength of the emitted light when 1.0×10⁻²⁷ g particle in a one-dimensional box of length 3 Å goes from nₓ = 2 to nₓ = 1 level. (ii) Explain the Heisenberg uncertainty principle. 10 (b) Draw Lewis dot structure of [Br₃]⁻ and H₂NCSNH₂ (central C atom is bonded to both the N atoms and to the S atom). Does thiourea contain polar bonds? If yes, which is the most polar bond? 10 (c) (i) Derive an expression that relates the wavelength of the X-rays with the distance between the layers of atoms in a crystal. (ii) The X-rays of wavelength 220 pm are diffracted from an ionic crystal at an angle of 23°. What is the distance between the layers that are responsible for this diffraction? 10 (d) (i) Find the temperature at which the water molecules can have the root-mean-square speed of 719 m s⁻¹. 5 (ii) What is the root-mean-square velocity of water molecules at 473 K? 5 (e) (i) Calculate the E° value for the half-reaction Cr³⁺(aq)+3e⁻ → Cr Given that at 25 °C Cr³⁺(aq)+e⁻ → Cr²⁺(aq) E° = –0.424 V Cr²⁺(aq)+2e⁻ → Cr E° = –0.90 V (ii) The surface tension of liquid A is seven times higher than that of liquid B. (1) Which liquid is expected to have higher contact angle with glass? (2) 10 mL of each of these liquids are placed in separate 100 mL glass beakers. How do these liquids respond if the gravitational field is switched off?

Answer approach & key points

Solve this multi-part numerical and theoretical problem by allocating time proportionally to marks: spend ~20% on (a)(i) particle-in-a-box calculation, ~10% on (a)(ii) Heisenberg principle explanation, ~20% on (b) Lewis structures and polarity analysis, ~20% on (c) Bragg's law derivation and calculation, ~20% on (d) RMS velocity calculations, and ~10% on (e) electrochemistry and surface chemistry. Begin each part with the relevant formula, show step-by-step working with proper units, and conclude with brief conceptual explanations where asked.

  • (a)(i) Apply particle-in-a-box energy formula ΔE = (n₂²-n₁²)h²/8mL² and use E=hc/λ to find emitted wavelength (~657 nm or similar)
  • (a)(ii) State Heisenberg uncertainty principle Δx·Δp ≥ h/4π with physical interpretation and mention its role in establishing quantum mechanical nature of particles
  • (b) Draw correct Lewis structures: [Br₃]⁻ as linear with 3 lone pairs on central Br and single bonds; thiourea with C=S double bond, C-N single bonds, and lone pairs; identify C=S as most polar bond due to electronegativity difference
  • (c)(i) Derive Bragg's law nλ = 2d sinθ from constructive interference of X-rays scattered by crystal planes with path difference analysis
  • (c)(ii) Calculate interplanar spacing d = λ/2sinθ = 220 pm/(2×sin23°) ≈ 282 pm
  • (d)(i) Use v_rms = √(3RT/M) to find T = Mv²_rms/3R ≈ 373 K (100°C) for water
  • (d)(ii) Calculate v_rms = √(3×8.314×473/0.018) ≈ 808 m s⁻¹ at 473 K
  • (e)(i) Apply ΔG° = -nFE° and Hess's law: E°(Cr³⁺/Cr) = [1×(-0.424)+2×(-0.90)]/3 = -0.741 V
  • (e)(ii)(1) Liquid B has higher contact angle (lower surface tension → poorer wetting); (2) Liquid A forms more spherical cap/lower meniscus, liquid B spreads more in zero gravity
Q2
50M derive Thermodynamics, quantum mechanics, solid state chemistry, chemical equilibrium

(a) Using the Gibbs equation for a closed system in the absence of non-expansion work at constant composition, answer the following : (i) Deduce the thermodynamic relations for the variation of G with T, and with P. (ii) What are the implications of the above relations? (iii) Draw G versus T graph and identify the phase transition temperatures, if any. (iv) Explain how the presence of (1) attractive and (2) repulsive molecular interactions affects the molar Gibbs free energy of a gas relative to its normal value. (b) Explain why the energy of a free particle can vary continuously but the energy of a particle in a box is quantized. (c) Consider a primitive cubic lattice structure of an element. (i) How many lattice points are present in this unit cell? (ii) What is the coordination number of the atom present in this structure? (iii) What is the percentage void volume of this structure? (iv) If the radius of the atom present in this lattice is 178·1 pm, then find the radius of the sphere that can fit in the centre of this cubic unit cell. (v) What is the coordination number of this sphere? 10 (d) Consider the equilibrium reaction A₂(g) → 2A(g), in which A₂ gas is 18·5% dissociated at 25 °C and 1 bar. (i) Calculate K_eq at 25 °C. (ii) Calculate K_eq at 100 °C. Given that ΔH° = 57·2 kJ mol⁻¹ (at the above temperature range). (iii) What is the effect of compression on this reaction? 10

Answer approach & key points

Derive the thermodynamic relations in part (a) starting from dG = VdP − SdT, then apply these to explain phase behavior and molecular interactions. For (b), contrast the boundary conditions of free particle versus particle in a box to explain quantization. Part (c) requires systematic calculation of primitive cubic parameters and void geometry. Part (d) involves equilibrium calculations using van't Hoff equation. Allocate ~35% effort to (a), ~20% to (b), ~25% to (c), and ~20% to (d), ensuring all nine sub-parts are addressed.

  • Part (a)(i): Derivation of (∂G/∂T)_P = −S and (∂G/∂P)_T = V from dG = VdP − SdT with proper Maxwell relation justification
  • Part (a)(ii)-(iv): Implications including spontaneity criterion, G vs T plot showing melting/boiling points as discontinuities, and explanation of how attractive interactions lower G while repulsive interactions raise G relative to ideal gas
  • Part (b): Explanation that free particle has no boundary conditions allowing continuous k values, while particle in a box has quantized k = nπ/L leading to discrete energy levels E_n = n²h²/8mL²
  • Part (c): Primitive cubic has 1 lattice point, coordination number 6, 47.6% void volume, body cavity radius = 0.732r = 130.4 pm, and cavity coordination number 8
  • Part (d): Calculation of K_p = 4α²/(1−α) = 0.168 at 25°C, then K_p at 100°C using van't Hoff equation giving ~1.12, with compression favoring reverse reaction (Le Chatelier)
Q3
50M calculate Interhalogen compounds, phase diagrams, fuel cells

(a) Determine the electronic and molecular geometry of [BrF₅] and [ICl₂]⁻ interhalogen compounds. 10 (b) Answer the following questions based on the phase diagram given below : (i) How many components does this phase diagram represent? (ii) Identify the points A to D with corresponding degrees of freedom. (iii) Explain the changes expected in the paths E → B → H and E → F → G → H. 20 (c) Consider the reaction H₂(g) + ½O₂(g) → H₂O(l), which occurs in a H₂–O₂ fuel cell. (i) Identify the elements that undergo oxidation and reduction. (ii) Calculate the standard reaction Gibbs free energy (ΔᵣG°) at 25 °C. (iii) Write down the two reduction half-reactions for the cell. (iv) Calculate the E_cell. Given that Δ_fH°(H₂O, l) = –285.83 kJ mol⁻¹ S°_m(H₂O, l) = 69.91 J K⁻¹ mol⁻¹ S°_m(H₂, g) = 130.68 J K⁻¹ mol⁻¹ S°_m(O₂, g) = 205.14 J K⁻¹ mol⁻¹ 20

Answer approach & key points

Calculate and derive the required parameters across all three parts, allocating approximately 20% time to part (a) for VSEPR analysis, 40% to part (b) for phase diagram interpretation with clear identification of invariant points and path descriptions, and 40% to part (c) for thermodynamic calculations and electrochemical equations. Structure the answer with clear headings for each sub-part, showing step-by-step working for all numerical derivations, and conclude with brief contextual significance where applicable.

  • For (a): Apply VSEPR theory to determine BrF₅ has square pyramidal molecular geometry (AX₅E) with octahedral electronic geometry, and [ICl₂]⁻ has linear molecular geometry (AX₂E₃) with trigonal bipyramidal electronic geometry; include lone pair counts and hybridization (sp³d² and sp³d respectively)
  • For (b)(i): Identify the phase diagram represents a one-component system (typically water or similar single component)
  • For (b)(ii): Correctly identify points A-D as triple point, critical point, normal boiling point, normal freezing point (or equivalent) with corresponding degrees of freedom F = 0, 0, 1, 1 using Gibbs phase rule
  • For (b)(iii): Explain E→B→H as heating at constant pressure through liquid-vapor equilibrium to superheated vapor, and E→F→G→H as compression at constant temperature showing phase transitions from gas to liquid to solid
  • For (c)(i): Identify H₂ undergoes oxidation (0 to +1) and O₂ undergoes reduction (0 to -2)
  • For (c)(ii)-(iv): Calculate ΔᵣS° = -163.17 J K⁻¹ mol⁻¹, ΔᵣG° = -237.13 kJ mol⁻¹, write correct half-reactions (cathode: O₂ + 4H⁺ + 4e⁻ → 2H₂O; anode: 2H₂ → 4H⁺ + 4e⁻), and E°cell = 1.23 V using ΔG° = -nFE°
Q4
50M calculate Van der Waals gas, surface tension, silicate structures

(a) The volume of a certain gas is found to be 5.0×10⁻⁴ m³ mol⁻¹ at 273 K and 3.0×10⁶ Pa. This gas obeys the van der Waals' equation with a = 0.50 m⁶ Pa mol⁻². (i) Calculate the other van der Waals' constant, b. (ii) What is the compression factor for this gas at the same temperature and pressure? (iii) Comment on the nature of the molecular interactions of this gas. 20 (b) A 15 cm drinking straw is inserted in a glass of water at an angle 45°. What pressure difference (in torr) must be generated across the length of the straw to drink water? The density of water is 1.0 g cm⁻³. 10 (c) A capillary tube of radius r is inserted into a liquid to blow a bubble of the same radius r. If the excess pressure required to blow the bubble is 2·16 torr, then what is the diameter of the capillary tube in cm? The surface tension of the liquid is 0·072 N m⁻¹. 10 (d) Pyroxenes, amphiboles and phyllosilicates are well-known groups of silicates that occur in crust of the earth. Write the empirical formulae and draw the basic structural units of the above-mentioned silicates. 10

Answer approach & key points

This is primarily a calculation-based question demanding precise numerical work across thermodynamics and surface chemistry, with a structural component for silicates. Allocate approximately 40% of time to part (a) given its 20 marks and triple sub-parts requiring van der Waals manipulation; 20% each to parts (b) and (c) for pressure calculations involving hydrostatic and Laplace equations; and 20% to part (d) for silicate structures. Begin with clear statement of relevant equations, show systematic substitution with units, and conclude with brief physical interpretation where asked.

  • For (a)(i): Correct rearrangement of van der Waals equation and calculation of b = 8.314×10⁻⁵ m³ mol⁻¹ (or 8.3×10⁻⁵ m³ mol⁻¹) showing proper unit handling
  • For (a)(ii): Calculation of compression factor Z = PV/RT or Z = PVₘ/RT yielding Z ≈ 0.66, with recognition that Z < 1 indicates attractive forces dominate
  • For (a)(iii): Physical interpretation that negative deviation from ideality (Z < 1) means attractive intermolecular forces predominate over repulsive at these conditions
  • For (b): Correct application of hydrostatic pressure ΔP = ρgh with effective vertical height h = 15×sin45° cm, yielding ΔP ≈ 7.8 torr (or ~8 torr)
  • For (c): Application of Laplace equation for spherical bubble ΔP = 4γ/r (not 2γ/r, as bubble has two surfaces), solving for diameter d = 2r ≈ 0.27 cm
  • For (d): Empirical formulae: pyroxene (SiO₃)₂ⁿ⁻ or MgSiO₃, amphibole (Si₄O₁₁)₆ⁿ⁻, phyllosilicate (Si₂O₅)₂ⁿ⁻; with correct 1D chain, 2D double chain, and 2D sheet structures respectively
  • Recognition that silicate structures relate to Indian geological context: pyroxenes in Deccan traps, amphiboles in Himalayan metamorphic rocks, phyllosilicates (mica) in Jharkhand/Bihar pegmatites
Q5
50M Compulsory solve Physical, Inorganic and Bioinorganic Chemistry

The decomposition of AB₂ to AB and B is a first-order reaction with k = 2·8 × 10⁻⁷ s⁻¹ at T = 1000 K. The atomic weights of A and B are 12 and 32, respectively. (i) Find the half-life of this reaction at 1000 °C. (ii) In how many days will 1 g of AB₂ decompose to the extent that 0·6 g of AB₂ remains? (iii) How much of 1 g of AB₂ would remain after 35 days? Explain radiative and non-radiative processes by singlet and triplet electronic states of molecule. Also explain it through Jablonski diagram. Assign a geometry and hybridization to each carbon atom present in cytosine and thymine nucleotide bases. Explain three main types of electronic transitions observed in UV-visible absorption spectra of actinide ions. Identify A and B in the substitution reaction given below: [PtCl₄]²⁻ + NO₂⁻ → [A] → [B] NH₃ Justify by explaining the kinetic trans-effect using polarization theory.

Answer approach & key points

Solve the chemical kinetics problem (parts i-iii) first using first-order rate equations, allocating ~25% time; then explain radiative/non-radiative processes with Jablonski diagram (~20%), assign geometries to nucleotide bases (~15%), explain actinide electronic transitions (~20%), and finally identify Pt complexes with trans-effect justification (~20%). Structure as: numerical solutions → photochemistry explanation with diagram → structural chemistry → coordination chemistry mechanism.

  • (i-iii) Apply first-order kinetics: t₁/₂ = ln2/k = 2.47×10⁶ s ≈ 28.6 days; for 0.6g remaining, t = (1/k)ln(1/0.6) = 1.84×10⁶ s ≈ 21.3 days; after 35 days, mass remaining = exp(-k×35×24×3600) = 0.42 g
  • Radiative processes: fluorescence (S₁→S₀, spin-allowed, fast), phosphorescence (T₁→S₀, spin-forbidden, slow); non-radiative: internal conversion (IC, S₂→S₁), intersystem crossing (ISC, S₁→T₁), vibrational relaxation
  • Jablonski diagram showing: ground state S₀, excited singlet states S₁/S₂, triplet state T₁, with arrows for absorption, fluorescence, phosphorescence, IC, ISC, and vibrational relaxation levels
  • Cytosine: C2 sp² (C=O), C4 sp² (C-NH₂), C5 sp² (C=C), C6 sp² (part of ring); Thymine: C2 sp² (C=O), C4 sp² (C=O), C5 sp³ (CH₃), C6 sp² (C=C) — both pyrimidine bases with planar ring systems
  • Actinide UV-Vis transitions: f-f transitions (Laporte-forbidden, sharp, weak), charge-transfer transitions (ligand-to-metal, intense, broad), 5f-6d transitions (allowed, moderate intensity, sensitive to oxidation state)
  • [A] = [PtCl₃(NO₂)]²⁻ (NO₂⁻ enters opposite to Cl⁻, trans-effect: NO₂⁻ < Cl⁻ initially); [B] = cis-[PtCl₂(NO₂)(NH₃)]⁻; trans-effect order: NO₂⁻ > Cl⁻, so NH₃ replaces Cl⁻ trans to NO₂⁻; polarization theory explains through π-acceptor ability of NO₂⁻ weakening Pt-Cl bond trans to it
Q6
50M draw Inorganic Chemistry - Main Group and Coordination Compounds

Complete the following reactions and draw the structure of the major product(s) formed: (i) 2XeF₆ + SiO₂ → ____ 50 °C (ii) NH₄NO₃ → ____ + ____ 520 K (iii) N₂O + NaNH₂ → ____ 470 K (iv) 2B₂H₆ + 6NH₃ → ____ + ____ 180°C (v) 6SCl₂ + 16NH₃ → ____ + ____ + ____ Draw all possible stereoisomers for [Co(CN)₂(H₂O)₂(NH₃)₂]⁺ complex ion. Write the IUPAC nomenclature of the following complexes: (i) [Cr(H₂O)₄Cl₂]Cl (ii) [Co(en)₃][Fe(CN)₆] (iii) Na[Cr(H₂O)₂(ox)₂] (iv) [Pd(CO)₂(H₂O)Cl]⁺ (v) Na₄[(H₂O)₄V(μ-OH)₂V(H₂O)₄] Explain the structural and other features of rubredoxin. How does it differ from ferredoxins? Predict the number of framework bonding electrons and the structure of the following boranes: (i) B₇H₇²⁻ (ii) B₁₁H₁₃²⁻ (iii) B₂H₇⁻

Answer approach & key points

Begin by completing all five inorganic reactions with correct products and conditions, then systematically draw all stereoisomers of the cobalt complex showing optical and geometrical isomerism. Write precise IUPAC names for all five coordination compounds, paying special attention to bridging ligands and oxidation states. Explain rubredoxin's Fe-S₄ tetrahedral structure and contrast it with 2Fe-2S and 4Fe-4S ferredoxin clusters. Finally, apply Wade-Mingos rules to predict borane structures with correct styx numbers and polyhedral shapes.

  • Reaction (i): 2XeF₆ + SiO₂ → 2XeOF₄ + SiF₄ at 50°C; xenon oxyfluoride formation
  • Reaction (ii): NH₄NO₃ → N₂O + 2H₂O at 520K; ammonium nitrate decomposition to nitrous oxide
  • Reaction (iii): N₂O + NaNH₂ → NaN₃ + H₂O at 470K; azide synthesis from nitrous oxide
  • Reaction (iv): 2B₂H₆ + 6NH₃ → 2[BH₂(NH₃)₂]⁺[BH₄]⁻ at 180°C; ionic product formation
  • Reaction (v): 6SCl₂ + 16NH₃ → S₄N₄ + S₅N₂ + 12NH₄Cl; sulfur-nitrogen heterocycle formation
  • Stereoisomers of [Co(CN)₂(H₂O)₂(NH₃)₂]⁺: draw all five geometrical isomers (cis-cis, cis-trans, trans-cis, trans-trans, and mer/fac distinctions) and identify optical activity where applicable
  • IUPAC nomenclature: tetraaquadichloridochromium(III) chloride; tris(ethane-1,2-diamine)cobalt(III) hexacyanoferrate(III); sodium bis(oxalato)diaquachromate(III); dicarbonylaquachloridopalladium(II); sodium μ-hydroxido-bis[tetraaquavanadium(II)]
  • Rubredoxin: single Fe with four cysteine sulfur ligands in tetrahedral geometry; ferredoxins contain Fe-S clusters with bridging sulfide; rubredoxin has higher redox potential and simpler electron transfer
  • Borane structures: B₇H₇²⁻ (nido, 16 framework electrons, pentagonal bipyramid); B₁₁H₁₃²⁻ (nido, 26 framework electrons, octadecahedron fragment); B₂H₇⁻ (arachno, 8 framework electrons, pentagonal bipyramid fragment)
Q7
50M explain Coordination chemistry, bioinorganic chemistry, thermodynamics, kinetics

(a) Explain the common structural features of two major iron-containing proteins—haemoglobin and cytochrome c present in the human body. Explain the coordination chemistry involved at the central metal atom in case of oxyhaemoglobin and deoxyhaemoglobin. Give the details of the spin states, magnetic moment and oxidation number of central metal ion in both the cases. (10 marks) (b) Write the ground-state electronic configuration of lanthanides mentioned below: (i) ₅₉Pr (Praseodymium) (ii) ₆₃Eu (Europium) (iii) ₆₄Gd (Gadolinium) Calculate the predicted effective magnetic moment (μₛ₊ₗ) for the metal ions in +3 oxidation state in the units of Bohr magneton. (10 marks) (c) Derive a rate expression for a bimolecular surface reaction. Discuss the kinetics of such a reaction, when the gaseous reactants, say A and B, are adsorbed in the following way: A + B → Product (i) A and B are sparsely adsorbed. (ii) A is relatively more strongly adsorbed than B. (10 marks) (d) Nickel was found to be coordinated with oxygen in the UV-visible spectrum of [Ni(OS(CH₃)₂)₆]²⁺ complex ion. Predict theoretically the number of peaks and assign them to the corresponding electronic transitions. (10 marks) (e) An ideal gas (V_i = 0.05 L and P_i = 8 atm) is subjected to reversible isothermal expansion (V_f = 0.40 L and P_f = 1 atm) at 25 °C. Calculate the work done, ΔU, ΔH and ΔS for this process. Is the heat (q) same as ΔH in this process? If not, why? (10 marks)

Answer approach & key points

Begin with a brief introduction acknowledging the interdisciplinary nature of the question spanning bioinorganic, coordination, kinetic and thermodynamic chemistry. Allocate approximately 25% time to part (a) on haemoglobin/cytochrome c due to its conceptual depth; 15% each to parts (b) and (d) involving electronic configurations and spectral predictions; 20% to part (c) requiring derivation of Langmuir-Hinshelwood kinetics; and 25% to part (e) for thermodynamic calculations. Present each part clearly separated with appropriate headings, ensuring derivations show all steps and numerical answers include proper units.

  • Part (a): Common structural features of haemoglobin and cytochrome c (iron porphyrin/protoporphyrin IX ring, axial ligands, protein environment); coordination chemistry differences between oxyhaemoglobin (Fe²⁺, low-spin, diamagnetic, μ=0 BM, O₂ as π-acceptor) and deoxyhaemoglobin (Fe²⁺, high-spin, paramagnetic, μ=4.90 BM, weak field)
  • Part (b): Ground state electronic configurations—₅₉Pr [Xe]4f³6s², ₆₃Eu [Xe]4f⁷6s², ₆₄Gd [Xe]4f⁷5d¹6s²; M³⁺ configurations and μₛ₊ₗ calculation using μₛ₊ₗ = √[4S(S+1) + L(L+1)] BM yielding ~3.62 BM (Pr³⁺), ~3.40 BM (Eu³⁺), ~7.94 BM (Gd³⁺)
  • Part (c): Derivation of rate expression for bimolecular surface reaction: rate = kθₐθᵦ; Langmuir isotherm application; Case (i) sparse adsorption—first order in both A and B, rate ∝ PₐPᵦ; Case (ii) strong A adsorption—rate independent of Pₐ, first order in Pᵦ
  • Part (d): [Ni(OS(CH₃)₂)₆]²⁺ as octahedral Ni²⁺ (d⁸) with O-donor ligands; prediction of three spin-allowed d-d transitions: ³A₂g→³T₂g (ν₁), ³A₂g→³T₁g(F) (ν₂), ³A₂g→³T₁g(P) (ν₃); expected weak field from DMSO oxygen coordination
  • Part (e): Isothermal reversible expansion calculations—W = -nRT ln(Vf/Vi) = -2.303nRT log(Pi/Pf); ΔU=0 and ΔH=0 for ideal gas isothermal process; ΔS = nR ln(Vf/Vi); q = -W ≠ ΔH because ΔH=0 but q is non-zero; explicit numerical values with n calculated from ideal gas law
Q8
50M explain Organometallic chemistry, magnetic properties, spectroscopy, reaction kinetics

(a) Sketch the synthesis of [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COCH₃)] and [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COOH)] complexes starting from [Fe(η⁵-C₅H₅)₂]. (10 marks) (b) Calculate the spin only magnetic moment (μ_s.o.) of the central metal atom in the following complexes: (i) [Fe(H₂O)₅NO]²⁺ (ii) [Cr(NCS)₆]³⁻ (iii) [V(H₂O)₆]³⁺ (iv) [Co(bpy)₃]²⁺ (10 marks) (c) When an incident light of wavelength 300 nm is passed through a solution in a 1 cm cell, it transmits only 10% of the incident light. What percentage of light would be absorbed by the same solution if taken in a 0.5 cm cell? (10 marks) (d) Explain the transition-state theory for reaction rates. How is this theory considered superior to collision theory in providing a much more complete interpretation of the pre-exponential factor A in the Arrhenius equation? (20 marks)

Answer approach & key points

Begin with a brief introduction acknowledging the interdisciplinary nature of the question spanning organometallic synthesis, magnetism, spectroscopy, and kinetics. Allocate approximately 15% time to part (a) on ferrocene acylation chemistry, 20% to part (b) magnetic moment calculations with proper oxidation state determination, 15% to part (c) Beer-Lambert law application, and 50% to part (d) transition-state theory including detailed comparison with collision theory and statistical mechanical treatment of the pre-exponential factor. Conclude by synthesizing how these diverse topics illustrate fundamental coordination chemistry principles.

  • Part (a): Friedel-Crafts acylation of ferrocene using acetic anhydride/AlCl₃ to give monoacetylferrocene, followed by haloform reaction with NaOBr/NaOH or oxidation to yield carboxylic acid derivative; regioselectivity favoring single substitution
  • Part (b): Correct oxidation state assignment—Fe(II) with NO⁺ in (i) giving d⁷ low-spin μ=1.73 BM, Cr(III) d³ in (ii) μ=3.87 BM, V(III) d² in (iii) μ=2.83 BM, Co(II) d⁷ high-spin in (iv) μ=3.87 BM; application of μ_s.o.=√[n(n+2)] BM
  • Part (c): Application of Beer-Lambert law A=εcl; calculation showing A₁=1.0 for 1 cm cell, hence εc=1, then A₂=0.5 for 0.5 cm cell, giving 68.4% transmission and 31.6% absorption
  • Part (d): Transition-state theory fundamentals—equilibrium between reactants and activated complex, Eyring equation k=(k_BT/h)K‡, partition function derivation of pre-exponential factor
  • Part (d): Superiority over collision theory—incorporation of vibrational/rotational degrees of freedom, entropy of activation, steric and orientation factors through partition functions, temperature-dependent A vs constant A in collision theory
  • Part (d): Statistical mechanical expression A=(k_BT/h)(q‡/q_Aq_B) showing explicit dependence on molecular properties and configuration of activated complex
  • Cross-connection: How spectroscopic techniques (UV-Vis in part c) relate to determination of activation parameters in TST through thermodynamic formulation
  • Contemporary relevance: Applications in catalysis design (Indian context: homogeneous catalysis research at NCL Pune, IISc Bangalore) where TST guides catalyst optimization

Paper II

8 questions · 400 marks
Q1
50M Compulsory explain Organic chemistry reaction mechanisms and stereochemistry

1.(a)(i) pKₐ value of cyclopentadiene is almost similar to water. Explain. 5 marks 1.(a)(ii) Rate of hydrogen exchange reaction in the above compound (A) is 6000 times faster than that of (B). Explain. 5 marks 1.(b)(i) Write the IUPAC nomenclature of the above compound by assigning the stereochemistry. 5 marks 1.(b)(ii) Arrange the above radicals in ascending order of their dimerisation ability. 5 marks 1.(c) The reaction of methyl iodide with sodium azide is faster in N,N-dimethyl formamide (DMF) than in methanol. Explain. 10 marks 1.(d) The above compounds both undergo photo-induced electrocyclic reactions. What are the structures and stereochemistry of the products? 10 marks 1.(e)(i) Identify the major product of the above reaction. 5 marks 1.(e)(ii) Identify the name reaction which produces nitrogen as a byproduct. (A) Fischer Indole synthesis (B) von Richter reaction (C) Stobbe reaction (D) Bischler-Napieralski reaction 5 marks

Answer approach & key points

Explain the underlying chemical principles for each sub-part, allocating time proportionally: ~15% on (a)(i)-(ii) aromaticity and kinetic acidity, ~15% on (b)(i)-(ii) stereochemical nomenclature and radical stability, ~20% on (c) solvent effects in SN2 reactions, ~25% on (d) Woodward-Hoffmann rules for electrocyclic reactions, and ~25% on (e)(i)-(ii) reaction identification and named reactions. Begin with clear structural representations, develop mechanistic reasoning with orbital diagrams where relevant, and conclude with comparative summaries.

  • For 1(a)(i): Explanation of cyclopentadiene's enhanced acidity (pKa ~16) due to aromatic stabilization of cyclopentadienyl anion (6π-electron Hückel system) making it comparable to water (pKa ~15.7)
  • For 1(a)(ii): Kinetic vs thermodynamic acidity distinction; compound A (cyclopentadiene) undergoes rapid H/D exchange via aromatic transition state, while compound B (e.g., acetone or similar non-aromatic enolizable compound) lacks this stabilization
  • For 1(b)(i): Correct IUPAC name with E/Z or R/S stereochemical descriptors based on Cahn-Ingold-Prelog priority rules; proper numbering and identification of principal functional group
  • For 1(b)(ii): Radical dimerization ability correlates inversely with stability; order reflects degree of conjugation, steric hindrance, and resonance stabilization (tertiary < secondary < primary < methyl, or specific order based on given structures)
  • For 1(c): Explanation of SN2 rate enhancement in polar aprotic solvents (DMF) vs polar protic (methanol); hard-soft acid-base considerations, nucleophile solvation effects, and transition state stabilization
  • For 1(d): Application of Woodward-Hoffmann rules for 4n and 4n+2 π-electron systems; conrotatory vs disrotatory ring closure under photochemical conditions with stereochemical outcome prediction
  • For 1(e)(i): Identification of major product based on named reaction mechanism (likely Fischer indole synthesis or related transformation)
  • For 1(e)(ii): Recognition that Fischer indole synthesis produces N2 as byproduct via hydrazone intermediate and [3,3]-sigmatropic rearrangement with subsequent elimination
Q2
50M explain Organic chemistry aromaticity and reaction mechanisms

2.(a)(i) Based on Hückel rule, predict the above compounds as aromatic, antiaromatic, and nonaromatic. 5 marks 2.(a)(ii) Identify the above reactions that show primary kinetic isotope effect and secondary kinetic isotope effect. 5 marks 2.(a)(iii) Identify (A) and (B) in the above reactions and explain the mechanism. 5 marks 2.(b)(i) The rate of hydrolysis (k₁ and k₂) of the reaction (A) is much faster than that of (B). Explain. 5 marks 2.(b)(ii) The reaction of the compounds (A) and (B) with AgClO₄ in MeOH gives the same product (C). Explain. 5 marks 2.(b)(iii) Write the major product of the above reaction showing proper stereochemistry and explain the mechanism. 10 marks 2.(c)(i) Write the structure of the product of the above reaction and provide suitable mechanism. 10 marks 2.(c)(ii) Write the preferred position (C-2 or C-3) in electrophilic substitution of indole. Explain your observation with the help of resonance structures. 5 marks

Answer approach & key points

Explain requires systematic demonstration of reasoning with evidence. Structure: brief introduction stating Hückel's rule and kinetic isotope effect principles; body addressing each sub-part sequentially with clear mechanistic diagrams, rate comparisons, and stereochemical analysis; conclusion summarizing key electronic effects governing aromaticity and reaction outcomes.

  • Correct application of Hückel (4n+2)π rule to classify rings as aromatic, antiaromatic (4nπ, planar), or nonaromatic (non-planar/insufficient conjugation)
  • Distinction between primary KIE (C-H/D bond cleavage in rate-determining step) and secondary KIE (hybridization change at adjacent carbon)
  • Identification of intermediates (A) and (B) with arrow-pushing mechanisms showing carbocation, carbanion, or radical pathways
  • Explanation of rate differences via anchimeric assistance, neighboring group participation, or ring strain effects in hydrolysis
  • Stereochemical analysis using chair conformations, anti-periplanar geometry, and orbital overlap requirements for elimination/substitution
  • Resonance stabilization of indole electrophilic substitution intermediates at C-2 vs C-3 positions
Q3
50M explain Organic chemistry reactions and mechanisms

3.(a) Would you expect the above conversion to require heat or light? Explain using molecular orbital diagram. (15 marks) 3.(b) 3-Phenyl-4-pentenal is synthesised in the following manner: (i) Identify the type of pericyclic reaction involved in the formation of unsaturated intermediate. (ii) What elements are lost when the intermediate is converted to 3-phenyl-4-pentenal? (iii) Identify the carbon atom in the starting acrylic acid that becomes the aldehyde carbon in the pentenal. (iv) Write the steps involved for this transformation. (15 marks) 3.(c) Explain the regioselectivity of a Hoffmann elimination reaction with the help of Newman projection formula. (10 marks) 3.(d) Write down the structure(s) of the product(s) obtained in the above reactions. Provide suitable justification and propose the mechanisms. (i) H₃CO + △ (ii) OCH₃ + △ (10 marks)

Answer approach & key points

Explain the photochemical/thermal requirements for each pericyclic transformation using orbital symmetry principles. For part (a), construct HOMO-LUMO diagrams to justify heat vs light conditions. For part (b), identify the [3,3]-sigmatropic rearrangement (Claisen/Cope type), trace carbon atom mapping from acrylic acid to aldehyde, and show retro-ene or oxidation steps. For part (c), use Newman projections along Cα-Cβ bond to demonstrate anti-periplanar geometry preference for less substituted alkene formation. For part (d), analyze thermal [2+2] cycloadditions or electrocyclic reactions of methoxy-substituted systems. Allocate approximately 30% time to (a), 30% to (b), 20% to (c), and 20% to (d), with diagrams constituting roughly 40% of total response.

  • Part (a): Correct identification of conrotatory/disrotatory mode based on 4n/4n+2 π-electron system; construction of HOMO under thermal vs photochemical conditions showing symmetry-allowed pathway
  • Part (b)(i): Recognition of [3,3]-sigmatropic rearrangement (oxy-Cope or Claisen variant) as the pericyclic step forming the unsaturated intermediate
  • Part (b)(ii)-(iii): Identification of CO₂ or formaldehyde loss; precise carbon mapping from C-1 or C-3 of acrylic acid derivative to aldehyde carbon via isotopic labeling logic
  • Part (c): Newman projection showing anti-periplanar β-hydrogen from less substituted carbon (Hofmann rule); explanation of steric vs electronic factors favoring terminal alkene
  • Part (d): Structure determination of cycloaddition/electrocyclic products; thermal allowedness based on orbital symmetry; methoxy substituent effects on regioselectivity
Q4
50M solve Organic synthesis and reaction mechanisms

4.(a)(i) Complete the above reaction and write the steps involved in the reaction. (5 marks) 4.(a)(ii) Arrange the above alkenes in ascending order of their relative rate of bromination in methanol. (5 marks) 4.(a)(iii) Complete the above reactions and give suitable mechanism. (10 marks) 4.(b) Complete the above reaction and give suitable mechanism. (10 marks) 4.(c)(i) How many β-hydroxy carbonyl compounds may be theoretically formed in the above reaction? Write the structure of the products formed. (10 marks) 4.(c)(ii) Write the synthesis of benzonitrile starting from benzene (Hint: may involve more than one step). (10 marks)

Answer approach & key points

Solve each sub-part systematically, beginning with reaction completion and mechanism elucidation for 4(a)(i), (iii) and 4(b), followed by rate analysis for 4(a)(ii), stereochemical enumeration for 4(c)(i), and multi-step synthesis for 4(c)(ii). Structure the answer with clear sub-headings, balanced chemical equations with electron-pushing arrows, and concise structural diagrams.

  • Correct identification of reaction types: electrophilic addition, nucleophilic substitution, aldol condensation, and Sandmeyer/Gattermann-type transformations
  • Accurate depiction of carbocation stability and Markovnikov/anti-Markovnikov regioselectivity in alkene bromination
  • Proper arrow-pushing mechanisms showing intermediates: cyclic bromonium ions, enolates, tetrahedral intermediates
  • Stereochemical analysis for β-hydroxy carbonyl formation: syn/anti aldol products, racemic mixtures, and crossed aldol possibilities
  • Logical synthetic sequence for benzonitrile: nitration → reduction → diazotization → Sandmeyer cyanation or Rosenmund-von Braun alternative
Q5
50M Compulsory explain Organic spectroscopy and reaction mechanisms

(a) How many signals would you expect in the ¹H NMR spectrum of above compounds ? Mark these protons. 10 marks (b) Compare the C=C stretching vibrations in the above compounds and give a suitable explanation for your answer. 10 marks (c) (i) Identify A and B. The polymerisation of the rearranged product of B, unaided by any catalyst, gives rise to a 'synthetic rubber'. Name this rubber along with its structural formula. 2 CH≡CH →[Cu₂Cl₂/NH₄Cl] A →[HCl] B (ii) When rubber balls and other objects made of rubber are exposed to the air for long periods of time, they turn brittle and crack. This does not happen to objects made of polyethylene. Explain. 10 marks (d) Reduction of camphor with LiAlH₄ leads to 90% of the isomer in which the OH group is cis to the bridge. Give a suitable explanation of this observation. 10 marks (e) Identify the products in the above reactions with plausible mechanism. (i) CH₃—C(=O)—CH₃ →[hν/Vapour phase] (ii) CH₃—C(=O)—CH₃ →[hν/Room temperature] 10 marks

Answer approach & key points

Explain the spectroscopic, mechanistic, and synthetic aspects across all seven sub-parts with balanced coverage: allocate ~15% each to (a) NMR signals and (b) IR vibrations; ~25% to (c) acetylene chemistry and rubber degradation; ~20% to (d) camphor stereochemistry; and ~25% to (e) photochemical mechanisms. Begin with clear structural diagrams, proceed with systematic analysis using chemical principles, and conclude with real-world applications where relevant.

  • For (a): Correct number of ¹H NMR signals with proton labeling on given compounds, explaining chemical equivalence and splitting patterns
  • For (b): Comparison of C=C stretching frequencies with explanation based on conjugation, ring strain, and substituent effects on bond strength
  • For (c)(i): Identification of A as vinylacetylene (CH₂=CH-C≡CH) and B as chloroprene (2-chloro-1,3-butadiene), with neoprene rubber structure and polymerization
  • For (c)(ii): Explanation of rubber oxidation via allylic hydrogen abstraction and peroxide formation versus polyethylene stability due to saturated backbone
  • For (d): Stereochemical outcome of LiAlH₄ reduction of camphor favoring endo alcohol (isoborneol) via steric approach control and Cieplak model
  • For (e)(i): Vapor phase photolysis of acetone giving biacetyl and methane via Norrish Type II cleavage
  • For (e)(ii): Room temperature photolysis giving pinacol via radical coupling in liquid phase with different cage effects
Q6
50M solve Spectroscopy, polymer chemistry and organic structure determination

(a)(i) The frequencies of vibration of the following molecules in their v = 0 states are HCl : 2885 cm⁻¹; D₂ : 2990 cm⁻¹; DCl : 1990 cm⁻¹ and HD : 3627 cm⁻¹. Calculate the energy change of the following reaction : HCl + D₂ → DCl + HD. Determine whether energy is liberated or absorbed. [Given : h = 6·626 × 10⁻³⁴ Js, c = 2·998 × 10⁸ ms⁻¹, Nₐ = 6·022 × 10²³ mol⁻¹] 10 marks (a)(ii) The IR spectra of butyric acid and ethyl butyrate show sharp strong singlet absorption at 1725 cm⁻¹ and 1740 cm⁻¹, respectively. By contrast, the IR spectrum of butyric anhydride shows a broad, sharp doublet at 1750 cm⁻¹ and 1825 cm⁻¹. Why are these so different ? 5 marks (b)(i) Write the structure of product(s) in the above reactions : 10 marks (b)(ii) What is meant by 'Tacticity' of a polymer ? Distinguish among isotactic, syndiotactic and atactic polymers. 5 marks (c)(i) An organic compound having molecular formula C₁₆H₂₅NO gave following IR and ¹H NMR data : IR(cm⁻¹) = 1690; ¹H NMR(CDCl₃, 400 MHz) : δ 1·11(t, J = 7Hz, 6H), 1·29(d, J = 7Hz 6H), 2·40 (q, J = 7Hz, 4H), 2·55(t, J = 7Hz, 2H), 2·65(t, J = 7 Hz, 2H), 3·12(septet, 1H), 7·21(d, J = 8Hz, 2H), 7·81(d, J = 8Hz, 2H). Determine the structure of the compound. 10 marks (c)(ii) Assign and arrange the lettered protons in the increasing order of their chemical shift value in ¹H NMR spectrum. 10 marks

Answer approach & key points

Solve this multi-part spectroscopy and polymer chemistry problem by allocating approximately 35% time to part (a) covering vibrational energy calculations and IR interpretation, 25% to part (b) on reaction products and tacticity definitions, and 40% to part (c) involving complete structure elucidation from spectral data. Begin each sub-part with clear identification of the chemical principle involved, show all calculations with proper units, draw unambiguous structures with stereochemistry where relevant, and conclude with explicit answers to each directive.

  • For (a)(i): Apply zero-point energy formula E = ½hcν̃ for each molecule, calculate ΔE = [E(DCl) + E(HD)] - [E(HCl) + E(D₂)], convert to kJ/mol using Avogadro's number, and correctly identify energy liberation (exothermic)
  • For (a)(ii): Explain Fermi resonance in anhydrides (coupling of C=O stretch with overtone of C-O stretch), symmetric/asymmetric stretching modes, and contrast with isolated C=O in esters/acids
  • For (b)(i): Draw correct product structures for unspecified reactions (typically Grignard, reduction, or substitution sequences common in UPSC papers) with proper stereochemistry
  • For (b)(ii): Define tacticity as stereochemical arrangement of substituents; distinguish isotactic (same side), syndiotactic (alternating), and atactic (random) with 3D representations
  • For (c)(i): Deduce structure as N,N-diisopropyl-4-ethylbutyrylbenzamide or similar amide from IR (1690 cm⁻¹, amide C=O), molecular formula, and complete NMR analysis including coupling patterns and integration
  • For (c)(ii): Assign all lettered protons and arrange in order: methyl/methylene (δ 0.9-2.8) < methine (δ 3.1) < aromatic (δ 7.2-7.8), citing shielding/deshielding effects
Q7
50M draw Nucleic acids, photochemistry and organic spectroscopy

(a) (i) Draw the structure of 2'-deoxycytidine-3'-monophosphate. (ii) Why nucleotides and nucleic acids are acidic ? Mention the factor(s) that stabilize the DNA duplex. (iii) Show the hydrogen bonding in between cytosine and guanine base pair. 15 (b)(i) Identify all the possible products in the above reaction showing the sequential pathways of their formation : 10 (b)(ii) 1,3-Butadiene solution on irradiation with UV light follows path I. However, irradiating 1,3-butadiene in the presence of benzophenone at 366 nm follows path II. Give a suitable explanation. 5 (c)(i) Write the structure of the compounds (A), (B), (C), (D) and (E). 10 (c)(ii) From the reaction sequence below, answer the following questions : (I) Write structure of (A) and (B) (II) Write the oxidation state of Osmium in the intermediate (A) and its geometry. 5 (c)(iii) Write the structure of (A) and (B) in the above reactions. 5

Answer approach & key points

Begin with (a) parts (i)-(iii) on nucleic acids (15 marks), spending ~30% time on accurate structural drawings and explanations of acidity/stabilization. For (b)(i)-(ii) photochemistry (15 marks), allocate ~30% time to identify products with mechanistic pathways and explain photosensitization by benzophenone. Devote ~40% time to (c) spectroscopy/organometallic problems (20 marks), solving all five structures in (c)(i) and the osmium complex in (c)(ii)-(iii) with correct oxidation states and geometries. Use clear sequential numbering for all structures.

  • For (a)(i): Correct Haworth projection of 2'-deoxycytidine-3'-monophosphate showing β-configuration at C-1', 2'-deoxy (no OH), phosphate at 3'-position, and cytosine base
  • For (a)(ii): Explanation that phosphate groups (pKa ~1-2) make nucleotides acidic; DNA duplex stabilization via Watson-Crick H-bonding, base stacking (van der Waals), and hydrophobic effects in aqueous medium
  • For (a)(iii): Accurate depiction of three hydrogen bonds between cytosine (N-3, O-2, N-4) and guanine (N-1, N-2, O-6) with correct donor-acceptor geometry
  • For (b)(i)-(ii): Identification of electrocyclic ring closure products (4π conrotatory thermal vs photochemical); explanation of benzophenone as triplet sensitizer enabling intersystem crossing to T1 state of butadiene for disrotatory closure
  • For (c)(i): Spectroscopic deduction of five compounds using IR, NMR, and MS data with correct functional group identification and structural elucidation
  • For (c)(ii)-(iii): Osmium tetroxide dihydroxylation mechanism showing cyclic osmate ester intermediate with Os(VI) oxidation state and trigonal bipyramidal/octahedral geometry; correct diol products
Q8
50M solve Spectroscopy: mass, UV, rotational, NMR and IR

(a)(i) For the following compound : (i) Identify the site of initial ionization under EI conditions. (ii) Draw the structure of ion having m/z = 58 value. (iii) Calculate the m/z value of metastable ion formed during the formation of above ion. 10 (a)(ii) Draw the structural formula of a ketone with MF C₇H₁₂O that absorbs in the UV with λₘₐₓ = 249 nm. 5 (b)(i) (A) Which of the above molecule(s) will show a microwave rotational spectrum ? Justify your answer. H₂, HCl, BrF, CH₄ and H₂O (B) The first rotational absorption of ¹²C¹⁶O was observed at 3·84235 cm⁻¹ while that of ¹³C¹⁶O was observed at 3·67337 cm⁻¹. Find their rotational constants. 10 (b)(ii) Estimate the expected splitting (J in Hz) for the lettered protons in the above compounds : 5 (c)(i) In the ¹H NMR spectrum of acetyl acetone the height of the integration curve at methylene (–CH₂) signal was found to be 10 mm and that of methine (=CH) signal was 22 mm. Calculate the percentage of keto and enol form in the sample. 10 (c)(ii) How could the above pair of isomeric compounds be differentiated by mass spectrometry ? 5 (c)(iii) How many fundamental vibrational frequencies would be expected to be observed in the IR spectrum of CO₂ ? Sketch them. Identify the IR-active vibrations with justification. 5

Answer approach & key points

Solve this multi-part spectroscopy problem by allocating time proportionally to marks: spend ~40% on part (a) [15 marks], ~30% on part (b) [15 marks], and ~30% on part (c) [20 marks]. Begin with clear identification of the compound in (a)(i), then systematically work through each sub-part showing all calculations and structures. For rotational and NMR problems, state relevant formulas before substituting values. Conclude each section with boxed final answers.

  • (a)(i) Correct identification of ionization site under EI (lone pair on oxygen), accurate structure of m/z=58 fragment (McLafferty rearrangement product), and correct metastable ion calculation using m* = (m₂)²/m₁
  • (a)(ii) Correct structural formula of C₇H₁₂O ketone with extended conjugation matching λₘₐₓ=249 nm (Woodward-Fieser rules application)
  • (b)(i)(A) Correct selection of microwave-active molecules (HCl, BrF, H₂O) with justification based on permanent dipole moment requirement for pure rotational spectra
  • (b)(i)(B) Accurate calculation of rotational constants B for both isotopologues using ṽ = 2B(J+1) with J=0→1 transition
  • (b)(ii) Correct estimation of spin-spin coupling constants (J values) for lettered protons using typical vicinal, geminal, and long-range coupling constants
  • (c)(i) Correct calculation of keto-enol equilibrium percentages using integration ratio and the 2:1 proton count relationship
  • (c)(ii) Appropriate differentiation strategy using mass spectrometry (fragmentation patterns, McLafferty rearrangement, or molecular ion stability differences)
  • (c)(iii) Correct determination of 3N-5 = 4 fundamental vibrations for linear CO₂, with proper sketching and IR activity assignment (asymmetric stretch active, symmetric stretch and bends inactive in IR)

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