All 8 questions from UPSC Civil Services Mains Chemistry
2022 Paper I (400 marks total). Every stem reproduced in full,
with directive-word analysis, marks, word limits, and answer-approach pointers.
8Questions
400Total marks
2022Year
Paper IPaper
Topics covered
Quantum chemistry, thermodynamics and electrochemistry (1)Thermodynamics, quantum mechanics and solid state chemistry (1)Physical chemistry - thermodynamics and chemical bonding (1)Physical chemistry - thermodynamics and electrochemistry (1)Chemical kinetics, photochemistry, bioinorganic chemistry, coordination compounds, organosilicon chemistry (1)Organometallic chemistry, lanthanide chemistry, coordination chemistry, noble gas chemistry, boron chemistry, transition metal chemistry (1)Coordination chemistry and chemical kinetics (1)Bioinorganic chemistry and surface chemistry (1)
A
Q1
50MCompulsorycompareQuantum chemistry, thermodynamics and electrochemistry
1.(a) Compare average and most probable values of position of an electron in the ground state of hydrogen atom. Explain with the help of drawing, why two values differ. (10 marks)
1.(b) Consider the following atomic orbitals of A and B atoms in a heterodiatomic AB molecule.
A
2s
2px
B
2py
2pz
Depict the nonbonding interactions among these atomic orbitals with reason. (10 marks)
1.(c) (i) F-centre defect can be introduced in several ways. Regardless of the method used, the colour produced in any particular crystal is always same. Explain the reasons.
(ii) How would the formation of F-centre affect the density of the crystal ? (10 marks)
1.(d) Calculate ΔG at 298 K for the formation of O3 from O2 in urban smog, where [O2] = 0·21 atm and [O3] = 5×10⁻⁷ atm.
Given; ΔG°f(O3) = 163 kJ mol⁻¹.
R = 8·314 J mol⁻¹K⁻¹,
F = 96485 C mol⁻¹. (10 marks)
1.(e) For a cell reaction
Cu²⁺(aq) + Zn(s) → Cu(s) + Zn²⁺(aq)
the standard electrode potential for Zn/Zn²⁺ = 0·339 V and for Cu²⁺/Cu = 0·762 V at 25°C. Calculate standard change in free energy ΔG° and equilibrium constant K for the reaction.
[R = 8·314 J mol⁻¹ k⁻¹] (10 marks)
हिंदी में पढ़ें
1.(a) हाइड्रोजन परमाणु की मूल अवस्था में इलेक्ट्रॉन की स्थिति की औसत और सर्वाधिक प्रायिक मूल्यों की तुलना करें । आरेख की सहायता से व्याख्या करें कि दोनों मूल्य अलग क्यों हैं ? (10 अंक)
1.(b) एक विषम द्विपरमाणुक अणु, AB, में परमाणु A और B के निम्नलिखित परमाणु कक्षकों को मान लीजिए ।
A
2s
2px
B
2py
2pz
इन परमाणु कक्षकों के बीच में अनाबंधित अन्योन्य क्रियाओं का तर्क सहित चित्रण करें । (10 अंक)
1.(c) (i) F-केंद्र दोष कई विधियों से शामिल किया जाता है । विधियों को अनपेक्ष करते हुए, किसी भी विशेष क्रिस्टल में सदैव समान रंग पैदा होता है । तर्क की व्याख्या कीजिए ।
(ii) F-केंद्र का निर्माण/संभवन क्रिस्टल के घनत्व को कैसे प्रभावित करता है ? (10 अंक)
1.(d) नगर धूमुकुहा में [O2] = 0·21 atm और [O3] = 5×10⁻⁷ atm पाई गई है, वहाँ O2 से O3 के संभवन का 298 K पर ΔG का परिकलन कीजिए ।
दिया गया है कि ΔG°f(O3) = 163 kJ mol⁻¹,
R = 8·314 J mol⁻¹K⁻¹,
F = 96485 C mol⁻¹ । (10 अंक)
1.(e) सेल अभिक्रिया के लिए
Cu²⁺(aq) + Zn(s) → Cu(s) + Zn²⁺(aq)
25°C पर Zn/Zn²⁺ और Cu²⁺/Cu का मानक इलेक्ट्रोड विभव क्रमानुसार 0·339 V और 0·762 V है । इस अभिक्रिया में मुक्त ऊर्जा के बदलाव का मानक मूल्य, ΔG° और साम्य स्थिरांक, K का परिकलन कीजिए ।
[R = 8·314 J mol⁻¹ k⁻¹] (10 अंक)
Answer approach & key points
Begin with a brief introduction acknowledging the diverse nature of the five sub-parts spanning quantum mechanics, chemical bonding, solid state, and electrochemistry. Allocate approximately 20% time each to parts (a), (b), (c), (d), and (e) since all carry equal marks. For (a), compare <r> and r_mp with radial probability distribution diagrams; for (b), apply symmetry rules for orbital overlap; for (c), explain electron trapping and density changes; for (d) and (e), show step-by-step thermodynamic calculations with proper units. Conclude by briefly connecting how quantum mechanical principles underpin macroscopic observations in electrochemistry and materials science.
Part (a): Average position <r> = 3a₀/2 and most probable position r_mp = a₀ for 1s hydrogen; radial probability distribution 4πr²|ψ|² peaks at a₀ while <r> integrates over all space weighted by r
Part (b): Nonbonding interactions arise from zero net overlap: A(2s) with B(2py, 2pz) due to symmetry mismatch; A(2px) with B(2py, 2pz) due to orthogonality; only σ/π bonding possible if symmetry allows
Part (c)(i): F-centre colour depends only on crystal lattice parameter and electron trap depth (Mollwo-Ivey relation), not method of introduction; trapped electron absorbs specific wavelength
Part (c)(ii): Density decreases because anion vacancies create mass deficit without proportional volume change; Schottky-type defect mechanism
Part (d) and (e): Correct application of ΔG = ΔG° + RTlnQ and ΔG° = -nFE° = -RTlnK with proper unit conversions (kJ to J, atm handling, n values)
50McalculateThermodynamics, quantum mechanics and solid state chemistry
2.(a) An automobile tyre contains air at 320×10³ Pa at 20°C. The stem valve is removed and the air is allowed to expand adiabatically against a constant external pressure of 100×10³ Pa until P = P_external. For air, C_v, m = 5/2 R. Calculate the final temperature of the gas in the tyre. Assume ideal gas behaviour. (10 marks)
2.(b) A particle is in the nth energy state, φ_n(x), of an infinite square well potential with width L (box size from O to L). Calculate the probability that the particle is confined to the first 1/a of the width of the well. (20 marks)
2.(c) In a certain material of simple cubic structure, (100) diffraction is obtained at θ = 14·88° with radiation of λ = 1·541 Å. Can this material accommodate an atom of 1·08 Å radius interstitially in void space without lattice distortion ?
[Sin 14·88 = 0·257] (20 marks)
हिंदी में पढ़ें
2.(a) एक ऑटोमोबाइल टायर में 20°C पर वायु का दबाव 320×10³ Pa है । स्टेम वाल्व को हटाने पर वायु को एक अपरिवर्ती बाह्य दबाव, 100×10³ Pa के विरुद्ध रुद्धोष्म के आधार पर प्रसारित होने की छूट मिल गई, जब तक वायु का दबाव, P, अपरिवर्ती बाह्य दबाव, P_external, के समान नहीं हो जाता, (P = P_external) । वायु के लिए C_v, m = 5/2 R टायर में गैस के अंतिम तापमान का परिकलन कीजिए । आदर्श गैस आचरण मान लीजिए । (10 अंक)
2.(b) एक अंत वर्ग विभव कूप, जिसकी चौड़ाई, L, है (बॉक्स का आकार O से L है), उसमें एक कण अपनी nth ऊर्जा अवस्था, φ_n(x), में है । अगर कण कूप की चौड़ाई के प्रथम 1/a भाग में सीमित है, तो कण की इस भाग में होने की प्रायिकता का परिकलन कीजिए । (20 अंक)
2.(c) सरल घन संरचना के किसी पदार्थ में विकिरण, जिसकी तरंगदैर्घ्य, λ = 1·541 Å के साथ, (100) विवर्तन, θ = 14·88° पर प्राप्त किया गया । बिना जालक विक्षेपण के क्या यह पदार्थ, एक परमाणु, जिसका त्रिज्या 1·08 Å है को अपने अंतराकाशी रिक्त स्थान में समायोजित कर सकता है ?
[Sin 14·88 = 0·257] (20 अंक)
Answer approach & key points
Calculate requires systematic numerical problem-solving across three distinct physical chemistry domains. Structure the answer by tackling each sub-part sequentially: (a) adiabatic irreversible expansion using first law, (b) quantum probability integration for infinite square well, and (c) Bragg's law analysis with void geometry. Present clear step-wise derivations with proper unit handling and physical reasoning before final numerical answers.
Part (a): Apply first law for adiabatic irreversible expansion against constant external pressure: q=0, so ΔU = -W_ext, leading to nCv(T2-T1) = -P_ext(V2-V1) with ideal gas substitution
Part (b): Set up probability integral P = ∫₀^(L/a) |φₙ(x)|²dx = (2/L)∫₀^(L/a) sin²(nπx/L)dx and evaluate to [1/a - sin(2nπ/a)/(2nπ)]
Part (c): Apply Bragg's law nλ = 2d sinθ to find a = λ/(2sinθ) = 3.00 Å, then compare octahedral void radius (0.414a = 1.24 Å) vs tetrahedral (0.225a = 0.68 Å) with atomic radius 1.08 Å
Clear identification of irreversible adiabatic vs reversible process in part (a) - must NOT use TV^(γ-1) = constant
Proper handling of quantum number n as general variable in part (b), not assuming ground state
50MexplainPhysical chemistry - thermodynamics and chemical bonding
(a) Identify the least stable ion of the following ions and justify your answer. OCN⁻ ONC⁻ SCN⁻ (10 marks)
(b) A 74·6 g ice cube floats in the sea. The temperature and pressure of the system and surroundings are 0°C and 1 atm. Calculate ΔS_syst, ΔS_surr and ΔS_univ for the melting of ice cube. What can you conclude about the nature of process from the value of ΔS_univ ? (The molar heat of fusion of water is 6·01 kJ/mol) (10 marks)
(c) The graph above shows the distribution of molecular speeds for Argon and Helium at the same temperature.
(i) Which curve, 1 or 2 better represents the behavior of Argon ?
(ii) Which curve represents the gas that effuses more slowly ?
(iii) Which curve more closely represents the behavior of fluorine gas ? Explain. (10 marks)
(d) Construct a phase-diagram for a one component system (water) and explain all the three curves. Also describe the significance of critical pressure, critical temperature and triple point. (10 marks)
(e) Provide briefly a qualitative account of different forces which influence the speed of an ion in solution of strong electrolyte moving under an externally applied electric field. (10 marks)
हिंदी में पढ़ें
(a) निम्नलिखित आयनों में से कम-से-कम (अल्पतम) स्थायी आयन को पहचानें और अपने उत्तर को उचित सिद्ध करें । OCN⁻ ONC⁻ SCN⁻ (10 अंक)
(b) 74·6 g का बर्फ का एक क्यूब समुद्र में तैर रहा है । तंत्र (system) और परिवेश (surroundings) का तापमान और दबाब 0°C और 1 atm है । बर्फ के क्यूब के पिघलने पर ΔS_syst, ΔS_surr और ΔS_univ का परिकलन कीजिए । ΔS_univ के मूल्य से आप इस प्रक्रम के स्वभाव के बारे में क्या निष्कर्ष निकालते हैं ? (जल की ग्रामाणुक संगलन ऊष्मा का मूल्य 6·01 kJ/mol है ।) (10 अंक)
(c) नीचे दिए गए ग्राफ में आर्गन और हीलियम का समान तापमान पर आण्विक चाल का वितरण दिया गया है :
(i) कौन-सी वक्र रेखा, 1 या 2 आर्गन के बेहतर आचरण का निरूपण करता है ?
(ii) कौन-सी वक्र रेखा, गैस के धीरे निस्सरण का निरूपण करता है ?
(iii) कौन-सी वक्र रेखा, फ्लुओरिन गैस के आचरण को ज्यादा निकट से निरूपण करता है ?
व्याख्या कीजिए । (10 अंक)
(d) एक घटक तंत्र (जल) के प्रावस्था आरेख का निर्माण कीजिए और तीनों वक्र रेखाओं की व्याख्या कीजिए । क्रांतिक दाब, क्रांतिक ताप और त्रिक बिंदु की सार्थकता/महत्व की भी व्याख्या कीजिए । (10 अंक)
(e) बाहत: अनुप्रयुक्त विद्युत क्षेत्र के अधीन गति कर रहे प्रबल वैद्युत अपघट्य के विलयन में आयन की चाल को प्रभावित करने वाले अलग-अलग बलों का गुणात्मक स्पष्टीकरण करते हुए संक्षिप्त विवरण दें । (10 अंक)
Answer approach & key points
Explain the stability trends, entropy calculations, kinetic theory applications, phase diagram construction, and ionic mobility factors across all five parts. Allocate approximately 15-18 minutes each for parts (a), (b), and (d) due to their conceptual depth and diagrammatic requirements; 10-12 minutes each for parts (c) and (e). Begin with a brief introduction acknowledging the interconnected themes of thermodynamics and bonding, then address each part sequentially with clear sub-headings, and conclude with a synthesis of how molecular-level understanding enables prediction of macroscopic behavior.
For (a): Identify ONC⁻ as least stable based on formal charges, electronegativity placement, and resonance structures; compare with OCN⁻ (cyanate) and SCN⁻ (thiocyanate) stability
For (b): Calculate moles of ice (4.14 mol), ΔS_syst = +22.0 J/K, ΔS_surr = -22.0 J/K, ΔS_univ = 0 for reversible process at equilibrium; conclude process is reversible/equilibrium
For (c)(i)-(iii): Curve 1 = Ar (heavier, slower), Curve 2 = He; slower effusion = Curve 1; F₂ matches Curve 1 due to comparable molar mass (~38 vs 40 g/mol)
For (d): Sketch water's phase diagram with fusion curve (negative slope), vaporization curve, sublimation curve; mark triple point (0.01°C, 0.006 atm) and critical point (374°C, 218 atm)
For (e): Describe interplay of ionic atmosphere (relaxation effect), electrophoretic effect, solvation/hydration shell, interionic attractions, and viscous drag on ionic mobility
50MsolvePhysical chemistry - thermodynamics and electrochemistry
(a) By using the following given data, find that under what conditions is H₂ in the state corresponding to N₂ at 126 K and 1 atm ?
| Gas | Tc/K | Pc/atm |
|---|---|---|
| H₂ | 33 | 13 |
| N₂ | 126 | 39 |
(10 marks)
(b) The vapour pressure of water at 363·2 K is 529 torr. Use the Clausius-Clapeyron equation to determine the average value of molar heat of vaporization, ΔH̄, of water between 363·2 K and 373·2 K. [R = 8·314 J mol⁻¹ k⁻¹] (10 marks)
(c) Consider two liquids A and B such that A has half of the surface tension and twice the density of B. If liquid A rises to a height of 2·0 cm in a capillary, what will be the height to which liquid B will rise in the same capillary. (10 marks)
(d) Write down the basic principle of polarography. With the help of a neat typical polarogram discuss the significance of halfwave potential, diffusion current and limiting current. (10 marks)
(e) Determine the percentage of ionic character (bond polarity) of BrCl and comment on the nature of Br–Cl bond.
(Dipole moment of BrCl = 1·42×10⁻³⁰ cm,
bond length, d_Br–Cl = 214×10⁻¹⁴ m,
charge of an electron = 1·6×10⁻¹⁹ C) (10 marks)
हिंदी में पढ़ें
(a) निम्नलिखित दिए गए आंकड़ों के आधार पर पता लगाएं कि कौन सी शर्तें हैं, जिन पर H₂, N₂ (126 K, 1 atm) की संगत अवस्था में हो ?
| गैस | Tc/K | Pc/atm |
|---|---|---|
| H₂ | 33 | 13 |
| N₂ | 126 | 39 |
(10 अंक)
(b) 363·2 K पर जल का वाष्पदाब 529 torr है । क्लॉजियस-क्लेपेरॉन समीकरण का प्रयोग करके जल की वाष्पन की मोलरऊष्मा, ΔH̄, का औसत मूल्य 363·2 K और 373·2 K के बीच में निर्धारित करें । [R = 8·314 J mol⁻¹ k⁻¹] (10 अंक)
(c) मान लीजिए दो द्रव A और B हैं, जिनमें A का पृष्ठीय तनाव आधा और घनत्व B से दुगुना है। यदि द्रव A 2·0 cm की ऊँचाई तक एक केशिका में चढ़ता है, तो द्रव B, उसी केशिका में कितनी ऊँचाई तक चढ़ेगा ? (10 अंक)
(d) ध्रुवणलेखिकी (पोलेरोग्राफी) का मूल सिद्धांत लिखें। विशुद्ध प्ररूपी (विशिष्ट) ध्रुवणलेख (पोलेरोग्राम) की मदद से अर्धतरंग विभव, विसरण धारा और सीमांत धारा के महत्व/सार्थकता की व्याख्या करें। (10 अंक)
(e) BrCl में आयनी लक्षण (आबंध ध्रुवता) की प्रतिशतता को ज्ञात करें और Br–Cl आबंध की प्रकृति पर टिप्पणी करें।
(BrCl का द्विध्रुव आघूर्ण = 1·42×10⁻³⁰ cm,
आबंध लंबाई d_Br–Cl = 214×10⁻¹⁴ m,
इलेक्ट्रॉन का आवेश = 1·6×10⁻¹⁹ C) (10 अंक)
Answer approach & key points
This is a multi-part calculation and descriptive problem requiring systematic solving of five independent sub-parts. Allocate approximately 20% time to each part: for (a) apply reduced variables and law of corresponding states; for (b) use integrated Clausius-Clapeyron equation with proper unit conversion; for (c) apply capillary rise formula with given ratios; for (d) explain polarography principle with labeled diagram; for (e) calculate % ionic character using dipole moment formula. Present each part clearly with given data, formula, substitution, and final answer with units.
For (a): Apply law of corresponding states using reduced temperature (Tr = T/Tc) and reduced pressure (Pr = P/Pc) to find H₂ conditions equivalent to N₂ at 126 K, 1 atm; calculate Tr(N₂) = 1.0, Pr(N₂) = 0.0256, then find T(H₂) = 33 K and P(H₂) = 0.333 atm
For (b): Apply integrated Clausius-Clapeyron equation ln(P₂/P₁) = (ΔHvap/R)(1/T₁ - 1/T₂) with P₁ = 529 torr at 363.2 K, P₂ = 760 torr at 373.2 K; solve for ΔHvap ≈ 40.6 kJ/mol
For (c): Use capillary rise formula h = 2γcosθ/(ρgr); establish ratio hA/hB = (γA/γB)×(ρB/ρA) = (1/2)×(2/1) = 1; thus hB = hA = 2.0 cm (or 4.0 cm if angle differs)
For (d): State Ilkovic equation principle; draw typical polarogram with S-shaped curve showing residual, limiting, and diffusion currents; explain E½ as characteristic identification potential, id as concentration-proportional, il as total limiting current
For (e): Calculate % ionic character = (μobserved/μionic)×100 = (1.42×10⁻³⁰)/(1.6×10⁻¹⁹ × 2.14×10⁻¹⁰)×100 ≈ 4.15%; comment on predominantly covalent nature with slight polarity
(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)
हिंदी में पढ़ें
(a) N₂O₂ की सांद्रता के आधार पर अभिक्रिया N₂O₂(g) → 2NO(g) का दर नियम प्रथम कोटि का है। [NO] की उत्पाद सांद्रता के कालानुक्रम आचरण की अभिव्यक्ति व्युत्पन्न करें। (10 अंक)
(b) निम्नलिखित प्रक्रमों को उचित व्याख्या के साथ जेब्लॉन्स्की आरेख में अंकित (लेबल) करें: (क) अनुमत अवशोषण, (ख) प्रतिदीप्ति, (ग) स्फुरदीप्ति, (घ) आंतरिक रूपांतरण, (ङ) अंतरतंत्र पारगमन। प्रकाशरासायनिक अभिक्रिया के लिए अनुकूल संक्रमण की विधि की व्याख्या कीजिए। (10 अंक)
(c) एलोस्टेरिक प्रभाव क्या है? एलोस्टेरिक प्रोटीन का उदाहरण दें। होमोट्रोपिक एलोस्टेरिक मॉडुलक की व्याख्या उदाहरणों के साथ करें। (10 अंक)
(d) [Ni(CO)₄] और [Ni(CN)₄]⁴⁻ की IUPAC नामपद्धति लिखें। व्याख्या के साथ इनकी संरचना दें और इनके आकार का चित्र बनाएं। (10 अंक)
(e) साइक्लिक डाइमेथिलसिलॉक्सेन ट्राइमर [(Me₂SiO)₃] के जैसे निम्न साइक्लोसिलॉक्सेनों की सामान्यतः संश्लिष्ट प्रक्रिया लिखें। इसकी संरचना का चित्र बनाएं। इसके संश्लेषण के लिए MeSiCl₃ को आरंभिक पदार्थ के रूप में प्रयुक्त/इस्तेमाल क्यों नहीं किया जाता है? (10 अंक)
Answer approach & key points
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)
50MexplainOrganometallic chemistry, lanthanide chemistry, coordination chemistry, noble gas chemistry, boron chemistry, transition metal chemistry
(a) (i) Calculate the number of metal-metal bond in Cp₂Fe₂(CO)₄. (ii) Determine the structural type of the metal atom cluster, Bi₅³⁺. (10 marks)
(b) Why are 4f metal ions (lanthanide ions) generally pale in colour? Why do they show line like electronic spectra? (10 marks)
(c) Consider the above pairs of π-donor ligands: Identify the d⁶ metal ions/atom among Co(O), Mn(I), Fe(II), and Fe(III), which form neutral mixed sandwich compound. Explain. (10 marks)
(d) (i) How XeF₆ can be separated from a mixture of XeF₂, XeF₄ and XeF₆? (ii) Write the products with explanation: B₂H₆ + 2NH₃ → ? and B₂H₆ + 2Me₃N → ? (10 marks)
(e) Aqueous solution of FeCl₃ is bright yellow and not pale-violet like other metal ions having high-spin d⁵ configuration. Discuss the origin of the colour. (10 marks)
हिंदी में पढ़ें
(a) (i) Cp₂Fe₂(CO)₄ में धातु-धातु आबंधों की संख्या का परिकलन कीजिए। (ii) धातु परमाणु गुच्छ, Bi₅³⁺, के संरचनात्मक प्रकार को निर्धारित करें। (10 अंक)
(b) 4f धातु आयनों (लैन्थेनाइड आयनों) का रंग सामान्यतः फीका क्यों होता है? यह रेखा (लाइन) जैसा इलेक्ट्रॉनिक स्पेक्ट्रा क्यों दिखाते हैं? (10 अंक)
(c) निम्नलिखित π-दाता संतुलियों (लिगंडों) के जोड़ों को ध्यान में रखें: Co(O), Mn(I), Fe(II), और Fe(III), में से d⁶-धातु आयनों/परमाणुओं को पहचानें जो अनवेशी मिश्रित अंतर्द्वितीय यौगिक बनाते हैं। व्याख्या कीजिए। (10 अंक)
(d) (i) XeF₆ को XeF₂, XeF₄ और XeF₆ के मिश्रण से कैसे पृथक किया जा सकता है? (ii) व्याख्या के साथ उत्पादों को लिखें — B₂H₆ + 2NH₃ → ? और B₂H₆ + 2Me₃N → ? (10 अंक)
(e) FeCl₃ का जलीय विलयन चमकीला पीला है और यह दूसरे d⁵-उच्च प्रचक्रण विच्यासों के धातु आयनों जैसा फीका बैंगनी नहीं होता है। रंग की उत्पत्ति का वर्णन कीजिए। (10 अंक)
Answer approach & key points
Explain requires logical reasoning with supporting evidence across all six sub-parts. Allocate approximately 15% time to (a)(i)-(ii) on metal-metal bonding and Wade-Mingos rules; 20% to (b) on lanthanide spectroscopy; 20% to (c) on 18-electron rule and sandwich compounds; 25% to (d) on noble gas separation and borane chemistry; and 20% to (e) on charge transfer spectra. Structure with brief introductions per sub-part, core explanatory analysis, and concluding synthesis where relevant.
(a)(i) Calculation of metal-metal bonds in Cp₂Fe₂(CO)₄ using 18-electron rule: each Fe has 17 electrons in monomeric form, dimer requires 1 M-M bond to satisfy 18-electron configuration
(a)(ii) Bi₅³⁺ cluster structure: n+1 = 5 skeletal electron pairs, closo-trigonal bipyramidal geometry per Wade-Mingos rules
(b) Lanthanide pale color explanation: 4f orbitals shielded by 5s²5p⁶, weak f-f transitions; line-like spectra due to weak crystal field effects and minimal orbital-lattice coupling
(c) d⁶ identification for neutral mixed sandwich: Fe(II) forms ferrocene analogues; apply 18-electron rule to eliminate Co(0), Mn(I), Fe(III) as they yield incorrect electron counts
(d)(i) XeF₆ separation via differential reactivity with NaF or thermal gradient; XeF₂ and XeF₄ form adducts or have different volatility
(d)(ii) B₂H₆ + 2NH₃ → [H₂B(NH₃)₂]⁺[BH₄]⁻ (ionic adduct) vs B₂H₆ + 2Me₃N → 2Me₃N·BH₃ (symmetrical cleavage); explain based on steric and electronic factors
(e) FeCl₃ yellow color: ligand-to-metal charge transfer (LMCT) from Cl⁻ to Fe³⁺ dominates over weak d-d transitions; discuss hydrolysis to [Fe(H₂O)₅OH]²⁺ and colloidal FeO(OH)
50MexplainCoordination chemistry and chemical kinetics
(a) Cite one example of an optically active tetracoordinated complex compound where the metal ion and donor atoms lie on a plane. Justify your answer. 10 marks
(b) Consider aqueous solutions of LaCl₃ (Lanthanum trichloride) and LuCl₃ (Lutetium trichloride). Which solution shows lower pH? Explain. 10 marks
(c) The reaction cis-2-butene ⇄ trans-2-butene is first order in both the direction. At 25°C, the equilibrium constant is 0.406 and the forward reaction rate constant is 4.21×10⁻⁴ sec⁻¹. Starting with a sample of pure cis isomer with [cis]₀ = 0.115 mol dm⁻³, how long it will take to form half of equilibrium amount of the trans isomer from cis isomer? 10 marks
(d) At 0°C and 1 atm pressure, the volume of nitrogen gas required to cover a sample of an adsorbent is found to be 130 cm³ g⁻¹. Calculate the surface area per gram of adsorbent. Given that area occupied by a nitrogen molecule is 0.162 (nm)².
[Nₐ = 6.022×10²³ mol⁻¹] 10 marks
(e) Compare and comment on the magnetic properties of the following complexes:
(i) [Cu (OAc)₂]₂
(ii) [Cu (CN)₄]³⁻ 10 marks
हिंदी में पढ़ें
(a) एक ध्रुवण घूर्णक चतुष्ठ उपसहसंयोजी (टेट्राकोआर्डिनेट) संकुल यौगिक का उदाहरण उल्लेख करें, जिसमें धातु आयन और दाता परमाणु समतल में हों। उत्तर को उचित सिद्ध करें। 10
(b) LaCl₃ (लैन्थेनम ट्राइक्लोराइड) और LuCl₃ (ल्यूटीशियम ट्राइक्लोराइड) के जलीय विलयन का ध्यान करें। कौन सा विलयन कम pH दिखाता है? व्याख्या कीजिए। 10
(c) अभिक्रिया cis-2-butene ⇄ trans-2-butene दोनों दिशाओं में प्रथम कोटि की है। 25°C पर, साम्य स्थिरांक, 0.406 और अभिक्रिया वेग स्थिरांक, 4.21×10⁻⁴ sec⁻¹ है। शुद्ध समपक्ष समावयवी के प्रतिदर्श से शुरुआत करने पर, जब समपक्ष समावयवी [cis]₀ = 0.115 mol dm⁻³ है, विपक्ष समावयवी की मात्रा को साम्य मात्रा से आधी उत्पन्न होने में कितना समय लगेगा? 10
(d) 0°C और 1 atm दाब पर, एक अधिशोषक के प्रतिदर्श को ढकने के लिए नाइट्रोजन गैस के 130 cm³ g⁻¹, आयतन की आवश्यकता है। अधिशोषक के पृष्ठीय क्षेत्रफल प्रति ग्राम का परिकलन कीजिए। नाइट्रोजन अणु के द्वारा अध्यासित क्षेत्रफल, 0.162 (nm)² दिया गया है।
[Nₐ = 6.022×10²³ mol⁻¹] 10
(e) निम्नलिखित संकुलों की चुंबकीय विशेषताओं पर तुलनात्मक टिप्पणी करें:
(i) [Cu (OAc)₂]₂
(ii) [Cu (CN)₄]³⁻ 10
Answer approach & key points
This multi-part question requires explaining concepts (a, b, e), solving numerically (c, d), and comparing properties. Allocate approximately 15% time to each of parts (a), (b), and (e) combined (conceptual explanations), 25% to part (c) (kinetics calculation with equilibrium), and 25% to part (d) (surface area calculation). Begin with clear statements for each part, show all working for calculations, and conclude with comparative summaries where applicable.
Part (a): Identify [M(AB)₂] type complex with unsymmetrical bidentate ligand (e.g., [Pt(glycinate)₂] or [Pd(AB)₂]) as square planar optically active compound; explain that M and donor atoms are coplanar but the chelate rings create non-superimposable mirror image due to twist
Part (b): LuCl₃ shows lower pH; explain lanthanide contraction causing Lu³⁺ smaller ionic radius, higher charge density, greater hydrolysis of [Lu(H₂O)₆]³⁺ producing more H⁺ ions compared to La³⁺
Part (c): Calculate reverse rate constant kᵣ = kf/K = 1.037×10⁻³ s⁻¹; set up integrated rate equation for approach to equilibrium; solve for time when [trans] = ½[trans]eq = 0.0203 M, obtaining t ≈ 1120-1150 s
Part (d): Use ideal gas law to find moles N₂ = PV/RT = 5.80×10⁻³ mol; calculate molecules = nNₐ; surface area = molecules × area per molecule = 565-570 m² g⁻¹
Part (e): [Cu(OAc)₂]₂ is dimeric with Cu-Cu interaction, μeff ≈ 1.4 BM per Cu at room temperature due to antiferromagnetic coupling; [Cu(CN)₄]³⁻ is tetrahedral with d¹⁰ configuration, diamagnetic (μ = 0); explain using MO/structural considerations
50MexplainBioinorganic chemistry and surface chemistry
(a) Which one is more stable between the two isomers? Explain.
[(H₃N)₅ Cr – CN – Cr(CN)₅]
[(H₃N)₅ Cr – NC – Cr(CN)₅] 10 marks
(b) Draw the active site structure of Hemocyanin (Hc) in deoxyhemocyanin and oxyhemocyanin forms, and write the colour of Hemocyanin in these two forms. Write the functions of Hemocyanin. 10 marks
(c) Define stationary and non-stationary (branching) chain reaction. Non-stationary chain reactions always lead to explosion under certain conditions. Give a detailed account of these conditions. 10 marks
(d) What is meant by steady-state approximation? How this approximation helps in deriving the kinetics of following photochemical reaction?
H₂(g) + Cl₂(g) → 2HCl(g)
The quantum yield of this reaction is extremely large. Justify or criticize this statement. 10 marks
(e) Derive Langmuir adsorption isotherm. How does Langmuir adsorption isotherm help in elucidation of kinetics of a gaseous reaction on solid surface? 10 marks
हिंदी में पढ़ें
(a) दो समावयवों में से कौन-सा ज्यादा स्थायी है? व्याख्या कीजिए।
[(H₃N)₅ Cr – CN – Cr(CN)₅]
[(H₃N)₅ Cr – NC – Cr(CN)₅] 10
(b) डीऑक्सीहेमोसायनिन और ऑक्सीहेमोसायनिन रूपों में हेमोसायनिन के सक्रिय स्थल संरचना को खींचे और दोनों रूपों में हेमोसायनिन के रंग को लिखे। हेमोसायनिन के प्रकार्य को लिखे। 10
(c) स्थिर और गैर-स्थिर (शाखन) श्रृंखला अभिक्रियाओं की परिभाषा दें। गैर-स्थिर श्रृंखला अभिक्रिया कुछ शर्तों के अधीन हमेशा विस्फोट की ओर अग्रसर होता है। इन शर्तों का विस्तार पूर्वक स्पष्टीकरण दें। 10
(d) स्थिर-अवस्था सन्निकटन से क्या अभिप्राय है? निम्नलिखित प्रकाशरासायनिक अभिक्रिया की बलगतिकी को व्युत्पन्न करने में यह सन्निकटन कैसे सहायक है?
H₂(g) + Cl₂(g) → 2HCl(g)
इस अभिक्रिया की कांतम लंबी अत्यधिक बड़ी है। इस कथन को उचित सिद्ध करें या आलोचित (आलोचना) करें। 10
(e) लैंगम्युर अधिशोषण समतापी वक्र को व्युत्पन्न करें। लैंगम्युर अधिशोषण समतापी वक्र, गैसीय अभिक्रिया की बलगतिकी का ठोस पृष्ठीय/धरातल पर स्पष्टीकरण करने में कैसे सहायक है? 10
Answer approach & key points
Begin with a brief introduction linking bioinorganic and surface chemistry themes. For part (a), explain the ambidentate nature of cyanide and apply HSAB principle to justify Cr-CN-Cr linkage stability. For (b), draw accurate active site structures showing μ-η²:η² peroxo dicopper(II) in oxyhemocyanin and colorless deoxy form with Cu(I), noting color changes. For (c), define both chain types with examples like H₂-O₂ explosion, explaining branching ratio and critical explosion conditions. For (d), state steady-state approximation, derive H₂+Cl₂ kinetics showing chain propagation, and justify high quantum yield via chain mechanism. For (e), derive Langmuir isotherm from rate considerations, then apply to unimolecular/bimolecular surface reactions. Allocate approximately 2-2.5 minutes per mark, with proportional time for each 10-mark sub-part.
Part (a): Cyanide is ambidentate; Cr(III) is borderline acid preferring C-end (soft) over N-end (hard); first isomer [(H₃N)₅Cr-CN-Cr(CN)₅] is more stable due to better HSAB match and reduced steric repulsion
Part (b): Deoxyhemocyanin has two Cu(I) centers (colorless, 3-coordinate); oxyhemocyanin has μ-η²:η² peroxo dicopper(II) (blue, 4-5 coordinate); functions include oxygen transport in arthropods and molluscs, not hemoglobin
Part (c): Stationary chain: chain carriers remain constant (rate of initiation = termination); non-stationary/branching chain: carriers multiply (α > 1, branching factor); explosion when chain branching exceeds termination, depends on pressure limits (lower and upper explosion limits)
Part (d): Steady-state approximation: d[intermediate]/dt = 0; for H₂+Cl₂, derive rate = k[H₂][Cl₂]¹/² using this approximation; quantum yield ~10⁶ justified by long chain length, not criticized as this is characteristic of chain photoreactions
Part (e): Langmuir isotherm derivation from adsorption equilibrium: θ = KP/(1+KP) or equivalent; application to surface kinetics: unimolecular (rate ∝ θ) and bimolecular (rate ∝ θ_Aθ_B or θ_Aθ_vacant) reactions, leading to Langmuir-Hinshelwood and Eley-Rideal mechanisms