Chemistry 2021 Paper I 50 marks Compulsory Derive

Q5

(a) Derive an equation for rate constant of a zero-order reaction. Show that half-life period of the reaction is proportional to the initial concentration of reactant. (10 marks) (b) State and derive Lambert-Beer law for absorption of light by solutions. (10 marks) (c) Give the mechanism of fatal formation of hematin in the binding of dioxygen by heme. How can it be averted by living systems? (10 marks) (d) How many geometrical isomers and stereoisomers are possible in the coordination compounds of the type (AB)Mb₂c₂(AB—bidentate ligand)? (10 marks) (e) Complete the following reactions: (i) XeF₄ + 12H₂O —→ ____ (ii) XeF₆ + ____ —→ XeOF₄ + PF₅ (iii) XeOF₄ + ____ —→ 2XeO₂F₂ (iv) 3XeF₂ + 2(SO₃)₃ —→ ____ (v) ____ + XeF₂ —→ (C₆H₅)₂ SF₂ + Xe (10 marks)

हिंदी में प्रश्न पढ़ें

(a) शून्य-कोटि अभिक्रिया में वेग स्थिरांक के समीकरण को व्युत्पन्न कीजिए। यह भी दिखाइए कि अभिक्रिया का अर्धायु काल, अभिक्रियक की प्रारंभिक सांद्रता के आनुपातिक है। (10 अंक) (b) विलयन में प्रकाश के अवशोषण के लिए लैम्बर्ट-बीयर नियम को स्पष्ट कीजिए और उसे व्युत्पन्न कीजिए। (10 अंक) (c) डाइऑक्सीजन का हीम से बंधन करके बनने वाले घातक हीमेटिन के निर्माण की क्रियाविधि दीजिए। इसका जीवित प्रणाली के द्वारा कैसे निवारण किया जाता है? (10 अंक) (d) (AB)Mb₂c₂(AB—द्विदंती संलग्नी) जैसे उपसहसंयोजन यौगिकों में कितने ज्यामितीय समावयव और विविध समावयव संभव हैं? (10 अंक) (e) निम्नलिखित अभिक्रियाओं को पूरा कीजिए : (i) XeF₄ + 12H₂O —→ ____ (ii) XeF₆ + ____ —→ XeOF₄ + PF₅ (iii) XeOF₄ + ____ —→ 2XeO₂F₂ (iv) 3XeF₂ + 2(SO₃)₃ —→ ____ (v) ____ + XeF₂ —→ (C₆H₅)₂ SF₂ + Xe (10 अंक)

Evaluate your answer to this question → See all 2021 Chemistry questions

Directive word: Derive

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

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Begin with the directive 'derive' for part (a), applying systematic derivation methodology across all five parts. Allocate approximately 20% time to each part given equal 10-mark weighting: (a) derive zero-order kinetics with integrated rate law and half-life proof; (b) state and derive Beer-Lambert law with extinction coefficient significance; (c) explain heme-oxygen binding mechanism with proximal histidine role and globin protection; (d) analyze geometrical and optical isomerism for M(AB)b₂c₂ with clear counting; (e) complete five xenon reactions showing hydrolysis patterns and fluorinating behavior. Structure as five distinct sections without introduction or conclusion.

Key points expected

Part (a): Derivation of rate constant k = [A]₀ - [A]/t for zero-order reaction; proof that t₁/₂ = [A]₀/2k showing direct proportionality to initial concentration
Part (b): Statement of Beer-Lambert law (A = εcl or I = I₀10^(-εcl)); derivation from differential form -dI/dl = k'Ic; definition of molar extinction coefficient ε and its units
Part (c): Mechanism of heme Fe(II) oxidation to Fe(III) hematin via μ-oxo dimer formation; role of distal and proximal histidine in globin preventing autoxidation; mention of picket-fence porphyrin model by Collman
Part (d): Analysis of M(AB)b₂c₂ showing 5 geometrical isomers; identification of which geometrical isomers possess optical isomerism leading to total stereoisomer count
Part (e): (i) XeF₄ + 12H₂O → Xe + ½O₂ + 4HF + 11H₂O or Xe + 2O₂ + 4HF; (ii) XeF₆ + OPF₃ or H₂O; (iii) XeOF₄ + SiO₂ → 2XeO₂F₂ + SiF₄; (iv) 3XeF₂ + 2S₂O₆F₂ → 3Xe + 6SF₂ + 6O₂; (v) (C₆H₅)₂S + XeF₂ → (C₆H₅)₂SF₂ + Xe

Evaluation rubric

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding across all parts: correctly identifies zero-order characteristics (rate independence of concentration), distinguishes between absorbance and transmittance in Beer-Lambert law, accurately describes Fe-O₂ binding geometry and autoxidation pathway, correctly applies C₂ symmetry analysis for isomer counting, and shows comprehensive knowledge of xenon fluoride reactivity patterns including hydrolysis mechanisms	Shows generally correct concepts with minor errors: may confuse zero-order with first-order half-life dependence, states Beer-Lambert law without proper constant definitions, describes heme oxidation superficially without μ-oxo bridge detail, counts isomers with some omissions or duplicates, and completes 3-4 xenon reactions correctly	Displays fundamental conceptual errors: treats zero-order as concentration-dependent, confuses Beer-Lambert with other laws, fails to distinguish heme from hemoglobin oxidation mechanisms, cannot systematically enumerate isomers, and shows poor knowledge of noble gas chemistry with multiple incorrect products
Mechanism / equation	20%	10	Presents rigorous stepwise derivations: integrates -d[A]/dt = k₀ properly with boundary conditions; derives Beer-Lambert from first principles showing logarithmic transformation; illustrates heme-oxygen binding with electron transfer steps and dimerization to Fe-O-Fe; employs systematic substitution pattern analysis for isomer enumeration; balances all xenon equations with correct stoichiometry and physical states	Provides correct final equations with incomplete derivations: states integrated rate law without showing integration steps, presents Beer-Lambert as empirical relation without derivation, describes heme oxidation qualitatively without electron accounting, uses trial method for isomer counting, and balances most xenon reactions with minor errors	Shows inability to construct proper mechanisms: cannot perform integration for zero-order kinetics, merely quotes Beer-Lambert without any derivation attempt, describes heme binding without mechanistic insight, guesses isomer numbers without systematic approach, and fails to balance majority of xenon reactions
Numerical accuracy	20%	10	Delivers precise quantitative results: explicit half-life formula t₁/₂ = [A]₀/2k with proportionality constant identified; correct ε values with proper units (L mol⁻¹ cm⁻¹); accurate Fe-O bond distances (~1.8 Å) and O-O stretching frequencies; exact isomer counts (5 geometrical, 7-8 total stereoisomers depending on symmetry); correct stoichiometric coefficients in all five xenon reactions	Provides generally correct numbers with minor inconsistencies: correct half-life trend but wrong formula constant, correct ε definition but wrong units, approximate bond parameters for heme, correct geometrical isomer count but wrong optical isomer addition, and 3-4 correct reaction stoichiometries	Demonstrates poor quantitative handling: incorrect half-life concentration dependence, missing or wrong units throughout, no numerical parameters for heme structure, completely wrong isomer counts, and multiple incorrect stoichiometric coefficients
Diagram / structure	20%	10	Includes clear illustrative elements: concentration-time plot for zero-order with slope -k; schematic of spectrophotometer with beam path through cuvette; detailed heme structure showing porphyrin ring, Fe center, proximal His, and bound O₂ with bent geometry; all five geometrical isomers of M(AB)b₂c₂ drawn with proper wedge-dash notation; structures of xenon compounds showing square planar XeF₄, distorted octahedral XeF₆, and square pyramidal XeOF₄	Provides some diagrams with incomplete labeling: simple plot without axis labels, basic Beer-Lambert setup without components, generic heme structure without specific residues, 2-3 isomer structures with unclear stereochemistry, and 1-2 xenon compound structures	Lacks essential visual aids: no concentration-time plot, no spectroscopic diagram, no heme structure, no isomer drawings, and no xenon compound structures despite geometric complexity of question parts
Application context	20%	10	Connects theory to practical significance: enzyme kinetics (catalase zero-order at high [H₂O₂]), spectrophotometric analysis in Indian pharmaceutical QC (IP/USP compliance), clinical relevance of methemoglobinemia and blood substitutes, importance of isomerism in cisplatin anticancer activity and Indian coordination chemistry research, and industrial applications of xenon compounds in silicon etching and aerospace propulsion	Mentions some applications without depth: generic enzyme example without specificity, basic analytical use without standards reference, mentions hemoglobin without clinical condition, notes isomer importance without bioinorganic example, and states noble gas compound existence without applications	Fails to establish real-world relevance: no applications mentioned for any part, purely theoretical treatment, no connection to Indian scientific contributions or contemporary research in any sub-discipline

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →