(a) (i) Calculate the number of moles of HCl (g) produced by the absorption of one Joule of radiant energy of wavelength 480 nm in the reaction H₂ (g) + Cl₂ (g) → 2HCl (g) if the quantum yield of the photochemical reaction is 1·0 × 10⁶.
[Given: Nₐ =

Question

(a) (i) Calculate the number of moles of HCl (g) produced by the absorption of one Joule of radiant energy of wavelength 480 nm in the reaction H₂ (g) + Cl₂ (g) → 2HCl (g) if the quantum yield of the photochemical reaction is 1·0 × 10⁶.
[Given: Nₐ = 6·022 × 10²³ mol⁻¹, h = 6·626 × 10⁻³⁴ Js, c = 2·998 × 10⁸ ms⁻¹] (10 marks)

(ii) On passing monochromatic light through a 0·04 molar solution kept in a cell of thickness 2 cm, the intensity of the transmitted light was reduced to 50%. Calculate the molar extinction coefficient. (5 marks)

(b) What is meant by heterogeneously catalyzed reactions? Mention the consecutive steps for a reaction to occur on a surface.

Using Langmuir adsorption theory, account for the experimental observation that the decomposition of PH₃ on tungsten follows first order kinetics at low pressure and zeroth order kinetics at high pressure. (15 marks)

(c) (i) What is 'sodium pump'? Explain the role of sodium pump in biological system. (10 marks)

(ii) What is Bohr effect? Explain the role of Cytochrome P450. (10 marks)

UPSC Answer Check · Accepted Answer

Begin with the directive 'calculate' for part (a), applying photochemical principles and Beer-Lambert law; for (b) 'explain' heterogeneous catalysis using Langmuir adsorption isotherm; for (c) 'explain' bioinorganic concepts. Allocate ~30% time to (a)(i) quantum yield calculation, ~15% to (a)(ii) molar extinction coefficient, ~30% to (b) catalysis with derivation, and ~25% to (c) sodium pump and cytochrome P450. Structure: direct calculations → theoretical explanation with equations → biological applications with mechanisms.
- Part (a)(i): Calculate moles of HCl using E = Nhc/λ, then moles = (Φ × E × λ)/(Nₐ × h × c) with correct unit conversion and significant figures
- Part (a)(ii): Apply Beer-Lambert law A = εcl, calculate A = log(I₀/I) = 0.301, then ε = A/(cl) with proper unit handling (cm to m conversion awareness)
- Part (b): Define heterogeneous catalysis; list five consecutive steps (diffusion, adsorption, surface reaction, desorption, diffusion away); derive Langmuir isotherm θ = KP/(1+KP); show low P gives first order (rate ∝ P) and high P gives zero order (rate independent of P) for PH₃ decomposition on tungsten
- Part (c)(i): Define Na⁺/K⁺-ATPase as sodium pump; explain 3Na⁺ out/2K⁺ in against gradient using ATP hydrolysis; role in nerve impulse transmission, osmotic balance, and cellular homeostasis
- Part (c)(ii): Define Bohr effect as H⁺ and CO₂ influence on O₂ binding to hemoglobin; explain Cytochrome P450 as heme-thiolate monooxygenase, its role in drug metabolism, xenobiotic detoxification, and steroid biosynthesis in liver microsomes
- Correct use of all given constants (Nₐ, h, c) with proper SI unit conversions throughout numerical parts
- Clear distinction between photochemical quantum yield (Φ) and primary quantum yield in part (a)

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Accurately defines quantum yield, distinguishes primary vs overall yield in (a); correctly identifies Langmuir assumptions for (b); precisely describes Na⁺/K⁺-ATPase mechanism and Bohr effect physiology for (c); no conceptual confusion between homogeneous and heterogeneous catalysis	Basic definitions correct but misses nuances (e.g., treats quantum yield as simple ratio without chain reaction context; states Langmuir assumptions without applying to rate order transition; describes sodium pump function but misses 3:2 stoichiometry)	Fundamental errors: confuses quantum yield with extinction coefficient; applies Freundlich instead of Langmuir isotherm; describes sodium pump as passive transport; conflates Bohr effect with Haldane effect
Mechanism / equation	25%	12.5	Writes complete Einstein-Stark law for photochemical equivalence; derives rate equation from Langmuir isotherm showing explicit θ dependence; details E1-E2-P phosphorylation states of Na⁺/K⁺-ATPase; explains P450 catalytic cycle with Compound I formation	States Beer-Lambert law without derivation; gives Langmuir isotherm without connecting to rate orders; lists catalytic steps generically; mentions P450 cycle but misses key intermediates (Fe⁴⁺=O porphyrin radical cation)	Missing key equations: no energy-mole conversion for (a)(i); no rate law derivation for (b); no mechanistic detail for sodium pump or P450; incorrect stoichiometry in ATP hydrolysis
Numerical accuracy	25%	12.5	Part (a)(i): Correctly computes moles HCl = 4.02 × 10⁻⁶ mol (or equivalent with proper SF); shows E = Nhc/λ = 4.14 × 10⁻¹⁹ J/photon, photons per joule, then applies Φ; Part (a)(ii): ε = 3.76 L mol⁻¹ cm⁻¹ (or 376 m² mol⁻¹ if converted); all unit conversions explicit; 3-4 significant figures maintained	Correct method but arithmetic errors (wrong powers of 10); misses unit conversion (nm to m); calculates A correctly but ε wrong due to path length unit confusion; acceptable range ±10% for final values	Order of magnitude errors; confuses wavelength and frequency; applies log₁₀ vs ln incorrectly; no unit analysis; missing quantum yield multiplication entirely; leaves answers in intermediate forms
Diagram / structure	15%	7.5	Clear Langmuir isotherm plot showing θ vs P with asymptotic approach to 1; schematic of heterogeneous catalysis steps with energy profile; labeled diagram of Na⁺/K⁺-ATPase αβ-subunit with phosphorylation sites; P450 heme-thiolate coordination environment with cysteinate axial ligand	Generic adsorption curve without labels; simple flowchart for catalytic steps; basic membrane diagram for sodium pump; mentions heme without showing thiolate coordination distinctive to P450	No diagrams where essential for explanation; irrelevant structures (e.g., hemoglobin for P450); unlabeled sketches; confused Langmuir with BET isotherm plot
Application context	15%	7.5	Cites Indian relevance: photochemical smog formation (Φ for chain reactions); Haber-Bosch vs biological nitrogen fixation for heterogeneous catalysis comparison; mentions ouabain/Indian plant-derived cardiac glycosides as Na⁺/K⁺-ATPase inhibitors; connects P450 polymorphisms to drug metabolism variation in Indian populations	General applications: mentions photography for quantum yield, industrial catalysis broadly, nerve conduction for sodium pump, drug metabolism for P450 without specific Indian or contemporary context	No real-world connections; irrelevant applications (confuses P450 with hemoglobin oxygen transport); misses biological significance entirely; no mention of therapeutic or environmental relevance

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