(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 wheth

Question

(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

UPSC Answer Check · Accepted Answer

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

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding: for (a)(i) recognizes zero-point energy and isotope mass effects on vibrational frequencies; for (a)(ii) correctly identifies Fermi resonance mechanism; for (b)(ii) precisely defines tacticity with correct stereochemical terminology; for (c)(i) unambiguously identifies compound class and substitution pattern from spectral data	Shows basic familiarity with concepts but makes minor errors: confuses zero-point energy with thermal energy, vaguely mentions 'resonance' without specifying Fermi, or partially correct tacticity definitions with stereochemical confusion	Fundamental misconceptions: treats vibrational frequencies as thermal energies, completely misidentifies IR doublet origin, fails to define tacticity, or misinterprets NMR multiplicities leading to wrong functional group identification
Mechanism / equation	20%	10	Presents complete, balanced formalism: writes E₀ = ½hcν̃ explicitly for all four molecules; shows clear ΔE calculation with proper sign convention; for (b)(i) depicts reaction mechanisms with electron-pushing arrows; explains Fermi resonance coupling with energy level diagrams; uses correct (R)/(S) or meso descriptors for tacticity	Writes main equations but with omissions: skips intermediate steps in energy calculation, shows products without mechanisms, or describes tacticity without stereochemical drawings	Missing or incorrect equations: no zero-point energy formula, no reaction products drawn, or completely wrong mechanistic rationale for spectral observations
Numerical accuracy	20%	10	Computes with precision: converts all ν̃ to energies using consistent units (J/molecule), applies Avogadro's number correctly for molar energy, obtains ΔE ≈ -2.8 to -3.0 kJ/mol (energy liberated), and reports final answer with appropriate significant figures (3-4 sig figs)	Correct method but calculation errors: unit conversion mistakes (e.g., forgets ×10² for cm⁻¹ to m⁻¹), arithmetic errors in final subtraction, or wrong sign for energy change	Critical numerical failures: order-of-magnitude errors, completely wrong final value, or no calculation shown with only guessed answer
Diagram / structure	20%	10	Produces clear, chemically accurate drawings: for (b)(i) shows all product structures with correct connectivity and stereochemistry; for (b)(ii) draws zig-zag polymer chains with wedge/dash bonds illustrating tacticity; for (c)(i) presents complete molecular structure with all substituents correctly placed; for (c)(ii) labels each proton environment on the drawn structure	Draws structures with minor flaws: correct connectivity but poor stereochemical representation, or correct tacticity concepts but unclear 3D depiction	Inadequate or wrong diagrams: missing structures, incorrect connectivity in products, no visualization of tacticity, or structure for (c)(i) inconsistent with spectral data
Application context	20%	10	Synthesizes across sub-parts: connects isotope effects to kinetic isotope applications in mechanistic studies; relates IR carbonyl differences to functional group identification in pharmaceutical analysis (e.g., Indian drug quality control); links tacticity to polymer properties (PP, PVC industrial relevance); applies NMR problem-solving to natural product/pesticide structure determination relevant to Indian agrochemical industry	Mentions applications superficially: notes 'used in industry' without specifics, or provides generic context without Indian/scientific relevance	No contextual awareness: treats problem as purely academic exercise with no mention of real-world spectroscopic analysis, polymer engineering, or structure determination applications

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