Chemistry 2023 Paper I 50 marks Compulsory Solve

Q5

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.

हिंदी में प्रश्न पढ़ें

AB₂ का AB तथा B में अपघटन एक प्रथम-कोटि की अभिक्रिया है, जिसमें k = 2·8 × 10⁻⁷ s⁻¹ है T = 1000 K पर। A तथा B के परमाणु भार क्रमशः 12 और 32 हैं। (i) 1000 °C पर इस अभिक्रिया की अर्धायु ज्ञात कीजिए। (ii) कितने दिनों में 1 g AB₂ अपघटित होकर 0·6 g AB₂ रह जाएगा? (iii) 1 g AB₂ 35 दिनों के बाद कितना रह जाएगा? अणु की एकक और त्रिक इलेक्ट्रॉनिक अवस्थाओं के द्वारा विकिरणी और अविकिरणी प्रक्रियाओं की व्याख्या कीजिए। इसकी जेब्लॉन्स्की आरेख से भी व्याख्या कीजिए। साइटोसीन तथा थाइमीन न्यूक्लियोटाइड क्षारकों में मौजूद प्रत्येक कार्बन परमाणु को एक ज्यामिति और संकरण निर्धारित कीजिए। ऐक्टिनाइड आयनों के UV-दृश्यमान अवशोषण स्पेक्ट्रा में देखे गए तीन मुख्य प्रकार के इलेक्ट्रॉनिक संक्रमणों की व्याख्या कीजिए। नीचे दी गई प्रतिस्थापन अभिक्रिया में A और B को पहचानिए : [PtCl₄]²⁻ + NO₂⁻ → [A] → [B] NH₃ क्षुब्ध सिद्धांत के द्वारा गतिक ट्रांस-प्रभाव की व्याख्या करते हुए औचित्य सिद्ध कीजिए।

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Approach

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.

Key points expected

  • (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

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies first-order kinetics for all parts; accurately distinguishes radiative vs non-radiative processes; correctly assigns sp²/sp³ hybridization in nucleotide bases; properly identifies f-f, CT and 5f-6d transitions; applies trans-effect series correctly with polarization theoryMinor errors in kinetic order identification or hybridization assignment; incomplete distinction between radiative processes; partial knowledge of actinide transitions; basic understanding of trans-effect without clear mechanistic reasoningConfuses first-order with second-order kinetics; fails to distinguish singlet/triplet states; incorrect hybridization assignments; omits or misidentifies electronic transition types; misunderstands trans-effect direction or mechanism
Mechanism / equation20%10Writes integrated rate law ln[A] = ln[A]₀ - kt for all calculations; clearly explains ISC mechanism via spin-orbit coupling; details polarization theory with Pt(II) d⁸ configuration and π-backbonding from NO₂⁻; shows stepwise substitution mechanismUses correct rate equations with minor errors; basic explanation of intersystem crossing without spin-orbit coupling detail; general description of trans-effect without polarization theory elaboration; incomplete mechanistic stepsUses incorrect rate equations (e.g., second-order); no mechanistic explanation for ISC or radiative processes; missing polarization theory entirely; fails to show substitution steps or trans-effect application
Numerical accuracy20%10t₁/₂ = 2.47×10⁶ s or 28.6 days; time for 0.6g remaining = 1.84×10⁶ s or 21.3 days; mass after 35 days = 0.42 g; all unit conversions (K to °C noted, s to days) correct; proper significant figures (2-3) maintainedCorrect method with minor calculation errors (±10%); correct final answers with wrong units or significant figures; one part correct, others with arithmetic mistakesMajor calculation errors (>20% deviation); incorrect unit conversions (confuses 1000K vs 1000°C); wrong formula application; no numerical working shown
Diagram / structure20%10Complete Jablonski diagram with S₀, S₁, S₂, T₁, vibrational levels, all labeled transitions (absorption, fluorescence, phosphorescence, IC, ISC); clear structural drawings of cytosine and thymine with hybridization labeled on each carbon; proper square planar geometry for Pt(II) complexes showing trans positionsBasic Jablonski diagram missing vibrational levels or some transitions; structural formulas without explicit hybridization labels; simple representation of Pt complexes without clear stereochemistryNo Jablonski diagram; missing or incorrect structures for nucleotide bases; no representation of Pt complex geometries; diagrams unlabeled or illegible
Application context20%10Relates first-order kinetics to radioactive decay or industrial decomposition processes; connects photochemistry to photodynamic therapy or solar energy applications; links nucleotide base chemistry to DNA structure/mutation; relates actinide spectroscopy to nuclear fuel reprocessing (e.g., Indian BARC research); connects trans-effect to cisplatin anticancer drug designBrief mention of one application area; generic statements about importance without specific examples; no Indian research contextNo application context provided; purely theoretical treatment without real-world relevance; no connection to contemporary chemical research or technology

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