Q8
(a) Sketch the synthesis of [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COCH₃)] and [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COOH)] complexes starting from [Fe(η⁵-C₅H₅)₂]. (10 marks) (b) Calculate the spin only magnetic moment (μ_s.o.) of the central metal atom in the following complexes: (i) [Fe(H₂O)₅NO]²⁺ (ii) [Cr(NCS)₆]³⁻ (iii) [V(H₂O)₆]³⁺ (iv) [Co(bpy)₃]²⁺ (10 marks) (c) When an incident light of wavelength 300 nm is passed through a solution in a 1 cm cell, it transmits only 10% of the incident light. What percentage of light would be absorbed by the same solution if taken in a 0.5 cm cell? (10 marks) (d) Explain the transition-state theory for reaction rates. How is this theory considered superior to collision theory in providing a much more complete interpretation of the pre-exponential factor A in the Arrhenius equation? (20 marks)
हिंदी में प्रश्न पढ़ें
(a) [Fe(η⁵-C₅H₅)₂] से शुरू करते हुए [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COCH₃)] और [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COOH)] संकुलों के संश्लेषण की रूपरेखा बनाइए। (10 अंक) (b) निम्नलिखित संकुलों में केंद्रीय धातु परमाणु के केवल प्रचक्रण चुंबकीय आघूर्ण (μ_s.o.) का परिकलन कीजिए: (i) [Fe(H₂O)₅NO]²⁺ (ii) [Cr(NCS)₆]³⁻ (iii) [V(H₂O)₆]³⁺ (iv) [Co(bpy)₃]²⁺ (10 अंक) (c) जब 300 nm तरंगदैर्घ्य का आपतित प्रकाश एक विलयन में से गुजारा जाता है, जो कि 1 cm सेल में है, तो यह आपतित प्रकाश का केवल 10% भाग ही संचारित करता है। 0.5 cm सेल में समान विलयन लेने पर प्रकाश का कितना प्रतिशत अवशोषित होगा? (10 अंक) (d) अभिक्रिया दर के लिए संक्रमण-अवस्था सिद्धांत की व्याख्या कीजिए। कैसे इस सिद्धांत को अर्रेनियस समीकरण में पूर्व-चरघातांकी गुणक A की अधिक पूर्ण व्याख्या प्रदान करने में संघट्ट सिद्धांत से बेहतर माना जाता है? (20 अंक)
Directive word: Explain
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How this answer will be evaluated
Approach
Begin with a brief introduction acknowledging the interdisciplinary nature of the question spanning organometallic synthesis, magnetism, spectroscopy, and kinetics. Allocate approximately 15% time to part (a) on ferrocene acylation chemistry, 20% to part (b) magnetic moment calculations with proper oxidation state determination, 15% to part (c) Beer-Lambert law application, and 50% to part (d) transition-state theory including detailed comparison with collision theory and statistical mechanical treatment of the pre-exponential factor. Conclude by synthesizing how these diverse topics illustrate fundamental coordination chemistry principles.
Key points expected
- Part (a): Friedel-Crafts acylation of ferrocene using acetic anhydride/AlCl₃ to give monoacetylferrocene, followed by haloform reaction with NaOBr/NaOH or oxidation to yield carboxylic acid derivative; regioselectivity favoring single substitution
- Part (b): Correct oxidation state assignment—Fe(II) with NO⁺ in (i) giving d⁷ low-spin μ=1.73 BM, Cr(III) d³ in (ii) μ=3.87 BM, V(III) d² in (iii) μ=2.83 BM, Co(II) d⁷ high-spin in (iv) μ=3.87 BM; application of μ_s.o.=√[n(n+2)] BM
- Part (c): Application of Beer-Lambert law A=εcl; calculation showing A₁=1.0 for 1 cm cell, hence εc=1, then A₂=0.5 for 0.5 cm cell, giving 68.4% transmission and 31.6% absorption
- Part (d): Transition-state theory fundamentals—equilibrium between reactants and activated complex, Eyring equation k=(k_BT/h)K‡, partition function derivation of pre-exponential factor
- Part (d): Superiority over collision theory—incorporation of vibrational/rotational degrees of freedom, entropy of activation, steric and orientation factors through partition functions, temperature-dependent A vs constant A in collision theory
- Part (d): Statistical mechanical expression A=(k_BT/h)(q‡/q_Aq_B) showing explicit dependence on molecular properties and configuration of activated complex
- Cross-connection: How spectroscopic techniques (UV-Vis in part c) relate to determination of activation parameters in TST through thermodynamic formulation
- Contemporary relevance: Applications in catalysis design (Indian context: homogeneous catalysis research at NCL Pune, IISc Bangalore) where TST guides catalyst optimization
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Concept correctness | 25% | 12.5 | Demonstrates flawless understanding across all parts: recognizes ferrocene's aromaticity enabling electrophilic substitution, correctly identifies NO⁺ as nitrosyl cation in (b)(i) leading to Fe(II) d⁷ configuration, applies TST with proper thermodynamic and statistical mechanical foundations distinguishing ΔG‡, ΔH‡, ΔS‡ | Shows generally correct concepts with minor errors: misassigns oxidation state in one complex of part (b), or presents TST without clear distinction from collision theory, or confuses acylation conditions for ferrocene | Fundamental conceptual errors: treats ferrocene as simple alkane, calculates magnetic moments using wrong electron counts or ignoring spin-only formula limitations, confuses TST with intermediate-based mechanisms, or applies Beer-Lambert law incorrectly |
| Mechanism / equation | 20% | 10 | Presents complete mechanistic steps for ferrocene acylation with electron-flow arrows, writes Eyring equation and its thermodynamic form k=(k_BT/h)exp(-ΔG‡/RT), derives relationship to Arrhenius parameters with E_a=ΔH‡+RT and A=(k_BT/h)exp(ΔS‡/R), shows proper equilibrium treatment of activated complex | States key equations without full derivation: gives Eyring equation without showing connection to partition functions, presents acylation mechanism without arrow-pushing detail, or states Arrhenius-A relationship without statistical mechanical basis | Missing or incorrect equations: no Eyring equation stated, incorrect rate law for TST, confuses pre-exponential factor with frequency factor from simple collision theory, or presents incorrect organic mechanism for ferrocene functionalization |
| Numerical accuracy | 20% | 10 | All calculations precise: magnetic moments to two decimal places using correct unpaired electron counts (1.73, 3.87, 2.83, 3.87 BM), Beer-Lambert calculation yielding exactly 31.6% absorption for 0.5 cm cell, proper unit handling throughout | Correct methodology with arithmetic slips: one incorrect magnetic moment due to electron count error, or minor calculation error in logarithmic step for part (c), or correct final answers with inconsistent significant figures | Serious numerical errors: multiple wrong magnetic moments, failure to use spin-only formula, incorrect logarithmic calculation in part (c) yielding wrong percentage, or order-of-magnitude errors in any calculation |
| Diagram / structure | 15% | 7.5 | Clear sketches: ferrocene with η⁵-Cp rings showing acylation at single ring, products with correct connectivity; reaction coordinate diagram for TST showing activated complex at energy maximum with proper curvature; potential energy surface contour diagram illustrating saddle point | Adequate representations: linear reaction coordinate diagram without proper activated complex depiction, ferrocene structures without stereochemical indication, or missing one required diagram with verbal description substituting | Missing or misleading diagrams: no structures for organometallic compounds, confused reaction coordinate diagram showing intermediate instead of transition state, or entirely verbal description where visual representation is essential |
| Application context | 20% | 10 | Rich contextualization: cites Indian research (NCL Pune work on ferrocene derivatives, IIT Bombay studies on reaction dynamics), connects TST to enzymatic catalysis and industrial homogeneous catalysis, discusses limitations of TST (recrossing, non-adiabatic reactions), relates spectroscopy to activation parameter determination | Basic contextual links: mentions general catalysis applications, notes that TST improves upon collision theory without specific examples, or makes passing reference to industrial relevance without elaboration | Isolated treatment of topics: no connection between parts, no real-world applications mentioned, or irrelevant digressions into unrelated areas of chemistry without addressing the question's integrative demands |
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