Chemistry 2025 Paper I 50 marks Explain

Q6

(a) The following molecule shows the rigid or fluxional behaviour at higher temperature or in the presence of a base. Justify the answer with the help of ¹H NMR spectrum. (10 marks) (b) Consider the following photochemical reaction: H₂ (g) + Br₂ (g) →[hν] 2HBr (g). Give the mechanism of this reaction. Applying steady-state approximations to [Br] and [H], show that the rate of formation of HBr (g) varies with the square root of the intensity (Iₐ) of the absorbed radiation. What is the quantum yield for this reaction? Why is the value so low? (20 marks) (c) Mentioning the requisite assumptions, derive the equation of the Langmuir adsorption isotherm. Show that the Langmuir isotherm holds at low pressure but fails at high pressure. (20 marks)

हिंदी में प्रश्न पढ़ें

(a) निम्नलिखित अणु उच्च ताप या क्षारक की उपस्थिति में दृढ़ या फ्लक्सीयोनल (फ्लक्सनल) व्यवहार दर्शाता है। उत्तर की पुष्टि ¹H NMR स्पेक्ट्रम की सहायता से कीजिए। (10 अंक) (b) निम्नलिखित प्रकाश-रासायनिक अभिक्रिया पर विचार कीजिए: H₂ (g) + Br₂ (g) →[hν] 2HBr (g)। इस अभिक्रिया की क्रियाविधि दीजिए। स्थिर-अवस्था सन्निकटन को [Br] और [H] पर लागू करके, प्रदर्शित कीजिए कि HBr (g) के बनने की दर अवशोषित विकिरण की तीव्रता (Iₐ) के वर्गमूल के साथ परिवर्तित होती है। इस अभिक्रिया की क्वांटम लब्धि क्या है? यह मान इतना कम क्यों है? (20 अंक) (c) आवश्यक मान्यताओं का उल्लेख करते हुए, लैंगम्यूर अधिशोषण समतापी वक्र का समीकरण व्युत्पन्न कीजिए। प्रदर्शित कीजिए कि लैंगम्यूर समतापी वक्र कम दाब पर मान्य है लेकिन उच्च दाब पर असफल होता है। (20 अंक)

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Directive word: Explain

This question asks you to explain. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

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How this answer will be evaluated

Approach

Begin with a brief introduction acknowledging the three distinct areas: fluxional NMR behaviour, photochemical kinetics, and surface adsorption. Allocate approximately 20% of effort to part (a) (10 marks), 40% to part (b) (20 marks), and 40% to part (c) (20 marks). For part (a), identify the molecule (likely PF₅ or similar Berry pseudorotation system) and explain temperature-dependent NMR coalescence. For part (b), write the complete chain mechanism, apply steady-state approximation to both intermediates, and derive the rate law showing Iₐ^(1/2) dependence. For part (c), state all five Langmuir assumptions explicitly, derive θ = KP/(1+KP), and explain deviations at high pressure due to multilayer formation or surface heterogeneity. Conclude by summarizing the unifying theme of dynamic processes across timescales.

Key points expected

  • Part (a): Identification of fluxional molecule (e.g., PF₅, Fe(CO)₅, or metal hydride cluster) with Berry pseudorotation mechanism; explanation of temperature-dependent ¹H NMR showing coalescence of signals from axial/equatorial positions at low T to single averaged signal at high T; calculation of activation energy from coalescence temperature using Eyring equation
  • Part (b): Complete chain mechanism with initiation (Br₂ + hν → 2Br•), propagation steps (Br• + H₂ → HBr + H•; H• + Br₂ → HBr + Br•), and termination; correct steady-state approximation for [Br] and [H] leading to d[HBr]/dt = k[H₂][Iₐ]^(1/2)/[M]^(1/2); explicit derivation showing square root dependence on absorbed intensity
  • Part (b): Quantum yield calculation (Φ ≈ 2 at low conversion, decreasing due to recombination); explanation of low quantum yield via radical recombination, back reaction, and cage effect competing with product formation
  • Part (c): Five explicit Langmuir assumptions (monolayer, uniform surface, no interaction, dynamic equilibrium, constant adsorption enthalpy); step-by-step derivation from rate of adsorption = rate of desorption to obtain θ = KP/(1+KP) or equivalent linear forms
  • Part (c): Demonstration that at low P, θ ≈ KP (Henry's law region, linear) while at high P, θ → 1 (saturation); explanation of failure via BET multilayer adsorption, surface heterogeneity, or lateral interactions; mention of Temkin or Freundlich isotherms as corrections

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness25%12.5Precisely defines fluxionality with Berry pseudorotation; correctly identifies photochemical chain mechanism distinguishing thermal vs photochemical initiation; states all five Langmuir assumptions explicitly; distinguishes between kinetic and thermodynamic control in all three partsIdentifies fluxional behaviour but confuses with resonance; gives correct propagation steps but misses initiation/termination; lists 2-3 Langmuir assumptions; conflates Langmuir with Freundlich without clear distinctionMisidentifies fluxionality as tautomerism; writes incorrect radical mechanism or omits steady-state; fails to state assumptions or states incorrect assumptions; fundamental confusion between adsorption and absorption
Mechanism / equation25%12.5Writes complete photochemical chain mechanism with all elementary steps; applies steady-state approximation rigorously to both [Br] and [H] showing cancellation of termination terms; derives Langmuir equation with clear algebraic steps from kinetic equalityWrites most propagation steps correctly; applies steady-state to one intermediate only; derives Langmuir equation but skips key algebraic steps or makes minor errors in final expressionOmits initiation or termination steps; fails to apply steady-state or applies incorrectly to stable species; cannot derive Langmuir equation or writes incorrect final form; major algebraic errors
Numerical accuracy15%7.5Correctly calculates quantum yield with proper units and magnitude (~10⁻⁶ to 10³ context); derives exact exponent of 1/2 for intensity dependence; evaluates limiting cases θ→0 and θ→1 with correct mathematical limitsStates quantum yield qualitatively without calculation; derives rate law but exponent unclear; evaluates one limit correctlyIncorrect quantum yield magnitude or units; wrong exponent in rate law; fails to evaluate limits or evaluates incorrectly
Diagram / structure20%10Draws clear trigonal bipyramidal structure with axial/equatorial labels showing Berry pseudorotation; sketches NMR spectra at two temperatures showing coalescence; draws Langmuir isotherm plot with θ vs P showing approach to saturation; includes schematic of photochemical apparatus if relevantDraws basic structures without stereochemical detail; describes NMR changes verbally without sketch; draws linear Langmuir plot only; diagrams lack labels or clarityNo diagrams or structures; confusing or incorrect representations; omits essential features like coalescence temperature indication or saturation plateau
Application context15%7.5Cites Indian relevance: NMR facilities at IISc, TIFR, or CSIR labs for fluxional studies; mentions HBr synthesis in Indian chemical industry; connects Langmuir isotherm to catalytic converters, heterogeneous catalysis in Indian refineries, or BET method for surface area measurement (IS: 877, BIS standards)Mentions general industrial importance without Indian specificity; vague reference to catalysis or spectroscopyNo application context; irrelevant examples; confuses fundamental research with applied technology

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