(a) The rate Law for the reaction N₂O₂(g) → 2NO(g) is of first order in the concentration of N₂O₂. Derive an expression for the time-dependent behaviour of the product concentration [NO]. (10 marks)

(b) Label each of the following processes with pro

Question

(a) The rate Law for the reaction N₂O₂(g) → 2NO(g) is of first order in the concentration of N₂O₂. Derive an expression for the time-dependent behaviour of the product concentration [NO]. (10 marks)

(b) Label each of the following processes with proper explanation in Jablonski diagram: (A) Allowed absorption, (B) Fluorescence, (C) Phosphorescence, (D) Internal Conversion (IC), (E) Inter System Crossing (ISC). Discuss the mode of transition which is favourable for a photochemical reaction. (10 marks)

(c) What is allosteric effect? Give example of an allosteric protein. Discuss homotropic allosteric modulators with examples. (10 marks)

(d) Write IUPAC nomenclature of [Ni(CO)₄] and [Ni(CN)₄]⁴⁻. Give structure and draw their shapes with explanation. (10 marks)

(e) Write the general synthetic procedure of lower cyclosiloxanes like cyclic dimethylsiloxane trimer [(Me₂SiO)₃]. Draw its structure. Why MeSiCl₃ is not used as starting material for its synthesis? (10 marks)

UPSC Answer Check · Accepted Answer

Begin with the derivation directive in part (a): set up the rate law, integrate to obtain [NO] as function of time, and explicitly show the 2:1 stoichiometry factor. Allocate approximately 20% time to each sub-part (a)-(e) since marks are equal. For (b), draw a clear Jablonski diagram with labeled transitions and explain spin-allowed vs spin-forbidden processes. For (c), define allostery with hemoglobin as the canonical example, then explain cooperative binding. For (d), apply IUPAC rules for coordination compounds, show tetrahedral vs square planar geometries with hybridization. For (e), describe hydrolysis-condensation of Me₂SiCl₂, draw the six-membered ring, and explain why MeSiCl₃ gives cross-linked polymers instead.
- Part (a): Correct integration of first-order rate law with proper handling of stoichiometric coefficient (factor of 2) to yield [NO] = 2[N₂O₂]₀(1 - e^(-kt))
- Part (b): Accurate Jablonski diagram showing S₀, S₁, T₁ states with arrows for absorption, fluorescence, phosphorescence, IC, ISC; identification of singlet excited state as favorable for photochemistry
- Part (c): Definition of allosteric effect as regulation at distant site; hemoglobin as example; homotropic modulation as same-ligand interaction with cooperative binding explanation
- Part (d): IUPAC names: tetracarbonylnickel(0) and tetracyanidonickelate(II); tetrahedral sp³ for Ni(CO)₄ vs square planar dsp² for [Ni(CN)₄]⁴⁻ with clear 3D representations
- Part (e): Hydrolysis of Me₂SiCl₂ to Me₂Si(OH)₂ followed by acid/base catalyzed condensation; six-membered siloxane ring structure; MeSiCl₃ leads to 3D cross-linked polysilsesquioxanes preventing cyclization
- Cross-cutting: Integration of theoretical principles with industrial relevance (silicones in Indian polymer industry, Haber-Bosch connection to N₂O chemistry)

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding across all five parts: correct kinetic order interpretation in (a), precise definitions of electronic states in (b), accurate molecular biology terminology in (c), correct oxidation states and geometries in (d), and proper mechanistic reasoning for siloxane formation in (e)	Shows generally correct concepts with minor errors: integration direction confused in (a), IC/ISC distinction unclear in (b), allostery confused with feedback inhibition in (c), geometry assignments swapped in (d), or incomplete explanation of MeSiCl₃ behavior in (e)	Fundamental conceptual errors: treats (a) as second-order, confuses fluorescence with phosphorescence mechanisms, defines allostery incorrectly, assigns wrong geometries, or fails to explain why trifunctional silanes prevent cyclization
Mechanism / equation	20%	10	Presents complete, stepwise derivations and mechanisms: integrated rate law with explicit integration steps in (a), detailed spin-orbit coupling explanation for ISC in (b), T↔R state transition mechanism in (c), hybridization orbital diagrams in (d), and hydrolysis-condensation mechanism with catalytic cycle in (e)	Shows correct final equations/mechanisms but skips key steps: omits separation of variables in (a), states transitions without explaining selection rules in (b), describes cooperative binding without conformational change details in (c), gives geometries without orbital hybridization in (d), or gives synthesis without mechanistic steps in (e)	Missing or incorrect mechanisms: no integration shown in (a), no explanation of why phosphorescence is slow in (b), no mechanistic insight into hemoglobin cooperativity in (c), no orbital diagrams in (d), or completely wrong synthesis description in (e)
Numerical accuracy	15%	7.5	Handles all quantitative aspects correctly: proper stoichiometric factor of 2 in (a), correct relative rate constants (k_f >> k_p) with typical values in (b), correct Hill coefficient implications in (c), accurate bond angles (109.5° vs 90°) and Ni-C/Ni-CN bond lengths in (d), correct ring strain calculations or Si-O-Si bond angles in (e)	Minor numerical errors: forgets factor of 2 in (a), order of magnitude errors in rate constants in (b), vague quantitative treatment of cooperativity in (c), approximate bond angles in (d), or missing ring size-strain relationship in (e)	Serious numerical errors: wrong integrated form in (a), incorrect relative timescales for fluorescence vs phosphorescence in (b), no quantitative aspect in (c), wrong bond angles or geometries in (d), or completely wrong ring size in (e)
Diagram / structure	25%	12.5	Produces clear, labeled, chemically accurate diagrams: concentration vs time curves for (a), complete Jablonski diagram with all five labeled transitions in (b), oxygen-binding curves showing sigmoidal behavior for hemoglobin in (c), accurate 3D wedge-dash structures showing tetrahedral vs square planar in (d), and proper chair/boat conformation of (Me₂SiO)₃ six-membered ring in (e)	Diagrams present but incomplete or unclear: missing labels on axes in (a), missing T₁ state or unclear arrow directions in (b), linear binding curve instead of sigmoidal in (c), 2D representations only in (d), or flat hexagon instead of 3D ring in (e)	Diagrams absent or seriously flawed: no graphs in (a), no Jablonski diagram in (b), no binding curves in (c), wrong geometries drawn in (d), or linear siloxane chain instead of ring in (e)
Application context	20%	10	Integrates real-world relevance throughout: atmospheric chemistry/N₂O decomposition catalysts in (a), photostabilizers and OLED applications in (b), drug design and hemoglobinopathies (sickle cell in Indian context) in (c), organometallic catalysis and cyanide detoxification in (d), Indian silicone industry (Wacker, Dow Corning India) and applications in (e)	Mentions applications superficially: generic kinetic applications in (a), basic fluorescence uses in (b), blood transport only in (c), vague industrial mention in (d), or sealants/adhesives only in (e) without Indian context	No application context provided: purely theoretical treatment in all parts, or irrelevant/apocryphal examples cited

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